Research Foci
Topology
Ich interessiere mich für Topology vom Standpunkt der Homotopietheorie aus, also das Studium von geometrischen Objekten bis auf stetige Deformation.Die Homotopietheorie ist eng verwand mit der Höheren Kategorientheorie (insbesondere unendlich-Kategorien). Eines der Hauptgebiete in denen ich in den letzten Jahren gearbeitet habe ist die höhere Algebra, also das Studium von Ringspektren und Spektren mittels algebraischer und arithmetischer Techniken.
Homotopy Theory
Arithmetic
Higher Categories
CV
Academic Education
- PhD in Mathematics at the University of Hamburg, supervisor Prof. Dr. Christoph Schweigert Title of thesis: Higher Categorical Structures in Geometry - General Theory and Applications to Quantum Field Theory
- Study of mathematics ( secondary subjects: computer science and physics) at the University of Hamburg
Positions
- Professor at the University of Münster
- Head of junior research group at the May-Planck-Institute in Bonn
- Deputy professorship at the University of Bonn
- Assistant professor at the University of Regensburg
Honors
- von Kaven Award in the category Mathematik – von Kaven Foundation of the DFG
Publications
- . Trace methods for stable categories I: The linear approximation of algebraic K-theory arxiv.org. doi: 10.48550/arXiv.2411.04743. [submitted / under review]
- . An Alternative to Spherical Witt Vectors arxiv.org. doi: 10.48550/arXiv.2405.09606. [submitted / under review]
- . Maps between spherical group rings arxiv.org. doi: 10.48550/arXiv.2405.06448. [submitted / under review]
- . Polygonic spectra and TR with coefficients arXiv. doi: 10.48550/arXiv.2302.07686.
- . Prismatic cohomology relative to $\delta$-rings arxiv.org. doi: 10.48550/arXiv.2310.12770.
- . ‘Witt vectors with coefficients and characteristic polynomials over non-commutative rings.’ Compositio Mathematica 158, № 2: 366–408. doi: 10.1112/S0010437X22007254.
- . On the K-theory of Z/pn arxiv.org. doi: 10.48550/arXiv.2204.03420.
- . L-theory of C∗-algebras arxiv.org. : arXiv. doi: 10.48550/ARXIV.2208.10556.
- . ‘Cartier modules and cyclotomic spectra.’ Journal of the American Mathematical Society 34, № 1: 1–78. doi: 10.1090/jams/951.
- . ‘On the homotopy type of L-spectra of the integers.’ Journal of Topology 14, № 1: 183–214. doi: 10.1112/topo.12180.
- . K-theory and polynomial functors arxiv.org. doi: 10.48550/arXiv.2102.00936.
- . ‘Algebraic k-theory of planar cuspidal curves.’ In K-Theory in Algebra, Analysis and Topology, edited by , 139–148. Providence, RI: American Mathematical Society. doi: 10.48550/arXiv.1903.08295.
- . ‘Higher Geometry for Non-geometric T-Duals.’ Communications in Mathematical Physics 374, № 1: 317–366. doi: 10.48550/arXiv.1804.0067.
- . Hermitian K-theory for stable ∞-categories III: Grothendieck-Witt groups of rings arxiv.org. : arXiv. doi: 10.48550/ARXIV.2009.07225.
- . Hermitian K-theory for stable ∞-categories II: Cobordism categories and additivity arXiv. 4th Ed. : arXiv. doi: 10.48550/ARXIV.2009.07224.
- . Hermitian K-theory for stable ∞-categories I: Foundations arXiv. : arXiv. doi: 10.48550/ARXIV.2009.07223.
- . On the Beilinson fiber square arXiv. : arXiv. doi: 10.48550/ARXIV.2003.12541.
- . ‘The Balmer spectrum of the equivariant homotopy category of a finite abelian group.’ Inventiones Mathematicae 216, № 1: 215–240. doi: 10.48550/arXiv.1709.04828.
- . ‘Twisted differential cohomology.’ Algebraic and Geometric Topology 19, № 4: 1631–1710. doi: 10.2140/agt.2019.19.1631.
- . . ‘Topological cyclic homology.’ In Handbook of Homotopy Theory, edited by , 619–656. London: Chapman & Hall. doi: 10.48550/arXiv.1905.08984.
- . Bökstedt periodicity and quotients of DVRs arxiv.org. : arXiv. doi: 10.48550/ARXIV.1907.03477.
- . ‘On the Blumberg–Mandell Künneth theorem for TP.’ Selecta Mathematica (New Series) 24, № 5: 4555–4576. doi: 10.1007/s00029-018-0427-x.
- . ‘On topological cyclic homology.’ Acta Mathematica 221, № 2: 203–409. doi: 10.4310/ACTA.2018.v221.n2.a1.
- . ‘The Beilinson regulator is a map of ring spectra.’ Advances in Mathematics 333: 41–86. doi: 10.1016/j.aim.2018.05.027.
- . . ‘Lax colimits and free fibrations in ∞-categories.’ Documenta Mathematica 22: 1225–1266. doi: 10.48550/arXiv.1501.02161.
- . . ‘Presentably symmetric monoidal infinity-categories are represented by symmetric monoidal model categories.’ Algebraic and Geometric Topology 17, № 5: 3189–3212. doi: 10.2140/agt.2017.17.3189.
- . . ‘Homology of dendroidal sets.’ Homology, Homotopy and Applications 19, № 1: 111–134. doi: 10.4310/HHA.2017.v19.n1.a6.
- . . ‘On the Relation between K- and L-Theory of C∗-Algebras.’ Mathematische Annalen 317: 517–563. doi: 10.1007/s00208-017-1617-0.
- . . ‘LOCALIZATION OF COFIBRATION CATEGORIES AND GROUPOID C∗-ALGEBRAS.’ Algebraic and Geometric Topology 17, № 5: 3007–3020. doi: 10.2140/agt.2017.17.3007.
- . . ‘Differential cohomology theories as sheaves of spectra.’ Journal of Homotopy and Related Structures 11, № 1: 1–66. doi: 10.48550/arXiv.1311.3188.
- . Stable ∞-Operads and the multiplicative Yoneda lemma arXiv. : arXiv. doi: 10.48550/ARXIV.1608.02901.
- . . ‘Universality of multiplicative infinite loop space machines.’ Algebraic and Geometric Topology 15, № 6: 3107–3153. doi: 10.2140/agt.2015.15.3107.
- . . ‘T-duality via gerby geometry and reductions.’ Reviews in Mathematical Physics 27, № 5: 1550013, 46. doi: 10.1142/S0129055X15500130.
- . . ‘Principal infinity-bundles - Presentations.’ Journal of Homotopy and Related Structures 10: 565–622. doi: 10.1007/s40062-014-0077-4.
- . . ‘Principal infinity-bundles - General theory.’ Journal of Homotopy and Related Structures 10: 749–801. doi: 10.1007/s40062-014-0083-6.
- . . ‘Algebraic K-Theory of ∞-Operads.’ Journal of K-Theory 14, № 3: 614–641. doi: 10.1017/is014008019jkt277.
- . . ‘Dendroidal sets as models for connective spectra.’ Journal of K-Theory 14, № 3: 387–421. doi: 10.1017/is014005003jkt265.
- . . ‘Four equivalent versions of nonabelian gerbes.’ Pacific Journal of Mathematics 264, № 2: 355–420. doi: 10.2140/pjm.2013.264.355.
- . . ‘Lifting problems and transgression for non-abelian gerbes.’ Advances in Mathematics 242: 50–79. doi: 10.1016/j.aim.2013.03.022.
- . . ‘Bicategories in field theoriesan - invitation.’ In Strings, gauge fields, and the geometry behind. The legacy of Maximilian Kreuzer, edited by , 119–132. Singapore: World Scientific Publishing. doi: 10.1142/8561.
- . . ‘A smooth model for the string group.’ International Mathematics Research Notices 16, № 16: 3678–3721. doi: 10.1093/imrn/rns154.
- . . ‘Strictification of weakly equivariant Hopf algebras.’ Bulletin of the Belgian Mathematical Society - Simon Stevin 20, № 2: 269–285. doi: 10.48550/arXiv.1109.0236.
- . . ‘Equivariant Modular Categories via Dijkgraaf-Witten Theory.’ Advances in Theoretical and Mathematical Physics 16, № 1: 289–358. doi: 10.48550/arXiv.1103.2963.
- . . ‘Equivariance in higher geometry.’ Advances in Mathematics 226, № 4: 3367–3408. doi: 10.1016/j.aim.2010.10.016.
- . . ‘Algebraic models for higher categories.’ Indagationes Mathematicae 21, № 1-2: 52–75. doi: 10.1016/j.indag.2010.12.004.
- . . Higher Categorical Structures in Geometry - General Theory and Applications to Quantum Field Theory Dissertation thesis, Universität Hamburg. Hamburg.
- . . Bundle gerbes and surface holonomy Hamburger Beiträge zur Mathematik, № 323. Zürich / Berlin: EMS Press, . doi: 10.48550/arXiv.0901.2085.
Supervised Doctoral Studies
Mc Candless, Jonas Bastian Vedersø TR and its relation to algebraic K-theory Ariotta, Stefano Coherent cochain complexes and Beilinson t-structures Scientific Talk
- Nikolaus, Thomas : “Frobenius homomorphisms in higher algebra”. International Congress of Mathematics 2022, Virtual event, .DOI: 10.4171/ICM2022/?.