Research / Publications

Preprints

  1. Homology manifolds via six functor formalisms. Joint with M. Volpe. arXiv
  2. Grothendieck-Witt theory of derived schemes. Joint with M. Hoyois. arXiv
  3. Formality of E_n-algebras and cochains of spheres. Joint with G. Heuts. arXiv
  4. Homology manifolds and euclidean bundles. Joint with F. Hebestreit, C. Winges, and M. Weiss. arXiv
  5. A survey on operator K-theory via homotopical algebra. Joint with U. Bunke and U. Pennig. arXiv
  6. Remarks on chromatically localised hermitian K-theory. arXiv
  7. A stable \infty-category for equivariant KK-theory. arXiv

Publications

  1. Towards the classification of DGAs with polynomial homology. Accepted for publication at Compositio Mathematica. Joint with H. Ö. Bayındır. arXiv
  2. Paschke duality and assembly maps. Accepted for publication at New York Journal of Mathematics. Joint with U. Bunke and A. Engel. arXiv
  3. On the K-theory of pushouts. J. Eur. Math. Soc. (JEMS) 2026, published online first. Joint with G. Tamme. arXiv
  4. Hermitian K-theory for stable \infty-categories III: Grothendieck--Witt groups of rings. Accepted for publication at Ann. of. Math. Joint with B. Calmès, E. Dotto, Y. Harpaz, F. Hebestreit, K. Moi, D. Nardin, T. Nikolaus, and W. Steimle. arXiv
  5. Hermitian K-theory for stable infinity-categories II: Cobordism categories and additivity. Acta Math. 235 (2025), no. 2, 149--400. Joint with B. Calmès, E. Dotto, Y. Harpaz, F. Hebestreit, K. Moi, D. Nardin, T. Nikolaus, and W. Steimle. arXiv
  6. Purity in chromatically localized algebraic K-theory. J. Amer. Math. Soc. 37 (2024) no.4, 1011--1040. Joint with A. Mathew, L. Meier, and G. Tamme. arXiv
  7. L-theory of C*-algebras. Proc. London Math. Soc. (3) 127 (2023) no. 5, 1451--1506. Joint with T. Nikolaus and M. Schlichting. arXiv
  8. Gabber rigidity in hermitian K-theory. Proceedings of the Royal Society of Edinburgh Section A: Mathematics (Ranicki memorial issue). arXiv
  9. Hermitian K-theory for stable infinity-categories I: Foundations. Selecta Mathematica, Volume 29, Issue 1 (2023). Joint with B. Calmès, E. Dotto, Y. Harpaz, F. Hebestreit, K. Moi, D. Nardin, T. Nikolaus, and W. Steimle. arXiv
  10. Reducibility of low dimensional Poincaré duality spaces. Münster J. of Math. 15 (2022) 47--81. arXiv
  11. Topological 4-manifolds with 4-dimensional fundamental group. Glasgow Math. J. 64, (2022), no. 2, 454--461. Joint with D. Kasprowski. arXiv
  12. Topologically flat embedded 2-spheres in specific simply connected 4-manifolds. 2019--20 MATRIX annals, 111-116, MATRIX Book Ser., 4, Springer, Cham, 2021. Joint with D. Kasprowski, P. Lambert-Cole and A. G. Lecuona. arXiv
  13. Connected sum decompositions of high-dimensional manifolds. 2019--20 MATRIX annals, 5-30, MATRIX Book Ser., 4, Springer, Cham, 2021. Joint with I. Bokor, D. Crowley, S. Friedl, F. Hebestreit, D. Kasprowski, and J. Nicholson. arXiv
  14. On the homotopy type of L-spectra of the integers. J. Topol. 14, (2021), no. 1, 183--214. Joint with F. Hebestreit and T. Nikolaus. arXiv The published version contains an erroneous (but for the paper irrelevant) remark in the appendix. You can find a corrected version of said remark here.
  15. A Vanishing theorem for tautological classes of aspherical manifolds. Geometry & Topology 25-1 (2021), 47--110. Joint with F. Hebestreit, W. Lück and O. Randal-Williams. arXiv
  16. On the K-theory of pullbacks. Ann. of Math. (2) 190 (2019), no. 3, 877--930. Joint with G. Tamme. arXiv
  17. On the relation between K- and L-theory of C*-algebras. Math. Ann. 371 (2018), no. 1-2, 517--563. Joint with T. Nikolaus. arXiv
  18. Localization of Cofibration categories and groupoid C*-algebras. Algebr. Geom. Topol. 17 (2017), no. 5, 3007--3020. Joint with T. Nikolaus and K. Szumiło.
  19. Stable Classification of 4-manifolds with 3-manifold fundamental group. J. Topol. 10, (2017), no. 3, 827--881. arXiv
  20. The Analytical Assembly map and Index theory. J. Noncommut. Geom. 9 (2015), no. 2, 603--619. arXiv

 

Book

  1.  Introduction to Infinity-categories. Compact Textbooks in mathematics, Birkhäuser, Cham, 2021. Springer