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Forschungsschwerpunkte
- Topologie
- Homotopietheorie
- Arithmetik
- Höhere Kategorientheorie
Vita
Akademische Ausbildung
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- Promotion in Mathematik an der Uni Hamburg, Betreuer Prof. Dr. Christoph Schweigert Titel der Promotion: Higher Categorical Structures in Geometry - General Theory and Applications to Quantum Field Theory
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- Studium der Mathematik (Nebenfächer Informatik und Physik) an der Universität Hamburg
Beruflicher Werdegang
- seit
- Professor an der Universität Münster
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- Nachwuchsgruppenleiter (W2) am Max-Planck-Institut Bonn
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- Vertretungsprofessur an der Universität Bonn
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- Akademischer Rat auf Zeit an der Universität Regensburg
Publikationen
- . . Polygonic spectra and TR with coefficients arXiv. doi: 10.48550/arXiv.2302.07686.
- . ‘Witt vectors with coefficients and characteristic polynomials over non-commutative rings.’ Compositio Mathematica 158, Nr. 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, Nr. 1: 1–78. doi: 10.1090/jams/951.
- . ‘On the homotopy type of L-spectra of the integers.’ Journal of Topology 14, Nr. 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, Rhode Island: American Mathematical Society. doi: 10.48550/arXiv.1903.08295.
- . ‘Higher Geometry for Non-geometric T-Duals.’ Communications in Mathematical Physics 374, Nr. 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. : 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, Nr. 1: 215–240. doi: 10.48550/arXiv.1709.04828.
- . ‘Twisted differential cohomology.’ Algebraic and Geometric Topology 19, Nr. 4: 1631–1710. doi: 10.2140/agt.2019.19.1631.
- . . ‘Topological cyclic homology.’ In Handbook of Homotopy Theory, edited by , 619–656. Boca Raton: 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, Nr. 5: 4555–4576. doi: 10.1007/s00029-018-0427-x.
- . ‘On topological cyclic homology.’ Acta Mathematica 221, Nr. 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, Nr. 5: 3189–3212. doi: 10.2140/agt.2017.17.3189.
- . . ‘Homology of dendroidal sets.’ Homology, Homotopy and Applications 19, Nr. 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, Nr. 5: 3007–3020. doi: 10.2140/agt.2017.17.3007.
- . . ‘Differential cohomology theories as sheaves of spectra.’ Journal of Homotopy and Related Structures 11, Nr. 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, Nr. 6: 3107–3153. doi: 10.2140/agt.2015.15.3107.
- . . ‘T-duality via gerby geometry and reductions.’ Reviews in Mathematical Physics 27, Nr. 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, Nr. 3: 614–641. doi: 10.1017/is014008019jkt277.
- . . ‘Dendroidal sets as models for connective spectra.’ Journal of K-Theory 14, Nr. 3: 387–421. doi: 10.1017/is014005003jkt265.
- . . ‘Four equivalent versions of nonabelian gerbes.’ Pacific Journal of Mathematics 264, Nr. 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. Singapur: World Scientific Publishing. doi: 10.1142/8561.
- . . ‘A smooth model for the string group.’ International Mathematics Research Notices 16, Nr. 16: 3678–3721. doi: 10.1093/imrn/rns154.
- . . ‘Strictification of weakly equivariant Hopf algebras.’ Bulletin of the Belgian Mathematical Society - Simon Stevin 20, Nr. 2: 269–285. doi: 10.48550/arXiv.1109.0236.
- . . ‘Equivariant Modular Categories via Dijkgraaf-Witten Theory.’ Advances in Theoretical and Mathematical Physics 16, Nr. 1: 289–358. doi: 10.48550/arXiv.1103.2963.
- . . ‘Equivariance in higher geometry.’ Advances in Mathematics 226, Nr. 4: 3367–3408. doi: 10.1016/j.aim.2010.10.016.
- . . ‘Algebraic models for higher categories.’ Indagationes Mathematicae 21, Nr. 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 Dissertationsschrift, Universität Hamburg. Hamburg.
- . . Bundle gerbes and surface holonomy Hamburger Beiträge zur Mathematik, Nr. 323. Hamburg: EMS Publishing House, . doi: 10.48550/arXiv.0901.2085.
Promotionen
McCandless, Jonas TR and its relation to algebraic K-theory Ariotta, Stefano Coherent cochain complexes and Beilinson t-structures Vortrag
- Nikolaus, Thomas (): ‘Frobenius homomorphisms in higher algebra’. International Congress of Mathematics 2022, Virtual event, .