Literatur:

Commutative Ring Theory (Matsumura)

Introduction to Commutative Algebra (Atiyah, Macdonald)

 

 

 

Herzlichen Dank an Alexander Aycock für die Übersetzungen ins Englische.

Carl Gustav Jacob Jacobi

Dritte Abhandlung über die Transformation und Bestimmung von Doppelintegralen

Eine Bemerkung zum Abel’schen Theorem

Ein neuer Beweis des Abel’schen Theorems

New Foundations of the Theory of Elliptic Functions

Commentation Prima et altera - Two Treatises on elliptic functions

New fundamental Formulas in the Theory of elliptic transcendents

On irrational or inverse Transformations of elliptic Functions

On quadrouple periodic functions of two variables on which the theory
of the Abelian Transcendents is based

Demonstratio Formulae

On a certain singular transformation of a double integral

A Transformation Formula for definite Integrals

On the continued fraction the integral _ can be expanded into

On the legitimate Application of MacLaurin’s Summation Formula

Kleine Beobachtungen zur Theorie von Gleichungen

 

 

 

 

 

 

 

 

 

Timetable:

	Monday	Tuesday	Wednesday	Thursday	Friday
Times
9:00-10:00	Caldararu I	Caldararu II	Caldararu III	Caldararu IV	B5
10:15-11:15	Perutz I	Perutz II	A5	Perutz III	C3
11:30-12:00	B1 (+15)	A3	B3 (+30)	C1	C4 (+30)
14:30-15:30	A1	B2	/	C2	/
15:30-16:30	A2	A4	/	B4	/

Speakers:

A

A1a) Meazzini, Francesco: section 1 in https://arxiv.org/abs/q-alg/9709040

A1b) Poliakova, Dasha: section 3 in https://arxiv.org/abs/q-alg/9709040

A2a) Marchetti, Giovanni: L-infinity definition and equivalent coalgebra point of view https://arxiv.org/abs/math/0405485

A2b) Kaushal, Tanya: section 4 in https://arxiv.org/abs/q-alg/9709040

A3) Simi, Luca: L-infinity and formality criteria https://arxiv.org/abs/hep-th/9406095

A4) Filip, Matej: chapter 1-5 of https://arxiv.org/abs/alg-geom/9710032

A5) Arkhipov, Sergey: chapter 6-8 of https://arxiv.org/abs/alg-geom/9710032

B

B1) Barbieri, Anna: Classical Geometry of the Calabi-Yau moduli space (45min), chaper 2 in http://math.bu.edu/people/sili/thesis_SiLi.pdf

B2a) Buring, Ricardo: Kontsevich quantization and Feynman diagrams, section 3.1 plus background from Kontsevich's work

B2b) Tirelli, Andrea: Batalin-Vilkovisky formalism, section 3.2

B3a) Genovese, Francesco: Effective Field theory, Renormalization group flow and Chern Simons theory, section 3.3+3.4 until and including CS example 3.22

B3b) Belmans, Pieter: Quantum master equation, deformation obstruction complex and theory on the complex plane 3.4.2 to end of 3.5

B4a) Sutherland, Tom: Classical BCOV theory and its quantization, section 4

B4b) Melani, Valerio: Quantization of BCOV on the elliptic curve I, existence and uniqueness, section 5.1 until middle of page 98 (to the end of the proof of 5.12), i.e. section 5.1.1-5.3.1

B5a) Bousseau, Pierrick: Quantization of BCOV on the elliptic curve II, proving the dilaton axiom and holomorphicity, section 5.3.2-5.4

B5b) Ruddat, Helge: Proving higher genus mirror symmetry for the elliptic curve, section 6

C

C1) Anno, Rina: "Mumford toric degenerations", section 1.1 and 1.2 of https://arxiv.org/pdf/0808.2749.pdf

C2a) Felten, Simon: "From a toric degeneration to (B,P,phi)"

C2b) Logvinenko, Timothy: "Scattering I"

C3a) Nikolaev, Nikita: "Scattering II"

C3b) Zhi, Jin: "Overview of the Gross-Hacking-Keel construction"

C4a) Kelly, Tyler: "Broken lines"

C4b) van Garrel, Michel: "Generalized theta functions"

Andrei Caldararu: "Categorical Gromov-Witten Invariants"

Caldararu I: What are categorical Gromov-Witten invariants?

I will start my lecture by reviewing the construction of classical Gromov-Witten invariants, and working through a standard example, the g=1, n=1 GW invariants of an elliptic curve. Then I will outline how we can hope to obtain these invariants from the Fukaya category by an abstract categorical construction. In the case of an arbitrary abstract category I will discuss what properties the category should have, what replaces the quantum cohomology ring, etc. I will conclude with a discussion of potential applications of the construction of categorical Gromov-Witten invariants and a general discussion of how mirror symmetry is supposed to work.

Caldararu II: Chains on moduli space of curves, ribbon graphs, and A_infinity algebras

I will begin by reviewing the main algebraic structure on the space of chains on the moduli spaces of curves, namely that they form a Batalin-Vilkovisky algebra. We will study the Quantum Master Equation in such chains; by work of Costello its solution gives rise to the string vertices of Zwiebach and Sen. I will follow with an introduction to ribbon graphs and how they give a model for the chains on M_{g,n}. I will conclude with a quick review of A_infinity algebras and a description of the original Kontsevich partition function which pairs ribbon graphs with cyclic A_infinity algebras.

Caldararu III: Algebraic structures on the periodic cyclic complex

I will introduce the Hochschild chain complex of an A_infinity algebra, and its two main differentials, the Hochschild differential b and the Connes differential B, leading to the construction of the different variants of cyclic homology (periodic, negative, positive). Using this construction I will outline Kontsevich-Soibelman's construction of the action of the PROP of chains on M_{g,n} on the cyclic complex of an A_infinity algebra. Following Costello, part of this action allows us to regard the periodic cyclic complex as a symplectic vector space with a Lagrangian inside it. This leads to the construction of a Weyl algebra and Fock module associated with this structure. Costello constructs a deformation of this Fock module induced using a choice of string vertices. This leads to the construction of an abstract Gromov-Witten potential (a line in a Fock space).

Caldararu IV: Hodge-de Rham degeneration and applications

The periodic cyclic homology carries a natural filtration, the Hodge filtration. I will outline its construction, and explain how a choice of a splitting of this filtration allows us to regard the abstract Gromov-Witten potential previously constructed as an actual categorical Gromov-Witten potential. Everything will be put together into the calculation of the categorical B-model potential of the family of elliptic curves (joint work with Junwu Tu). I will conclude with a list of potential directions in which the whole construction can be extended, and expected applications and conjectures.

Tim Perutz: "From homological to Hodge-theoretic mirror symmetry"

(Based on work of S. Ganatra, N. Sheridan and myself, and various subsets of this trio.)

Perutz I: Fukaya categories, open-closed maps, and pairings.

I will review some of the mathematics of Fukaya categories of symplectic manifolds. These categories come with important structure: the closed-open map CO, which is a map of algebras from quantum cohomology to Hochschild cohomology of the category, and the open-closed map OC, from Hochschild homology to quantum cohomology, which is an isometry with respect to a “Mukai pairing” on Hochschild homology and a cup-product pairing on quantum cohomology. (The B-model analog of this structure was studied by Andrei Caldararu several years ago, and an abstract of OC is key to Costello’s construction, as discussed in Andrei’s lectures.) Abouzaid has shown that a subcategory generates the Fukaya category if OC is surjective on that subcategory.

Perutz II: Smoothness, automatic generation, and homological mirror symmetry.

Symplectic topologists have recently been learning a principle which Kontsevich has advocated for some time: the importance of categorical smoothness. The prototypical example of a smooth DG category is the derived category of a smooth algebraic variety. In the setting of homological mirror symmetry (HMS), the Fukaya category of the mirror symplectic manifold will then also be smooth. From smoothness many things flow: sharp versions of generation for the Fukaya category; that OC and CO are isomorphisms; that OC coincides with Costello’s abstract version, hence that his formal constructions are in fact geometric; and that HMS implies closed-string mirror symmetry.

Perutz III: The cyclic open-closed map, the categorical Gauss—Manin connection, and the mirror map.

The cyclic homology of an A-infinity category, defined over (say) a formal punctured disc, carries a Gauss—Manin connection, as constructed by Getzler. In the case of the derived category of a smooth algebraic variety over the punctured disc, this is expected (but not actually proven) to coincide with the classical GM connection in algebraic de Rham cohomology. I will explain that, in the case of a smooth Fukaya category, it coincides with the quantum differential operator, a connection in quantum cohomology. Under the assumption of HMS, the consequences are as follows: (i) that with an undetermined mirror map, the mirror map can be characterized Hodge-theoretically; and (ii) that the quantum differential equation matches the (derived) algebro-geometric GM connection. Statement (ii) is (genus 0) Hodge-theoretic mirror symmetry. It encompasses the famous rational curve-counts on the quintic 3-fold.

Spring School for Master & PhD students and Postdocs March 25 - 31, 2018 in Italy http://www.montegufoni.it/ Senior Speakers: Andrei Caldararu Tim Perutz Organizers: Helge Ruddat (ruddat) Tom Sutherland (sutherland) Estelle Bonmann (ebonmann) (respectively @uni-mainz.de)   TIMETABLE   Accepted participants will be provided shared rooms in the castle. We might be able to modestly subsidize travel costs by a lump sum per person.We will organize and prepare meals ourselves.Each participant will be asked to give a talk presenting material that we assign together beforehand. This will consist of works of Barannikov-Kontsevich, Costello-Li, Gross-Siebert and others.Sorry, the event has reached its participant capacity limit.Literature: Barannikov, Sergey; Kontsevich, Maxim: Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields. Caldararu, Andrei; Tu, Junwu: Computing a categorical Gromov-Witten invariant. Costello, Kevin J.; Li, Si: Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model Ganatra, Sheel; Perutz, Timothy; Sheridan, Nick: Mirror symmetry - from categories to curve Counts. Mark Gross, Bernd Siebert: Intrinsic mirror symmetry and punctured Gromov-Witten invariants.

This school is funded by the DFG Emmy-Noether grant RU 1629/4-1.

 

Sommersemester 2017

Das Seminar findet an den wie in der folgenden Tabelle angegebenen Terminen statt. Montags von 12-14 Uhr sind wir im Raum 04-432 und für die zusätzlichen Sitzungen um 10-12 Uhr, sind wir im Raum 04-230 für diese Uhrzeit.

Vortrag	Datum	Vortrags- kapitel	Vortragende(r)	zu bearbeitende Übungsaufgaben
1	24.4. 10-12 Uhr	§1	Anna Katharina Pnischeck	1.1, 1.11, 3.1, 3.14, 4.11, 5.3
2	24.4. 12-14 Uhr	§1	Lennart Kahl	1.10, 2.12, 3.2, 3.15, 4.12, 5.1
3	08.5.	§2	Patricia Müller	0.1, 2.3, 3.4, 3.16, 5.13, 6.1
4	15.5.	§2	Maximilian Oischinger	0.2, 2.11, 3.6, 4.1, 5.12, 6.3
5	22.5. 10-12 Uhr	§3	Jakob Werner	0.3, 2.10, 3.3, 4.2, 5.11, 6.4
6	22.5. 12-14 Uhr	§3	Lars Hofmann	1.8, 2.2, 3.12, 4.9, 5.5, 5.7
7	29.5.	§4	Ramona Hirschfelder	1.3, 2.8, 3.7, 4.5, 5.9, 6.6
8	12.6.	§4	Helge Ruddat
9	19.6.	§5	Janine Scholtes	1.9, 2.1, 3.13, 4.4, 4.10, 5.4
10	26.6.	§5	Charlotte Eckert	1.6, 2.5, 3.10, 4.7, 5.2, 6.7
11	03.7.	§6	Peter Lang	1.7, 2.4, 3.11, 4.8, 5.6, 6.2

siehe auch: Seminartermine u. -themen

Die Tabelle zeigt die Aufteilung der Seminarthemen und Seminartermine sowie Übungsaufgaben pro Student(in). Sie bezieht sich auf das unten angegebene Buch.

Jeder Vortrag soll nicht viel länger als eine Stunde gehen und danach noch um das Vortragen der Übungsaufgabe zu dem Kapitel (von dem/der jeweils Vortragenden, ca. 15min) ergänzt werden. Außerdem sollte Zeit für Fragen eingeplant werden. (Gutes Zeitmanagement gehört zu einem guten Vortrag)

Jede(r) Vortragende teilt zu Beginn ihres/seines Vortrags einen Handzettel aus, auf dem die wesentliche Begriffe, Definitionen und Resultate des Vortrags zusammengefasst sind. Bitte zur Erstellung davon Latex verwenden. Übungsaufgaben sind bis eine Woche nach dem letzten Vortrag zum jeweiligen Thema einzureichen (auch per Latex-pdf) per Email an elementare.alg.geo_ät_web.de.
Achtet bitte darauf, dass ihr auch die Aufgabenstellung mit aufschreibt und die Aufgaben in ein einziges pdf Dokument kompiliert (jeweils um jede neue Aufgabe ergänzen, bzw gegebenenfalls auch Korrekturen der alten Aufgaben machen, jede neue Aufgabe beginnt auf einer neuen Seite).
Bei mindestens einer Aufgabe ist ein Computerprogramm zu schreiben, schreibt dafür einfach die Beschreibung des Algorithmus auf. In die Seminarnote fließen der eigene Vortrag, die allgemeine Beteiligung im Seminar und die Bearbeitung der Aufgaben ein.

Bitte lest auch das (recht kurze) Kapitel Null im Buch, weil wir darüber keinen Vortrag haben werden, es aber als Allgemeinbildung und Hintergrundwissen hilfreich ist. Auch zum Appendix von Kapitel eins haben wir keinen Vortrag, bitte ebenso bei Zeiten eigenständig anschauen.
Je früher ihr mit der Materialsichtung anfangt, desto besser!

Literatur

• Miles Reid: "Undergraduate Algebraic Geometry", Cambridge University Press

Topics around Calabi-Yau and Fano manifolds, deformation theory and mirror symmetry

This colloquium invites mostly external speakers. It is loosely associated with the Emmy Noether
grant "Degenerations of Calabi-Yau Manifolds and Related Geometries".

Organizers are: Simon Felten, Matej Filip, Andrea Petracci, Helge Ruddat

 

Regular times: Tuesday 5-6 pm & Wednesday 9-10 am (German time zone)

Access to the life stream is provided here: https://researchseminars.org/seminar/EmmyKolloq

 

Upcoming talks (please find the abstracts below):

12.05.2021 09:00 Ziming Ma
SYZ Mirror Symmetry and Maurer-Cartan Equation 

19.05.2021 08:30 Taro Sano
Construction of non-Kähler Calabi-Yau manifolds by log deformations

26.05.2021 09:00 Yuto Yamamoto
Tropical contractions to integral affine manifolds with singularities

09.06.2021 09:00 Taro Fujisawa
Geometric polarized log Hodge structures on the standard log point

15.06.2021 17:00 Pieter Belmans
Hochschild cohomology of Fano 3-folds

23.06.2021 09:00 Wei Hong
BV operators of the Gerstenhaber algebras of holomorphic polyvector fields on toric varieties 

07.07.2021 09:00 Lawrence Barrott - cancelled due to illness - postphoned until october
Deforming Calabi-Yau subvarieties

20.07.2021 17:00 Benjamin Gammage
Homological mirror symmetry over the SYZ base

 

Abstracts

12.05. 2021 09:00
Ziming Ma - SYZ Mirror Symmetry and Maurer-Cartan Equation 

The Strominger-Yau-Zaslow conjecture for understanding Mirror Symmetry geometrically, leads to the Fukaya's conjectural reconstruction of mirror manifolds which solves Maurer-Cartan equation near large limits using quantum corrections. In this talk, we will discuss progesses of the Fukaya's conjecture and the formulation of the Maurer-Cartan equation near large structure limits by constructing a dgBV algebra PV *(X), a generalized version of the Kodaira-Spencer dgLa, associated to possibly degenerate Calabi-Yau variety X equipped with local thickening data. This talk is based on joint works with Kwokwai Chan, Conan Leung and Yat-Hin Suen.

19.05.2021 08:30
Taro Sano - Construction of non-Kähler Calabi-Yau manifolds by log deformations

Calabi-Yau manifolds (in the strict sense) form an important class in the classification of algebraic varieties. One can also consider its generalisation by removing the projectivity assumption. Clemens and Friedman constructed infinitely many topological types of non-Kähler Calabi-Yau 3-folds whose 2nd Betti numbers are zero. In this talk, I will present examples of non-Kähler Calabi-Yau manifolds with arbitrarily large 2nd Betti numbers. The construction is by smoothing normal crossing varieties. The key tools of the construction are some isomorphisms between general rational elliptic surfaces which induce isomorphisms between Calabi-Yau manifolds of Schoen type.

26.05.2021 09:00
Yuto Yamamoto - Tropical contractions to integral affine manifolds with singularities

We construct contraction maps from tropical Calabi -Yau varieties to the integral affine maifolds with singularities that arise as the dual intersection complexes of toric degenerations of Calabi-Yau varieties in the Gross-Siebert program. We show that the contractions preserve tropical cohomology groups, and send the eigenwaves to the radiance obstructions. As an application, we also prove the Poincaré-Verdier duality for integral affine manifolds with singularities.

09.06.2021 09:00
Taro Fujisawa - Geometric polarized log Hodge structures on the standard log point

I will talk about the following fact: a projective vertical exact log smooth morphism over the standard log point yields polarized log Hodge structures on the base. In the proof of this fact, the case of a strict log deformation is essential. So, I will mainly talk about this case, and explain how to relate my previous results on the mixed Hodge structures to log Hodge structures for a projective strict log deformation. If the time remaines, I will discuss a generalization to the case of a general base point. This talk is based on a joint work with C. Nakayama.

15.06.2021 17:00
Pieter Belmans - Hochschild cohomology of Fano 3-folds (notes/script)

The Hochschild-Kostant-Rosenberg decomposition gives a description of the Hochschild cohomology of a smooth projective variety in terms of the sheaf cohomology of exterior powers of the tangent bundle. In all but a few cases it is a non-trivial task to compute this decomposition, and understand the extra algebraic structure which exists on Hochschild cohomology. I will give a general introduction to Hochschild cohomology and this decomposition, and explain what it looks like for Fano 3-folds (joint work with Enrico Fatighenti and Fabio Tanturri), and time permitting also for partial flag varieties (joint work with Maxim Smirnov).

23.06.2021 09:00
Wei Hong - BV operators of the Gerstenhaber algebras of holomorphic polyvector fields on toric varieties 

The vector space of holomorphic polyvector fields on any complex manifold has a natural Gerstenhaber algebra structure. In this paper, we study BV operators of the Gersten- haber algebras of holomorphic polyvector fields on smooth compact toric varieties. We give a necessary and sufficient condition for the existence of BV operators of the Gerstenhaber algebra of holomorphic polyvector fields on any smooth compact toric variety

postphoned until October 2021 09:00
Lawrence Barrott - Deforming Calabi-Yau subvarieties

The Doran-Harder-Thompson conjecture is a duality on geometric structures under mirror symmetry. On one side we have smooth degenerations of Calabi-Yau's (CY's) to unions of normal crossings components, and on the other we have fibrations of the mirror CY's by CY subvarieties. In the simplest case it proposes that CY's with a Tyurin degeneration should be mirror to CY's fibred over P1. I will explain how some of the recent machinery of deformation theory for singular CY's of Chan-Leung-Ma and Felton-Filip-Ruddat, together with the mirror construction of the Gross-Siebert program leads to a proof of one direction of this conjecture in classes of examples. If time permits I will sketch how this relates to the period calculations appearing in other papers (Doran-Kostiuk-You) via more recent techniques in the Gross-Siebert program. This is based on joint work with Chuck Doran.

20.07.2021 17:00
Benjamin Gammage - Homological mirror symmetry over the SYZ base

The Gross-Siebert program suggests that mirror symmetry is mediated by the combinatorial data of a dual pair of integral affine manifolds with singularities and polyhedral decomposition. Much is now understood about the passage from the combinatorial data to complex spaces "near the large complex structure limit" - a toric degeneration and its smoothing. In this talk, we discuss the mirror procedure for moving from the combinatorial data to symplectic spaces "near the large volume limit" - a Weinstein symplectic manifold and its compactification -- and we will explain a proof of homological mirror symmetry between the complex and symplectic manifold associated to local pieces of the combinatorial data. This is part of a program with Vivek Shende to prove homological mirror symmetry globally over the SYZ base.

 

Abstracts of former talks

1. 1. Abstracts
      1. [toc title="Abstracts of former talks"]
   2. 12.05. 2021 Ziming Ma
   3. 19.05.2021 Taro Sano
   4. 26.05.2021 Yuto Yamamoto
   5. 09.06.2021 Taro Fujisawa
   6. 15.06.2021 Pieter Belmans
   7. 23.06.2021 Wei Hong
   8. 22.01.2020 Thomas Prince
   9. 21.06.2018 Michel van Garrel
   10. 08.06.2018 Ilia Zharkov
   11. 18.10.2017 Robin Guilbot
   12. 18.10.2017 Valentin Tonita
   13. 16.10.2017 Matej Filip
   14. 27.06.2017 Martin Ulirsch (University of Michigan, USA)
   15. 02.05.2017 Michel van Garrel (Universität Hamburg)
   16. 03.11.2016 Tom Sutherland (Università degli Studi di Pavia)
   17. 19.07.2016 Tim Kirschner (Universität Duisburg-Essen)
   18. Finite quotients of three-dimensional complex tori
   19. 14.07.2016 James Pascaleff (University of Illinois)
   20. 26.04.2016 Mohammad Akhtar (Imperial College London)
   21. 07.01.2016 Andreas Gross (Universität Kaiserslautern)
   22. 17.12.2015 Sara Filippini (Universität Zürich)
   23. 29.10.2015 Aleksey Zinger (MPIM Bonn)
   24. 25.06.2015 Peter Overholser (Leuven / Imperial College London)

12.05. 2021 Ziming Ma

SYZ Mirror Symmetry and Maurer-Cartan Equation 

The Strominger-Yau-Zaslow conjecture for understanding Mirror Symmetry geometrically, leads to the Fukaya's conjectural reconstruction of mirror manifolds which solves Maurer-Cartan equation near large limits using quantum corrections. In this talk, we will discuss progesses of the Fukaya's conjecture and the formulation of the Maurer-Cartan equation near large structure limits by constructing a dgBV algebra PV *(X), a generalized version of the Kodaira-Spencer dgLa, associated to possibly degenerate Calabi-Yau variety X equipped with local thickening data. This talk is based on joint works with Kwokwai Chan, Conan Leung and Yat-Hin Suen.

 

19.05.2021 Taro Sano

Construction of non-Kähler Calabi-Yau manifolds by log deformations

Calabi-Yau manifolds (in the strict sense) form an important class in the classification of algebraic varieties. One can also consider its generalisation by removing the projectivity assumption. Clemens and Friedman constructed infinitely many topological types of non-Kähler Calabi-Yau 3-folds whose 2nd Betti numbers are zero. In this talk, I will present examples of non-Kähler Calabi-Yau manifolds with arbitrarily large 2nd Betti numbers. The construction is by smoothing normal crossing varieties. The key tools of the construction are some isomorphisms between general rational elliptic surfaces which induce isomorphisms between Calabi-Yau manifolds of Schoen type.

 

26.05.2021 Yuto Yamamoto

Tropical contractions to integral affine manifolds with singularities

We construct contraction maps from tropical Calabi -Yau varieties to the integral affine maifolds with singularities that arise as the dual intersection complexes of toric degenerations of Calabi-Yau varieties in the Gross-Siebert program. We show that the contractions preserve tropical cohomology groups, and send the eigenwaves to the radiance obstructions. As an application, we also prove the Poincaré-Verdier duality for integral affine manifolds with singularities.

09.06.2021 Taro Fujisawa

 

 

15.06.2021 Pieter Belmans

 

 

23.06.2021 Wei Hong

BV operators of the Gerstenhaber algebras of holomorphic polyvector fields on toric varieties 

 

21.10.2020 Katharina Hübner

Logarithmic differentials on adic spaces

The object of interest in this talk is a certain subsheaf Omega_X of the sheaf of differentials Omega_X of a discretely ringed adic space X over a field k. The first part will be dedicated to an introduction to discretely ringed adic spaces. We will then define $\Omega^+_X$ using K\"ahler seminorms and establish a relation with logarithmic differentials. Finally we study the case where $X = Spa(U,Y)$ for a scheme $Y$ over $k$ and a subscheme $U$ such that the corresponding log structure on $Y$ is log smooth. It turns out that $\Omega^+_X(X)$ equals $\Omega^{log}_{(U,Y)}(U,Y)$.

 

22.01.2020 Thomas Prince

Calabi-Yau toric hypersurfaces using the Gross-Siebert algorithm

We explain how to form a novel dataset of simply connected Calabi-Yau threefolds via the Gross-Siebert algorithm. These are related to Calabi-Yau toric hypersurfaces with certain Gorenstein (not necessarily isolated) singularities by a family over a possibly reducible base. Specifically, we explain how to smooth the boundary of a class of 4-dimensional reflexive polytopes to obtain a polarised tropical manifolds. We also describe how to compute the Betti numbers of these Calabi-Yau threefolds. We also explain an extension of this project generalising work of Batyrev-Kreuzer on conifold transitions.

 

21.06.2018 Michel van Garrel

Number of rational curves in log versus local geometries

Let X be a smooth projective variety and let D be a nef divisor. It is well known that D corresponds to a line bundle O(-D), which leads one to consider two geometries associated to D. On one hand, there is the logarithmic geometry of the pair (X,D). On the other hand, there is the local geometry of the total space of
O(-D). In this collaboration with Tom Graber and Helge Ruddat, we show that in an appropriate sense (in terms of log and local Gromov-Witten invariants), the number of log rational curves of (X,D) equals (up to a factor) the number of rational curves of O(-D). 

 

08.06.2018 Ilia Zharkov

Topological model for affine hypersurfaces

Given an affine complex hypersurface I will define a phase tropical hypersurface and show that is homeomorphic to the complex one. I will also describe some immersed spheres which suppose to represent Lagrangian objects generating the Fukaya category of the hypersurface.

 

18.10.2017 Robin Guilbot

On embedded Mirror Symmetry

A wide majority of the known instances of Mirror Symmetry between families of Calabi-Yau varieties are realized as complete intersections in toric varieties.
In these examples the features of Mirror Symmetry are more or less direct consequences of convex-combinatorial dualities. But the elegance of these constructions
is somehow balanced by their peculiarity : toric complete intersections are expected to form a small minority of all the Calabi-Yau varieties.
I will Review the most famous toric mirror constructions, describe a generalization of the hypersurface case introduced in joint work with M. Artebani and P. Comparin,
and sketch the foundations of a new construction for non-complete intersections based on embedded toric degenerations, following J. Böhm’s PhD thesis.

 

18.10.2017 Valentin Tonita

K-theoretic mirror formulae

Permutation equivariant K-theoretic Gromov Witten invariants, introduced by Givental, are
certain Euler characteristics on the moduli spaces of stable maps to a (smooth, projective)
variety X. I will define the invariants and show how to write K-theoretic I-functions for large classes of varieties
(e.g. toric, certain complete intersections), i.e. certain q-hypergeometric series which are
generating series of these invariants in genus zero . Time permitting, I will discuss the ideas behind
the proofs of these results.

 

16.10.2017 Matej Filip

Hochschild cohomology and Deformation quantization of affine toric varieties

For an affine toric variety we give a convex geometric description of the Hodge decomposition of its Hochschild cohomology. Using this description we prove that every Poisson structure on a possibly singular affine toric variety can be quantized in the sense of deformation quantization. Restricting to the commutative case, recent developments in constructing the versal deformation of an affine toric variety will be explained.

 

27.06.2017 Martin Ulirsch (University of Michigan, USA)

A moduli stack of tropical curves

In this talk I am going to give an introduction to these fascinating moduli spaces and discuss recent work  with Renzo Cavalieri, Melody Chan, and Jonathan Wise (arXiv 1704.03806), where we propose the notion of a moduli stack of tropical curves as a geometric stack over the category of rational polyhedral cones. Using this 2-categorical framework one can give a natural interpretation of the forgetful morphism as a universal curve. Moreover, I will propose a way of describing the process of tropicalization via logarithmic geometry in the sense of Kato-Illusie using the theory of Artin fans. Finally, given time, I will also report on an ongoing  follow-up project (joint with Margarida Melo, Filippo Viviani, and Jonathan Wise) that uses these techniques to construct the universal Picard variety in logarithmic and tropical geometry.

 

02.05.2017 Michel van Garrel (Universität Hamburg)

Rational curves in log K3 surfaces

In this talk, we address the basic question of how to count rational curves in log K3 surfaces. We will present partial results in that direction and give a full conjectural description. This is baded on two joints works, one with T. Graber and H. Ruddat, and the other one with J. Choi, N. Takahashi ad S. Katz.

 

03.11.2016 Tom Sutherland (Università degli Studi di Pavia)

Stability conditions from periods of elliptic curves

I will describe spaces of stability conditions on some Calabi-Yau-3 categories with a simple combinatorial presentation through the study of the period map of meromorphic differentials on associated families of elliptic curves.

 

19.07.2016 Tim Kirschner (Universität Duisburg-Essen)

Finite quotients of three-dimensional complex tori

I will report on a current project with Patrick Graf (Bayreuth). Using Graf's recent results about the algebraic approximation of Kähler threefolds of Kodaira dimension zero, we show that a three-dimensional compact, connected Kähler space X with isolated canonical singularities is the finite quotient of a complex torus if and only if the first and second Chern classes of X vanish. This brings together an old theorem of Yau (where X is smooth) and a theorem of Shepherd-Barron and Wilson (where X is projective).

 

14.07.2016 James Pascaleff (University of Illinois)

Symplectic Cohomology and Wall Crossing

In this talk I will describe a way that certain wall-crossing formulae can be seen in terms of symplectic cohomology, which is a Floer theoretic invariant of non-compact symplectic manifolds. In the case of log Calabi-Yau manifolds, this invariant is supposed to be mirror-dual to the poly-vector fields. I will draw connections to the theory of cluster varieties as studied by Gross-Hacking-Keel-Kontsevich. This is partially based on discussions with Dmitry Tonkonog (Cambridge).

 

26.04.2016 Mohammad Akhtar (Imperial College London)

Mirror symmetry and the classification of Fano varieties

The classification of Fano varieties is an important long-standing problem in algebraic geometry. A new approach to this problem via mirror symmetry was recently proposed by Coates-Corti-Galkin-Golyshev-Kasprzyk. Their philosophy was that Fano varieties can be classified by studying their Laurent polynomial mirrors. This talk will survey the results of a collaborative effort to apply this philosophy to the classification of Fano orbifold surfaces. We will describe a conjectural picture which suggests that classifying suitable deformation classes of certain Fano orbifold surfaces is equivalent to classifying Fano lattice polygons up to an appropriate notion of equivalence. Central to this framework is the notion of mirror duality (between a Fano orbifold surface and a Laurent polynomial) and the closely related operations of algebraic and combinatorial mutations. We will also discuss how combinatorial mutations allow us to find mirror dual Laurent polynomials in practice and will give experimental evidence supporting our conjectures.

 

07.01.2016 Andreas Gross (Universität Kaiserslautern)

Intersection Theory on Tropicalizations of Torodial Embeddings

A central goal of tropical geometry is to give combinatoric descriptions of algebro-geometric objects. In enumerative geometry, these description ideally give rise to so-called correspondence theorems, which state that some given algebraic enumerative problem can be translated into a tropical enumerative problem with the same solution. The tropical intersection theory of Allermann and Rau has become a useful tool in tropical enumerative geometry, its connection to algebraic geometry being based on the description of the intersection ring of complete toric varieties by Fulton and Sturmfels. Unfortunately, moduli spaces are rarely toric, yet in many cases they are toroidal.
In my talk I will outline how to extend the scope of tropical intersection theory to be able to describe certain intersections on toroidal varieties.

 

17.12.2015 Sara Filippini (Universität Zürich)

Refined curve counting and the tropical vertex group

The tropical vertex group of Kontsevich and Soibelman is generated by formal symplectomorphisms of the 2-dimensional algebraic torus. It plays a role in many problems in algebraic geometry and mathematical physics. Based on the tropical vertex group, Gross, Pandharipande and Siebert introduced an interesting Gromov-Witten theory on weighted projective planes which admits a very special expansion in terms of tropical counts.

I will describe a refinement or "q-deformation" of this expansion, motivated by wall-crossing ideas, using Block-Goettsche invariants. This leads naturally to the definition of a class of putative q-deformed curve counts. We prove that this coincides with another natural q-deformation, provided by a result of Reineke and Weist in the context of quiver representations, when the latter is well defined. This is joint work with Jacopo Stoppa.

 

29.10.2015 Aleksey Zinger (MPIM Bonn)

Normal Crossings Divisors for Symplectic Topology

I will describe purely symplectic notions of normal crossings divisor and configuration. They are compatible with the existence of the desired auxiliary almost Kahler structures, provided ``existence" is suitably interpreted. These notions lead to a multifold version of Gompf's symplectic sum construction. They also imply that Brett Parker's work on exploded manifolds concerns a multifold version of the usual symplectic sum (or degeneration) formula for Gromov-Witten invariants. We hope our approach can be extended to more general singularities and provide purely symplectic analogues of the singularities and their deformations appearing in the Gross-Siebert program. This is joint work with Mark McLean and Mohammad Tehrani.

 

25.06.2015 Peter Overholser (Leuven / Imperial College London)

Descendent tropical mirror symmetry for P2

The Gross-Siebert program can be seen as an attempt to understand mirror symmetry from a tropical perspective.  Gross has realized this goal in a particular example, giving a tropical description of mirror symmetry for P2.  I will show how his construction can be modified to to yield a novel mirror symmetric relationship.

 

 

Singularity Theory

• Deformation Theory
• Normal Surface Singularities
• Lagrangian Singularities
• Topological Aspects of
  local Algebra
• Computational Aspects

Algebraic Geometry

• Surfaces in three-space
• Varieties with many Singularities
• Abelian Varieties
• Calabi-Yau Manifolds
• Computational Aspects
• Differential Equations

Differential Equations

• Picard-Fuchs Operators
• Mirror Symmetry
• Local Systems and Monodromy
• Integrable Systems
• Arithmetical Aspects

 

 

Der Eulerkreis ist eine Gruppe historisch interessierter Mathematiker und Mathematikerinnen, die sich mit den Schriften und dem Werk Leonhard Eulers (1707-1783) beschäftigen. The Euler Circle Mainz is a Group of historically interested mathematicians who are interested in Leonhard Euler's (1707-1783) work and writings. Die nachfolgenden Übersetzungen Eulerscher Werke ins Deutsche oder Englische wurden von A. Aycock angefertigt. Wir danken dem Institut für Mathematik für großzügige Unterstützung, welche diese Übersetzungen ermöglichte. The following translations of Euler's work into German or English were prepared by A. Aycock. We wish to thank the Institute of Mathematics for generous support, that made These translations possible. Contact: D. van Straten: straten@Mathematik.uni-mainz.de T. Sauer:           tsauer@uni-mainz.de

Archiv

 

 

Euler and the Multiplication - Formula for the G-Function

 

Eine Methode sich der Eigenschaft des Maximums oder Minimums erfreuender Kurven zu finden, oder die Lösung des im weitesten Sinn aufgefassten isoperimetrischen Problems

Originaltitel: Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti, erstmals publiziert 1744, Nachdruck in "Opera Omnia", Eneström-Nummer E065

E065

 

Grundlagen des Differentialkalküls, der vollständige Erklärung dieses Kalküls enthält, Teil 1

Originaltitel: "Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum, Partis Prioris, erstmals publiziert im Jahre 1755", Nachdruck in "Opera Omnia", Eneström-Nummer E212

Vorwort

Kapitel I

Kapitel II

Kapitel III

Kapitel IV

Kapitel V

Kapitel VI

Kapitel VII

Kapitel VIII

Kapitel IX

Kapitel XVI

Abhandlungen aus Leonhard Eulers "Opera Omnia"*:

E010 - Eine neue Methode unzählige Differentialgleichungen zweiten Grades auf Differentialgleichungen ersten Grades zurückzuführen

E011 - Konstruktion gewisser Differentialgleichungen, die die Trennung der Unbestimmten nicht zulassen

E019 - Über transzendente Progressionen oder deren allgemeine Terme algebraisch nicht gegeben werden können
E019 - On transcendental Progressions or those whose general terms can not be given algebraically

E020 - Über die Summation von unzähligen Progressionen

E025 - A general Method of Summing Progressions

E031 - Konstruktion der Differentialgleichung \( ax^n dx = dy + y^2 dx\)

E041 - Über die Summen reziproker Reihen
E041 - On the sums of series of reciprocals

E043 - Beobachtungen über harmonische Progressionen
E043 - Observations on harmonic Progressions

E44 - Über unendlich viele Kurven derselben Gattung oder eine Methode Gleichungen für unendlich viele Kurven derselben Art zu finden

E45 - Anhang zur Abhandlung über unendlich viele Kurven derselben Art

E047 - Das Finden einer jeden Summe einer Reihe aus dem gegebenen allgemeinen Term

E051 - Über die Konstruktion von Gleichungen mit Hilfe von Schleppbewegung und anderen sich auf die inverse Methode der Tangenten beziehenden Dinge

E052 - Lösung der Probleme, die die Rektifikation der Ellipse erfordern

E053 - Lösung eines sich auf die "Geometria situs" beziehenden Problems

E055 - Die allgemeine Methode Reihen zu summieren - weiterentwickelt
E055 - The universal Method to sum series further promoted

E059 - Theorems on the reduction of integral formulas to the quadrature of the cirlce

E060 - Über das Finden von Integralen, wenn nach der Integration der variablen Größe ein bestimmter Wert zugeteilt wird

E061 - Eine andere Dissertation über die Summen der aus den Potenzen der natürlichen Zahlen entspringenden Reihen, in welcher dieselben Summationen aus einer gänzlich anderen Quelle deriviert werden
E061 - Another Dissertation on the sums of the series of reciprocals arising from the powers of the natural
numbers, in which the same summations are derived from a completely difference source

E062 - Über die Integration von Differentialgleichungen höherer Grade
E062 - On the integration of differential equations of higher orders

E063 - Beweis der Summe der Reihe 1 + 1/4 + 1/9 + 1/16 + · · ·

E70 - Über die Konstruktion von Gleichungen

E071 - Eine Dissertation über Kettenbrüche

E072 - Verschiedene Bemerkungen über unendliche Reihen

E098 - Beweise bestimmter zahlentheoretischer Probleme

E119 - Treatise on the vibration of chords

E122 - Über aus unendlich vielen Faktoren entspringende Produkte
E122 - On Products arising from infinitely many factors

E123 - Beobachtungen über die Kettenbrüche
E123 - Observations on continued fractions

E125 - Betrachtung einer gewissen Progression, welche zum Finden der Quadratur des Kreises geeignet ist

E130 - Betrachtungen über gewisse Reihen
E130 - Considerations on certain series

E152 - Über befreundete Zahlen

E164 - Theoreme über die in dieser Form paa ± qbb enthaltenen Teiler von Zahlen

E188 - Die Methode Differentialgleichungen höherer Grade zu integrieren weiter entwickelt

E189 - Über die Bestimmung von Reihen oder eine neue Methode, die allgemeinen Terme von Reihen
zu finden
E189 - On the Determination of Series or a new Method to find the General Terms of Series

E190 - Consideration of certain series having singular properties

E191 - Über die Partition von Zahlen
E191 - On the partition of numbers

E212 
Kapitel 1 - On the transformation of series
Kapitel 2 - On the investigation of summable series
Kapitel 3 - On Finding finite differences
Kapitel 4 - On the Conversion of Functions into Series
Kapitel 5 - Investigation of the sum of series from the general Term
Kapitel 6 - On the Summation of Progressions by means of infinite Series
Kapitel 7 - A further Generalization of the summation method treated in chapter V
Kapitel 8 - On the Use of Differential Calculus in the Formation of Series
Kapitel 9 - On the use of Differential Calculus in the resolution of Equations
Kapitel 10 - On Maxima and Minima
Kapitel 11 - On Maxima and Minima of multiform functions and such containing several variables
Kapitel 12 - On the Use of Differentials in the Investigation of the real Roots of Equations
Kapitel 13 - On Criteria for imaginary roots
Kapitel 14 - On Differentials of Functions in only certain cases
Kapitel 15 - On the values of functions which in certain cases seem to be undetermined
Kapitel 16 - On the Differentiation of inexplicable Functions
Kapitel 17 - On the Interpolation of series
Kapitel 18 - On the use of Differential Calculus in the Resolution of Fractions

 

E228 - Über Zahlen, die Aggregate zweier Quadrate sind

E230 - Elemente der Lehre von Festkörpern

E231 - Beweis einiger vortrefflicher Eigenschaften, mit denen von ebenen Seitenflächen eingeschlossene Festkörper versehen sind

E241 - Beweis des Fermat'schen Lehrsatzes, dass jede Primzahl der Form \( 4n + 1 \) die Summe zweier Quadrate ist

E242 - Beweis des Fermat'schen Lehrsatzes, dass jede entweder ganze oder gebrochene Zahl die Summe von vier oder weniger Quadraten ist

E247 - Über divergente Reihen
E247 - On divergent series

E251 - Über die Integration der Differentialgleichung \( \frac{mdx}{\sqrt{1-x^4}} = \frac{ndy}{\sqrt{1-y^4}} \)

E252 - Beobachtungen über den Vergleich von Bögen irrektifizierbarer Kurven
E252 - Observations on the Comparison of
Arcs of irrectifiable curves

E254 - On the expression of integrals by means of factors

E255 - General Solution of certain Diophantine problems which usually seem to admit only special Solutions

E258 - Prinzipien der Bewegung von Fluiden

E261 - Ein anderes Beispiel der neuen Methode transzendente Größen miteinander zu vergleichen - Über den Vergleich von Ellipsenbogen
E261 - Another Specimen of the new Method to compare transcendental Quantities to each other - On the Comparison of the Arcs of an Ellipse

E265 - Über Differentialgleichungen zweiten Grades

E269 - On the Integration of Differential Equations

E271 - Zahlentheoretische Theoreme, mit einer neuen Methode bewiesen

E273 - Betrachtung von Formeln, deren Integration mithilfe von Kegelschnitten durchgeführt werden kann

E274 - Die Konstruktion der Differenzen-Differentialgleichung Aydu2 + (B + Cu)dudy + (D + Eu + Fuu)ddy = 0 für konstant angenommenes Element du

E275 - Bemerkungen zu einem gewissen Auszug des Descartes, der sich auf die Quadratur des Kreises bezieht

E280 - Über Progressionen von Kreisbogen, deren Tangenten nach einem gewissen Gesetz fortschreiten

E281 - Ein Beispiel für einen einzigartigen Algorithmus

E285 - Investigation of Functions from a given condition of the differentials

E295 - Über die Rückführung von Integralformeln auf die Rektifikation der Ellipse und der Hyperbel

E296 - Elemente des Variationskalküls
E296 - Elements of the Calculus of Variations

E297 - Analytische Erläuterungen der Methode der Maxima und Minima
- Teil A Deutsch
- Teil A Englisch

- Teil B Deutsch
- Teil B Englisch

E301 - On the motion of bodies attracted to two fixed centres of force

E321 - Beobachtungen über die Integrale der Formeln \( \int x^{p-1} dx (1 - x^n)^{\frac{q}{n}-1} \) nachdem nach der Integration \( x = 1 \) gesetzt worden ist
E321 - Observations on the integral of the formulas \( \int x^{p-1} dx (1 - x^n)^{\frac{q}{n}-1} \) having put x = 1 after the  integration

E322 - Über die Nützlichkeit von unstetigen Funktionen in der Analysis

E323 - Über den Gebrauch des neuen Algorithmus' beim Lösen des Pell'schen Problems

E324 - Eigenschaften von Dreiecken, deren Winkel in einem bestimmten Verhältnis zueinander stehen

E325 - Leichte Lösung gewisser sehr schwieriger geometrischer Probleme

E326 - Analytical Observations

E345 - Integration der Gleichung \( \frac{dx}{\sqrt{A+Bx+Cx^2+Dx^3+Ex^4}} = \frac{dy}{\sqrt{A+By+Cy^2+Dy^3+Ey^4}} \)
E345 - Integration of the Equation dx√ A+Bx+Cx2+Dx3+Ex4 = dy √A+By+Cy2+Dy3+Ey4

E347 - More general Discussion of the Formulas serving for the comparison of curves

E352 - Bemerkung über die wunderbare Relation zwischen der Reihe der direkten und reziproken Potenzen

E366 - Über die Konstruktion von Differenzen-Differentialgleichungen mit Quadraturen der Kurven

E368 - On the hypergeometric Curve expressed by the equation

E385 
Kapitel 1 - Über das Variationskalkül im Allgemeinen
Kapitel 2 - Über die Variation zwei Variablen involvierender Differentialformeln
Kapitel 4 - Über die Variation zwei Variablen involvierender zusammengesetzter Integralformeln
Kapitel 5 - Über die Variation drei Variablen involvierender und zwei Relationen verwickelnder Integralformeln
Kapitel 6 - Über die Variation drei Variablen involvierender Differentialformeln, deren Relation in einer einzigen Gleichung enthalten ist
Kapitel 7 - Über die Variation drei Variablen involvierender Integralformeln, von denen eine wie eine Funktion der zwei übrigen angesehen wird

E390 - Betrachtungen über orthogonale Trajektorien

E391 - Über Doppelintegrale

E392 - Entwicklung eines außerordentlichen Paradoxons über die Gleichheit von Flächen

E393 - Über Summen, deren Reihen die Bernoulli-Zahlen involvieren

E394 - Über die Partition von Zahlen in so von der Anzahl wie von der Gattung her gegebene Teile

E396 - Zweiter Abschnitt über die Grundsätze der Bewegung von Fluiden

E406 - Beobachtungen zu den Wurzeln von Gleichungen

E408 - Über rektifizierbare Kurven auf einer Kugeloberfläche

E419 - Über Körper, deren Oberfläche sich in die Ebene ausbreiten lassen
E419 - On Solids whose surface can be unfolded onto a plane

E420 - Eine neue und leichte Methode die Variationsrechnung zu behandeln

E421 - Entwicklung der Integralformel \( \int x^{f-1} DX (lnx)^{\frac{m}{n}} \) nach Erstreckung der Integration vom Wert \( x = 0 \) bis zu \( x = 1 \)
E421 - Expansion of the integral formula \( \int x^{f-1} DX (lnx)^{\frac{m}{n}} \) having extended the integration
from the value \( x = 0 \) to \( x = 1 \)

E422 - Entwicklung eines völlig einzigartigen geometrischen Problems

E429 - On various kinds of integrability

E431 - Consideration of the Difference-Differential equation

E432 - Analytische Übungen
E432 - Analytical Exercises

E433 - Eine Abschweifung zu orthogonalen wie schiefwinkligen Trajektorien

E439 - Further Investigation on vibrating chords

E445 - Neue Beweise über die Auflösung von Zahlen in Quadrate

E447 - Summation der Progressionen ...
E447 - Summation of the progressions … (englischer Text)

E448 - Eine neue unendliche Reihe, die sehr stark konvergiert und die Perimetrie einer Ellipse ausdrückt

E450 - A new way to express irrational quantities approximately

E454 - Über die Auflösung von Irrationalitäten durch Kettenbrüche, wo zugleich eine gewisse neue und einzigartige Gattung des Minimums dargestellt wird

E463 - Über den Wert der Integralformel zlwzl+w 1z2l dz z (ln z)m in dem Fall, in dem nach Integration z = 1 gesetzt wird

E464 - Eine neue Methode Integralgrößen zu bestimmen

E465 - Beweis des Newton'schen Lehrsatzes über die Entwicklung der Potenzen des Binoms für die Fälle, in denen die Exponenten keine ganzen Zahlen sind

E 465 - Proof of the Newtonian Theorem on the Expansion of the Powers of the Binomial for the cases in which the Exponents are not integer numbers

E475 - Analytische Betrachtungen

E477 - Gedanken über ein einzigartiges Geschlecht von Reihen
E477 - Meditations on a singular kind of series

E488 - Bemerkungen zur vorausgehenden Dissertation des illustren Bernoulli

E489 - Über iterierte Exponentialformeln

E490 - Über die Repräsentation einer sphärischen Oberfläche auf einer Ebene

E491 - Über die geographische Projektion einer sphärischen Oberfläche

E492 - Über die von De Lisle gebrauchte geographische Projektion bei der gesamten Karte des russischen Reichs

E499 - On the Integration of the Formula ∫ dx log x / √1-xx extended from x = 0 to x = 1

E500 - Über den Wert der von der Grenze \(x=0 \) bis hin zu \(x=1\) erstreckten Integralformal \( \int \frac{x^{a-1}dx}{ln \,x} \frac{(1-x^b)(1-x^c)}{1-x^n} \)

E 501 - Betrachtungen über Brachystochronen

E506 - Erläuterungen zur höchst eleganten Methode, welche der illustre Lagrange beim Integrieren der Differentialgleichung dx/√X = dy/√Y verwendet hat

E513 - Über Dreieckskurven

E514 - Über das Maß von Raumwinkeln

E522 - Über die Bildung von Kettenbrüchen
E522 - On the formation of continued fractions

E524 - Die allgemeine sphärische Trigonometrie unmittelbar aus ersten Prinzipien abgeleitet

E532 - Über die Lambert’sche Reihe und ihre vielen vorzüglichen Eigenschaften

E539 - Ein Supplement zum Integralkalkül für die Integration irrationaler Formeln

E540 - Eine neue Methode beliebige rationale Brüche in einfache Brüche aufzulösen

E541 - Entwicklung des unendlichen Produkts \( (1-x)(1-xx)(1-x^3)(1-x^4)(1-x^5)(1-x^6) \) etc. in eine einfache Reihe

E550 - Über Reihen, in denen die Produkte aus je zwei benachbarten Termen eine gegebene Progression festlegen

E551 - Various Artifices to investigate the Nature of Series

E552 - Bemerkungen über die Division von Quadraten durch Primzahlen

E553 - Analytische Bemerkungen

E555 - Über den außerordentlichen Nutzen der Interpolationsmethode in der Lehre der Reihen
E555 - On the extraordinary use of the method of Interpolation in the doctrine of Series

E562 - How Sines and Cosines of multiple angles can be expressed by Products

E565 - Über die vielen transzendenten Größen, die sich in keiner Weise mit Integralformeln ausdrücken  lassen

E575 - On the remarkable Properties of the Coefficients which occur in the Expansion
of the binomial raised to an arbitrary power

E581 - Eine umfassendere Darstellung des Vergleiches der in der Integralformel \( \int \frac{Zdz}{\sqrt{1+mzz+nz^4}} \) enthaltenen Größen, während \( Z \) irgendeine rationale Funktion \( zz \) bezeichnet
E581 - More Complete Explanation of the Comparison of Quantities contained in the Integral formula
R p Zdz 1+mzz+n4 while Z denotes any rational function of zz

E583 - Über die bemerkenswerte Zahl, die bei der Summation der natürlichen harmonischen Progression auftaucht
E583 - On the memorable number occurring in the summation of the natural harmonic Progression

E587 - Bemerkungen zu einigen Lehrsätzen des höchst illustren Lagrange

E588 - Investigation of the integral Formula∫((x^(m-1) dx)/(1+x^(k)n) )  in the case in which one set x = ¥ after the integration

E589 - Investigation of the Value of the Integral ∫xm-1dx\1-2xk cosq+x2k extended from x = 0 to x = ¥

E592 - Über die Auflösung von transzendenten Brüchen in unendlich viele einfache Brüche

E593 - Über die Transformation von Reihen in Kettenbrüche, wo zugleich die Theorie nicht unwesentlich erweitert wird

E594 - Eine Methode Integralformen zu finden, die in gewissen Fällen in einem gegebenen Verhältnis zueinander stehen, wo zugleich eine Methode angegeben wird, Kettenbrüche zu summieren
E594 - A Method of Finding Integral Formulas which in certain Cases have a given ratio, where at the same time a method of summing continued fractions is presented

E595 - Summation des Kettenbruches, dessen Indizes eine arithmetische Progression festlegen, während alle Zähler Einheiten sind, wo zugleich die Auflösung der Riccati-Gleichung durch Brüche
von dieser Art gelehrt wird

E598 - Über einen gewaltigen Fortschritt in der Zahlentheorie

E602 - Eine leichte Methode alle Eigenschaften von Raumkurven zu finden

E604 - Über rechtwinklige sowie schiefwinklige reziproke Trajektorien

E605 - Über die wundersamen Eigenschaften der Curvae elasticae, die in der Gleichung \( y = \int \frac{xx\mathrm{d}x}{\sqrt{1-x^4}} \) enthalten ist

E606 - Spekulation über die Integralformel \( \int \frac{x^n \mathrm{d}x}{\sqrt{aa-2bx+cxx}} \), wo zugleich herausragende Beobachtungen über Kettenbrüche entstehen
E606 - Speculations on the integral formulaR xndx √aa−2bx−cxx where at the same time extraordinary observations on continued fractions occur

E609 - Betrachtungen über orthogonale wie schiefwinklige Trajektorien

E610 - Neue Beweise über die Teiler von Zahlen der Form xx + nyy

E613 - Erläuternde Darstellungen zu den letzten Kapiteln meines Buches "Institutiones Calculi Differentialis" über unerklärbare Funktionen
E613 - Further Explanations to the last Chapter of my book Calculi Differentialis on inexplicable functions

E616 - Über die Transformation der divergenten Reihe \( 1 - mx + m (m+n)x^2-m(m+n)(m+2n)x^3 + \)  etc. in einen Kettenbruch
E616 - On the transformation of the divergent series 1−mx +m(m+n )x2−m(m+n)(m+2n)x3 +etc. into a continued fraction

E617 - Über die Summation von Reihen, in denen die Vorzeichen der Terme alternieren

E620 - Eine leichte Methode, das Integral ∂x x · xn+p−2xn cos ζ+xn−p x2n−2xn cos θ+1 im Fall zu finden, in welchem nach der Integration entweder x = 1 oder x = ∞ gesetzt wird

E621 - Über den immensen Nutzen des Kalküls imaginärer Größen in der Analysis

E629 - Entwicklung der von der Grenze \( x = 0 \) bis hin zu \( x = 1 \) erstreckten Integralformel \( \int \partial x \left( \frac{1}{1-x} + \frac{1}{\log x} \right) \)

E631 - Leichte und klare Analysis, die zu höchst abstrusen Reihen führt, mit welchen nicht nur die Wurzeln aller algebraischen Gleichungen sondern auch jedwede Potenzen derer ausgedrückt werden können

E637 - Ein neuer Beweis, dass die Newtonsche Entwicklung der Potenzen des Binoms auch für gebrochene Exponenten gilt

E652 - Über den allgemeinen Term der hypergeometrischen Reihen
E652 - On the general Term of hypergeometric Series

E655 - Beobachtung über Reihen, deren Terme nach den Sinus oder Kosinus vielfacher Winkel fortschreiten

E656 - Über höchst bemerkenswerte aus dem Kalkül der imaginären Größen herstammende Integrationen

E658 - Über das Finden der Kraftmomente bezüglich beliebiger Achsen, wo viele außerordentliche  Eigenschaften über zwei Geraden, die nicht in derselben Ebene liegen, erklärt werden

E659 - Eine leichte Methode die Momente aller Kräfte bezüglich einer beliebigen Achse zu bestimmen

E661 - Verschiedene Betrachtungen über hypergeometrische Reihen
E661 - Various Consideration on hypergeometric Series

E662 - On the true Value of the integral formula ∂ x log 1 xn  extended from the limit x = 0 to x = 1

E663 - Eine umfassendere Darstellung jener merkwürdigen Reihen, die aus den Koeffizienten der Potenzen des Binoms gebildet werden
E663 - A more complete Explanation of those memorable series which are formed from the binomial coefficients

E664 - Eine analytische Übung

E684 - Über die Wurzeln der unendlichen Gleichung 0=1 - x^2 / n(n+1) + x^4 / n(n+1)(n+2)(n+3) -
x^6 / n ... (n+5) + etc.

E671 - Über höchst irrationale von Winkeln abhängige Differentialformeln, welche sich  dennoch mit Logarithmen und Kreisbogen integrieren lassen

E672 - Ein höchst bemerkenswertes Theorem über die Integralformel

E673 - Eine auf Vermutungen beruhende Untersuchung über die Integralformel

E674 - Beweis des über eine Vermutung gefundenen außerordentlichen Theorems über die Integration der
Formel

E675 -  Über die Werte der von der Grenze der Variable x = 0 bis hin zu x = ∞ erstreckten Integrale

E676 - Eine kürzere Methode die Vergleiche der in der Form ... enthaltenen transzendenten Größen zu finden

E678 - A new Method to investigate the cases, in which it is possible to solve the difference-differential equation (1 - )-   - ^2= 0

E681 - Ein Beispiel von Differentialgleichungen unbestimmten Grades und deren Interpolation

E694 - Eine weitere Untersuchung über imaginäre Integralformeln

E698 - Verschiedene Betrachtungen über die Fläche von Kugeldreiecken

E700 - On differential formulas of second degree that admit an integration

E704 - Weitere Untersuchungen über die Reihen, die nach den Vielfachen eines Winkels fortschreiten

E707 - Über den außerordentlichen Nutzen des Kalküls mit imaginären Größen in der Integralrechnung

E710 - Beweis einer einzigartigen Transformation von Reihen
E710 - A specimen of a singular transformation of series

E711 - Eine neue und leichte Methode, nicht nur die Wurzeln selbst sondern auch beliebige Potenzen derer aller algebraischen Gleichungen mittels gefälliger Reihen auszudrücken

E722 - Analytische Untersuchungen über die Entwicklung der Trinomialpotenz \( (1 + x + xx)  \)
E722 - Analytical Investigations on the Expansion of the trinomial Power (1+ x + xx)n

E726 - Beweis des ausgezeichneten numerischen Theorems über die Koeffizienten der Binomialpotenzen

E734 - Integration dieser Differentialgleichung \(dy + yydx = \frac{Adx}{(a+bx+cxx)^2}\) 

E735 - Über ein riesiges Paradoxon, welches in der Analysis der Maxima und Minima auftritt

E736 - Über die Summation der Reihen, die in dieser Form enthalten sind \( \frac{a}{1}+\frac{a^2}{4}+\frac{a^3}{9}+\frac{a^4}{16}+\frac{a^5}{25}+\frac{a^6}{36}+etc\)
E736 - On the Summation of the series contained in this form \( \frac{a}{1}+\frac{a^2}{4}+\frac{a^3}{9}+\frac{a^4}{16}+\frac{a^5}{25}+\frac{a^6}{36}+etc\)

E740 - Über nicht in derselben Ebene gelegene gekrümmte Linien, die mit der Eigenschaft des Maximums oder Minimums versehen sind

E742 - Bemerkungen über die in dieser Form enthaltenen Kettenbrüche

E743 - Über eine höchst bemerkenswerte Reihe, mit welcher jede Binomialpotenz ausgedrückt werden kann

E744 - Über die Teiler der in der Form mxx + nyy enthaltenen Zahlen

E745 - Über die Kettenbrüche von Wallis
E745 - On Wallis’ continued fractions

E746 - Eine kurze Methode, Summen unendlicher Reihen durch Differentialformeln zu untersuchen

E750 - Ein Kommentar zum Kettenbruch, mit welchem der bedeutende Lagrange die Binomialpotenzen ausgedrückt hat

E751 - Leichte Analysis, die Riccati-Gleichung durch einen Kettenbruch aufzulösen

E752 - Über gewisse sehr schwer zu findende Integrale

E757 - Über das Problem der orthogonalen Trajektorien übertragen auf Flächen

E759 - Eine genauere Untersuchung über Brachystochronen

E760 - Über die wahre Brachystochrone oder die Linie des schnellsten Herabsinkens in einem widerstehenden Medium

E761 - Über die Brachystochrone in einem widerstehenden Medium, während
der Körper auf irgendeine Weise zu einem festen Kraftzentrum hingezogen wird

E768 - On the Binomial Coefficients and their Interpolation

E807 - Über die Logarithmen von negativen und imaginären Zahlen

E814 - Abschnitt III der Grundlagen des Differentialkalküls

 

 

Publikationen

2024
	A Category of Banach Space Functors Mauricio Garay, Duco van Straten Journal of Lie Theory, Vol. 34, No. 1, 207-236 (2024) arXiv:2010.02320 [math.CV]
	A Hyperelliptic Saga on Generating Function of the Squares of Legendre Polynomials Mark van Hoeij, Duco van Straten, Wadim Zudilin arXiv: 2306.04921 [math.NT]
2023	Calabi-Yau operators of degree two Gert Almkvist, Duco van Straten Journal of Algebraic Combinatorics arXiv:2103.08651 [math.AG]
	Quasi-periodic motions on symplectic tori Mauricio Garay, Arezki Kessi, Duco van Straten, Nesrine Yousfi Journal of Singularities, Vol. 26, 23-62 (2023)
	Congruences via fibered motives Vasily Golyshev, Duco van Straten Pure and Applied Mathematics Quarterly, Vol. 19, No. 1, 233–265 (2023)
2021	A special Calabi-Yau degeneration with trivial monodromy S. Cynk, D. van Straten Communications in Contemporary Mathematics (2021) arXiv:1812.01622.pdf (arxiv.org)
2020	A One Parameter Family of Calabi-Yau Manifolds with Attractor Points of Rank Two Philip Candelas, Xenia de la Ossa, Mohamed Elmi, Duco van Straten Journal of High Energy Physics, Vol. 10 2020, Art.nr. 202 (2020) arXiv:1912.06146
	Hilbert modularity of some double octic Calabi-Yau threefolds Slawomir Cynk, Matthias Schütt, Duco van Straten Journal of Number Theory, Vol. 210, May 2020, 313-332 (2020)
2019	Dimensional Interpolation and the Selberg integral Vasily Golyshev, Duco van Straten, Don Zagier Journal of Geometry and Physics, Vol. 145, 103455 (2019) arXive: 1906.00071
	Rationalizing roots: an algorithmic approach Marco Besier, Duco van Straten, Stefan Weinzierl Communications in Number Theory and Physics Vol. 13 No. 2, 253–297 (2019) hep-th; hep-ph; math-ph;  MITP/18-091 arXive: 1809.10983
	Bhabha Scattering and Special pencil of K3 surfaces Dino Festi, Duco van Straten Communications in Number Theory and Physics, Vol. 13, No. 2, 463-485 (2019)
	Periods of double octic Calabi-Yau manifolds Slawomir Cynk, Duco van Straten Annales Polonici Mathematici, Vol. 123 (2019)
	Picard-Fuchs operators for octic arrangements I (The case of orphans) Slawomir Cynk, Duco van Straten Communications in Number Theory and Physics, Vol. 13 No. 1, 1-52 (2019)
	Calabi-Yau Operators Duco van Straten in Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds & Picard-Fuchs Equations (Eds. Lizhen Ji, Shing-Tung Yau), Advanced Lectures in Mathematics, Vol. 42, 2018 arXive 1704.00164
2017	CY-Operators and L-Functions Duco van Straten MATRIX Annals 2017, 491-503 (2017)
	Logarithmic vector fields and the Severi strata in the discriminant Singularities in: Geometry, Topology, Foliations and Dynamics (A Celebration of the 60th Birthday of J. Seade, Merida, Mexico, 12/2014) Eds.: J. L. Cisneros-Molina, D.T. Lê, M. Oka, J. Snoussi 55-76, Birkhäuser (2017)
	On a theorem of Greuel and Steenbrink in: Singularities and computer algebra (Festschrift for Gert-Martin Greuel on the Occasion of his 70th Birthday) Eds.:  W. Decker, G. Pfister, M. Schulze 353–364, Springer (2017)
	Twisted cubics on cubic fourfolds Christian Lehn, Manfred Lehn, Christoph Sorger, Duco van Straten Crelle‘s J. reine u. angew. Math., Vol. 731, 87-128 (2017)
2016	Weak Whitney regularity implies equimultiplicity for families of complex hypersurfaces  David Trotman, Duco van Straten Ann. de la Faculté des Sciences de Toulouse, Vol. XXV no. 1, 161-170 (2016)
2015	Dwork congruences and reflexive polytopes Kira Samol, Duco van Straten Ann. Math. Quebec, Vol. 39, 185-203 (2015)
	From Briancon-Skoda to Scherk-Varchenko Duco van Straten in: Commutative Algebra and Noncommutative Algebraic Geometry I Eds: D. Eisenbud, S. B. Iyengar, A. K. Singh, J. T. Stafford, M. Van den Bergh MSRI Publications, Vol. 67, 347-370 (2015)
	Some Monodromy Groups of Finite Index Jörg Hofmann, Duco van Straten J. Aust. Math. Soc., Vol. 99, 48-62 (2015)
	Gorenstein-duality for one-dimensional almost complete intersections with an application to non-isolated real singularities Duco van Straten, Thorsten Warmt Math. Proc. Camb. Phil. Soc., Vol. 158, 249-268 (2015)
2014	Resurgent deformation quantisation Mauricio Garay, Axel de Goursac, Duco van Straten Annals of Physics, Vol. 342, 83-102 (2014)
2013	Tree Singularities: Limits, Series and Stability Duco van Straten in: Deformations of Surface Singularities Eds.: A. Némethi, A.Szilárd Bolyai Society Mathematical Studies, Vol. 23,  229-287, Springer (2013)
	Calabi-Yau conifold expansions Slawomir Cynk, Duco van Straten in: Arithmetic Geometry of K3 Surfaces and Calabi-Yau Threefolds Eds.: R. Laza, R. Schütt, N. Yui Fields Institute Communications, Vol. 67, 499-515 (2013)
	An Abelian Surface with (1, 6)-Polarisation Michael Semmel, Duco van Straten Nonlinearity, Vol. 26, 2973-2992, (2013) arXive: 1211.6200
	On symplectic hypersurfaces Manfred Lehn, Yoshinori Namikawa, Christoph Sorger, Duco van Straten in: Minimal models and extremal rays (Kyoto 2011) Eds.: J. Kollár, O. Fujino, S. Mukai, N. Nakayama Advanced Studies in Pure Mathematics, Vol. 99, 1-24 (2013)
	On the monodromy of the moduli space of Calabi-Yau threefolds coming from eight planes in P3 Ralf Gerkmann, Mao Sheng, Kang Zuo, Duco van Straten Math. Ann., Vol. 355, 187-214 (2012)
2012	Lines on the Dwork Pencil of Quintic Threefolds Philip Candelas, Xenia de la Ossa, Bert van Geemen, Duco van Straten Adv. Theor. Math. Phys., Vol. 16, No. 6, 1779-1836 (2012) arXive: 1206.4961
	An Index Theorem for Modules on a Hypersurface Singularity Ragnar Buchweitz, Duco van Straten Moscow Math. Journal, Vol. 12, No. 2, 237-259 (2012)
	Hyperelliptic integrals and generalized arithmetic-geometric mean Jeroen Spandaw, Duco van Straten Ramanujan Journal, Vol. 28, 61-78 (2012)
2011	Generalizations of Clausen's formula and algebraic transformations of Calabi-Yau differential equations G. Almkvist, Duco van Straten, Wadim Zudilin Proc. Edinb. Math. Soc. (2), Vol. 54, 273-295 (2011)
2010	Hodge classes associated to 1-parameter families of Calabi-Yau 3-folds Pedro Luis Del Angel, Stefan Müller-Stach, Duco van Straten, Kang Zuo Acta Math. Vietnam, Voll. 35 No. 1, 7-22 (2010)
	Classical and Quantum Integrability Mauricio D. Garay, Duco van Straten Moscow Math. Journal, Vol. 10, No. 3, 519-545 (2010)
2009	Small Resolutions and Non-Liftable Calabi-Yau threefolds Slawomir Cynk, Duco van Straten Manus. Math., Vol. 130, 233-249 (2009)
	Smoothing of Quiver Varieties Klaus Altmann, Duco van Straten Manus. Math., Vol. 129, 211-230 (2009)
2008	Apéry Limits of Differential Equations of Order 4 and 5 Gert Almkvist, Duco van Straten, Wadim Zudilin in: Modular Forms and String Duality Eds.: N. Yui, C. Doran, H. Verrill Fields Institute Communications, Vol. 54, 105-123 (2008)
	Frobenius polynomials for Calabi-Yau equations Kira Samol, Duco van Straten Comm. in Number Theory and Physics, Vol. 2, No. 3, 537-561 (2008)
	Real Line Arrangements and Surfaces with Many Real Nodes Sonja Breske, Oliver Labs, Duco van Straten in: Geometric modeling and algebraic geometry Eds.: B. Jüttler, R. Piene 47-54, Springer (2008)
2006	Some Problems on Lagrangian Singularities Duco van Straten in: Singularities and computer algebra Eds.: C. Lossen, G. Pfister London Math. Soc. Lecture Notes, Vol 324, 333-349, Cambridge Univ. Press (2006)
	Monodromy calculations of fourth order equations of Calabi-Yau type Christian van Enckevort, Duco van Straten in: Mirror symmetry V Eds: N. Yui, S.-T. Yau, J. Lewis Stud. in Adv. Math., Vol. 38, 539–559, AMS/IP, Providence, RI (2006) arXive: 0412539
	Infinitesimal Deformations of double covers of smooth algebraic varieties Slawomir Cynk, Duco van Straten Math. Nachr., Vol. 279, no. 7, 716-726 (2006)
2004	Rigid and complete intersection Lagrangian singularities Christian Sevenheck, Duco van Straten Manus. Math., Vol. 114, no. 2, 197-209 (2004)
2003	A visual introduction to cubic surfaces using the computer software SPICY Oliver Labs, Duco van Straten in: Algebra, Geometry, and Software Systems Eds.: M. Joswig, N. Takayama 225-238, Springer (2003)
	Deformation of singular lagrangian subvarieties Christian Sevenheck, Duco van Straten Math. Ann., Vol. 327, 79-102 (2003)
	On the Topology of Langrangian Milnor Fibres Mauricio D. Garay, Duco van Straten IMRN, Vol. 35, 1933-1943 (2003)
	Stochastic factorizations, sandwiched simplices and the topology of the space of explanations David Mond, Jim Smith, Duco van Straten Proc. R. Soc. Lond., Vol. 459, 2821-2845 (2003)
2002	A criterion for the equivalence of formal singularities Konrad Möhring, Duco van Straten Am. J. Math., Vol. 124, 1319-1327 (2002)
2001	The modularity of the Barth-Nieto quintic and its relatives Klaus Hulek, Jeroen Spandaw, Bert van Geemen, Duco van Straten Adv. Geom. 1, no. 3, 263-289 (2001)
	Milnor Number equals Tjurina Number for Functions on Space Curves David Mond, Duco van Straten J. of the London Math. Soc. (2), Vol. 63, 177-187 (2001)
	The structure of the discriminant of some space curve singularities David Mond, Duco van Straten Quart. J. Math., Vol. 52, No. 3, 355-365 (2001)
2000	Projective resolutions associated to projections Theo de Jong, Duco van Straten Manus. Math., Vol. 101, 415-427 (2000)
	Mirror symmetry and toric degenerations of partial flag manifolds Victor Batyrev, Ionut Ciocan-Fontanine, Bumsig Kim, Duco van Straten Acta Mathematica, Vol. 184 No. 1, 1-39 (2000)
	The polyhedral Hodge number h2,1 and vanishing of obstructions Klaus Altmann, Duco van Straten Tohuku Math J., Vol. 52 No. 4, 579-602 (2000)
1999	Knotted Milnor fibres David Mond, Duco van Straten Topology, Vol. 38 No. 4, 915-929 (1999)
1998	Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians Victor Batyrev, Ionut Ciocan-Fontanine, Bumsig Kim, Duco van Straten Nucl. Phys., Vol. B 514, 640-666 (1998)
	Euler number of the compactified Jacobian and multiplicities of rational curves Barbara Fantechi, Lothar Göttsche, Duco van Straten J. of Alg. Geometry, Vol. 8 No. 1, 115-133 (1998)
	Deformation theory of Sandwiched Singularities Theo de Jong, Duco van Straten Duke Math. J., Vol. 95 No. 3, 451-522 (1998)
1995	The intermediate Jacobians of the theta divisors of four-dimensional principally polarized abelian varieties Elham Izadi, Duco van Straten J. of Alg. Geometry, Vol. 4 No. 3, 557-590 (1995)
	A Note on the Discriminant of a Space Curve Duco van Straten Manus. Math., Vol. 87 No. 2, 167-177 (1995)
1994	On the deformation theory of rational surface singularities with reduced fundamental cycle Theo de Jong, Duco van Straten J. of Alg. Geometry, Vol. 3 No. 1, 117-172 (1994)
1993	Generalized Hypergeometric Functions and Rational Curves on Calabi-Yau Complete Intersections in Toric Varieties Victor Batyrev, Duco van Straten Comm. of Math. Physics, Vol. 168, 493-533 (1993)
	Algebraizations with minimal class group A. J. Parameswaran, Duco van Straten Int. J. of Math., Vol. 4 No.6, 989-996 (1993)
	A Quintic Hypersurface in P4 with 130 Nodes Duco van Straten Topology, Vol. 32 No. 4, 857-864 (1993)
	Quotient spaces and critical points of invariant functions for C∗-actions James Montaldi, Duco van Straten Crelle's J. reine u. Angew. Math., Vol. 437, 55-99 (1993)
	The cusp forms of weight 3 on Γ(2,4,8) Bert van Geemen, Duco van Straten Mathematics of Computation, Vol. 61 No. 204, 849-872 (1993)
1992	A construction of Q-Gorenstein smoothings of index two Theo de Jong, Duco van Straten Int. J. of Math., Vol. 3 No. 3, 341-347 (1992)
1991	Disentanglements Theo de Jong, Duco van Straten in: Singularity Theory and its Applications, Warwick 1989, vol 1 Eds.: D. Mond, J. Montaldi Lecture Notes Math., Vol. 1462, 199-211, Springer (1991)
	On the Base Space of a Semi-universal Deformation of Rational Quadruple points Theo de Jong, Duco van Straten Ann. of Math., Vol. 134, 653-678 (1991)
1990	Deformations of the Normalization of Hypersurfaces Theo de Jong, Duco van Straten Math. Ann., Vol. 288, 527-547 (1990)
	A Deformation Theory for Non-Isolated Singularities Theo de Jong, Duco van Straten Abh. Math. Sem. Univ. Hamburg, Vol. 60, 177-208 (1990)
	One-forms on singular curves and the topology of real curve singularities James Montaldi, Duco van Straten Topology, Vol. 29 No. 4, 501-510 (1990)
1998	Abelian surfaces of type (1, 4) Christina Birkenhage, Herbert Lange, Duco van Straten Math. Ann., Vol. 285, 625-646 (1989)
	A note on the number of periodic orbits near a resonant equilibrium point Duco van Straten Nonlinearity, Vol. 2, 445-458 (1989)
1985	On the Betti numbers of the Milnor fibre of a certain class of hypersurface singularities Duco van Straten in: Singularities, Representations of Algebras and Vector Bundles Eds.: G.-M. Greuel, G. Trautmann Lecture Notes Math., Vol. 1273, 203-220 (1985)
	Extendability of holomorphc differential forms near isolated hypersurface singularities Josef Steenbrink, Duco van Straten Abh. Math. Sem. Univ. Hamburg, Vol. 55, 97-110 (1985)

ArXive

2024	Paramodular forms from Calabi-Yau Operators Nutsa Gegelia, Duco van Straten ArXiv: 2408.10183[math.NT]
	A remarkable eelliptic curve D. van Straten arXiv: 2404.05852
	Product formulas for the Higher Bessel functions Ilia Gaiur, Vladimir Rubtsov, Duco van Straten arXiv: 2405.03015
2023
2020	Non-abelian Abel's theorems and quaternionic rotation V. Golyshev, A. Mellit, V. Rubtsov, D. van Straten arXiv:2102.09511 [math.NT]
2019	The Spectrum of Singularities Duco van Straten arXiv:2003.00519 [math.AG]
	Hamiltonian Normal Forms Mauricio Garay, Duco van Straten arXiv:1909.06053v1  [math.DS]
	Versal deformations of vector field singularities Mauricio Garay, Duco van Straten arXiv:2011.06802 [math.DS]
2018	KAM Theory. Part I, II, III Mauricio Garay, Duco van Straten I: Group actions and the KAM Problem II: Kolmogorov spaces III: Applications
2009	A Quintic Hypersurface in P8(C) with Many Nodes Oliver Labs, Oliver Schmidt, Duco van Straten arXiv:0909.3367v1 [math.AG]1981
2005	Tables of Calabi-Yau equations Gert Almkvist, Christian van Enckevort, Duco van Straten, Wadim Zudilin arXiv: math/0507430 [math.AG]

Qualifikationsarbeiten

1993	Habilitationsschrift:  Aspects of Singularity Theory
1987	Doktorarbeit:  Weakly normal Surface Singularities and their improvements
1983	Große Skriptie: Representaties,Simpele singulariteiten en verder....
1982	Kleine Skriptie: Singularitaeten

Weitere Arbeiten

1981	De invloed van meteorologische omstandigheden op de geluiddempende werking van een bos van Straten, Klumpen, Mulder, van Santen
1981	Enkele metingen aan drainerende zeepvliezen van Straten, Kloosterziel

 

 

 

Sprechstunden:

Nach Vereinbarung,
bitte melden Sie sich über das Sekretariat
bei Frau Bonmann an.

E-Mail: ebonmann@uni-mainz.de
Tel: 39 23335
Raum: 04-232

 

 

 

 

<img class="alignnone size-medium wp-image-9386"

 

 

 

 

Calabi-Yau Sequences & Instanton Numbers

To search the database - click here

 

 

 

Aktuelles / Termine:

 

Weiterlesen "Prof. Dr. Duco van Straten"