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 – von Kaven Foundation of the DFG
Publications
Selection
- Dotto, Emanuele, Krause, Achim, Nikolaus, Thomas, and Patchkoria, Irakli. . “Witt vectors with coefficients and characteristic polynomials over non-commutative rings.” Compositio Mathematica, № 158 (2): 366–408. doi: 10.1112/S0010437X22007254.
- Antieau, Benjamin, Mathew, Akhil, Morrow, Matthew, and Nikolaus, Thomas. . “On the Beilinson fiber square.” Duke Mathematical Journal, № 18: 3707–3806.
- Land, Markus, Nikolaus, Thomas, and Schlichting, Marco. . “L-theory of C∗-algebras.” Proceedings of the London Mathematical Society, № 127 (5): 1451–1506. doi: 10.1112/plms.12564.
- Antieau, Benjamin, and Nikolaus, Thomas. . “Cartier modules and cyclotomic spectra.” Journal of the American Mathematical Society, № 34 (1): 1–78. doi: 10.1090/jams/951.
- Barthel, Tobias, Hausmann, Markus, Naumann, Niko, Nikolaus, Thomas, Noel, Justin, and Stapleton, Nathaniel. . “The Balmer spectrum of the equivariant homotopy category of a finite abelian group.” Inventiones Mathematicae, № 216 (1): 215–240. doi: 10.1007/s00222-018-0846-5.
- Antieau, Benjamin, Mathew, Akhil, and Nikolaus, Thomas. . “On the Blumberg–Mandell Künneth theorem for TP.” Selecta Mathematica (New Series), № 24 (5): 4555–4576. doi: 10.1007/s00029-018-0427-x.
- Nikolaus, Thomas, and Scholze, Peter. . “On topological cyclic homology.” Acta Mathematica, № 221 (2): 203–409. doi: 10.4310/ACTA.2018.v221.n2.a1.
- Bunke, Ulrich, Nikolaus, Thomas, and Tamme, Georg. . “The Beilinson regulator is a map of ring spectra.” Advances in Mathematics, № 333: 41–86. doi: 10.1016/j.aim.2018.05.027.
- Gepner, David, Haugseng, Rune, and Nikolaus, Thomas. . “Lax colimits and free fibrations in ∞-categories.” Documenta Mathematica, № 22: 1225–1266. doi: 10.4171/DM/593.
- Land, Markus, and Nikolaus, Thomas. . “On the Relation between K- and L-Theory of C∗-Algebras.” Mathematische Annalen, № 317 (1-2): 517–563. doi: 10.1007/s00208-017-1617-0.
Complete List
- Harpaz Y; Nikolaus T; Saunier V. . “Trace methods for stable categories I: The linear approximation of algebraic K-theory.” arxiv.org doi: 10.48550/arXiv.2411.04743.
- Nikolaus T; Yakerson M. . “An Alternative to Spherical Witt Vectors.” arxiv.org doi: 10.48550/arXiv.2405.09606.
- Carmeli, S, Nikolaus, T, and Yuan, A. . “Maps between spherical group rings.” arxiv.org doi: 10.48550/arXiv.2405.06448.
- Krause, Achim, McCandless, Jonas, and Nikolaus, Thomas. . “Polygonic spectra and TR with coefficients.” arXiv doi: 10.48550/arXiv.2302.07686.
- Benjamin, Antieau, Achim, Krause, and Thomas, Nikolaus. . “Prismatic cohomology relative to $\delta$-rings.” arxiv.org doi: 10.48550/arXiv.2310.12770.
- Dotto, Emanuele, Krause, Achim, Nikolaus, Thomas, and Patchkoria, Irakli. . “Witt vectors with coefficients and characteristic polynomials over non-commutative rings.” Compositio Mathematica, № 158 (2): 366–408. doi: 10.1112/S0010437X22007254.
- Antieau, Benjamin, Krause, Achim, and Nikolaus, Thomas. . “On the K-theory of Z/pn.” arxiv.org doi: 10.48550/arXiv.2204.03420.
- Land, Markus, Nikolaus, Thomas, and Schlichting, Marco. . “L-theory of C∗-algebras.” arxiv.org arXiv. doi: 10.48550/ARXIV.2208.10556.
- Antieau, Benjamin, Mathew, Akhil, Morrow, Matthew, and Nikolaus, Thomas. . “On the Beilinson fiber square.” Duke Mathematical Journal, № 18: 3707–3806.
- Land, Markus, Nikolaus, Thomas, and Schlichting, Marco. . “L-theory of C∗-algebras.” Proceedings of the London Mathematical Society, № 127 (5): 1451–1506. doi: 10.1112/plms.12564.
- Antieau, Benjamin, and Nikolaus, Thomas. . “Cartier modules and cyclotomic spectra.” Journal of the American Mathematical Society, № 34 (1): 1–78. doi: 10.1090/jams/951.
- Hebestreit, F., Land, M., and Nikolaus, T. . “On the homotopy type of L-spectra of the integers.” Journal of Topology, № 14 (1): 183–214. doi: 10.1112/topo.12180.
- Barwick, Clark, Glasman, Saul, Mathew, Akhil, and Nikolaus, Thomas. . “K-theory and polynomial functors.” arxiv.org doi: 10.48550/arXiv.2102.00936.
- Hesselholt, L., and Nikolaus, T. . “Algebraic k-theory of planar cuspidal curves.” in K-Theory in Algebra, Analysis and Topology, Contemporary Mathematics, edited by Guillermo Cortinas and Charles A. Weibel. Providence, RI: American Mathematical Society. doi: 10.48550/arXiv.1903.08295.
- Nikolaus, T., and Waldorf, K. . “Higher Geometry for Non-geometric T-Duals.” Communications in Mathematical Physics, № 374 (1): 317–366. doi: 10.48550/arXiv.1804.0067.
- Calmès, B, Dotto, E, Harpaz, Y, Hebestreit, F, Land, M, Moi, K, Nardin, D, Nikolaus, T, and Steimle, W. . “Hermitian K-theory for stable ∞-categories III: Grothendieck-Witt groups of rings.” arxiv.org arXiv. doi: 10.48550/ARXIV.2009.07225.
- Calmès, B, Dotto, E, Harpaz, Y, Hebestreit, F, Land, M, Moi, K, Nardin, D, Nikolaus, T, and Steimle, W. . “Hermitian K-theory for stable ∞-categories II: Cobordism categories and additivity.” 4. edt. arXiv arXiv. doi: 10.48550/ARXIV.2009.07224.
- Calmès, B, Dotto, E, Harpaz, Y, Hebestreit, F, Land, M, Moi, K, Nardin, D, Nikolaus, T, and Steimle, W. . “Hermitian K-theory for stable ∞-categories I: Foundations.” arXiv arXiv. doi: 10.48550/ARXIV.2009.07223.
- Antieau, B, Mathew, A, Morrow, M, and Nikolaus, T. . “On the Beilinson fiber square.” arXiv arXiv. doi: 10.48550/ARXIV.2003.12541.
- Barthel, Tobias, Hausmann, Markus, Naumann, Niko, Nikolaus, Thomas, Noel, Justin, and Stapleton, Nathaniel. . “The Balmer spectrum of the equivariant homotopy category of a finite abelian group.” Inventiones Mathematicae, № 216 (1): 215–240. doi: 10.1007/s00222-018-0846-5.
- Bunke, U., and Nikolaus, T. . “Twisted differential cohomology.” Algebraic and Geometric Topology, № 19 (4): 1631–1710. doi: 10.2140/agt.2019.19.1631.
- Hesselholt, Lars, and Nikolaus, Thomas. . “Topological cyclic homology.” in Handbook of Homotopy Theory, edited by Haynes Miller. London: Chapman & Hall. doi: 10.48550/arXiv.1905.08984.
- Krause, A, and Nikolaus, T. . “Bökstedt periodicity and quotients of DVRs.” arxiv.org arXiv. doi: 10.48550/ARXIV.1907.03477.
- Antieau, Benjamin, Mathew, Akhil, and Nikolaus, Thomas. . “On the Blumberg–Mandell Künneth theorem for TP.” Selecta Mathematica (New Series), № 24 (5): 4555–4576. doi: 10.1007/s00029-018-0427-x.
- Nikolaus, Thomas, and Scholze, Peter. . “On topological cyclic homology.” Acta Mathematica, № 221 (2): 203–409. doi: 10.4310/ACTA.2018.v221.n2.a1.
- Bunke, Ulrich, Nikolaus, Thomas, and Tamme, Georg. . “The Beilinson regulator is a map of ring spectra.” Advances in Mathematics, № 333: 41–86. doi: 10.1016/j.aim.2018.05.027.
- Gepner, David, Haugseng, Rune, and Nikolaus, Thomas. . “Lax colimits and free fibrations in ∞-categories.” Documenta Mathematica, № 22: 1225–1266. doi: 10.4171/DM/593.
- Nikolaus, T, and Sagave, S. . “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.
- Bašić, M, and Nikolaus, T. . “Homology of dendroidal sets.” Homology, Homotopy and Applications, № 19 (1): 111–134. doi: 10.4310/HHA.2017.v19.n1.a6.
- Land, Markus, and Nikolaus, Thomas. . “On the Relation between K- and L-Theory of C∗-Algebras.” Mathematische Annalen, № 317 (1-2): 517–563. doi: 10.1007/s00208-017-1617-0.
- Land, M, Nikolaus, T, and Szumilo, K. . “LOCALIZATION OF COFIBRATION CATEGORIES AND GROUPOID C∗-ALGEBRAS.” Algebraic and Geometric Topology, № 17 (5): 3007–3020. doi: 10.2140/agt.2017.17.3007.
- Bunke, U, Nikolaus, T, and Völkl, M. . “Differential cohomology theories as sheaves of spectra.” Journal of Homotopy and Related Structures, № 11 (1): 1–66. doi: 10.48550/arXiv.1311.3188.
- Nikolaus, Thomas. . “Stable ∞-Operads and the multiplicative Yoneda lemma.” arXiv arXiv. doi: 10.48550/ARXIV.1608.02901.
- Gepner, D, Groth, M, and Nikolaus, T. . “Universality of multiplicative infinite loop space machines.” Algebraic and Geometric Topology, № 15 (6): 3107–3153. doi: 10.2140/agt.2015.15.3107.
- Bunke, U, and Nikolaus, T. . “T-duality via gerby geometry and reductions.” Reviews in Mathematical Physics, № 27 (5): 1550013, 46. doi: 10.1142/S0129055X15500130.
- Nikolaus, T, Schreiber, U, and Stevenson, D. . “Principal infinity-bundles - Presentations.” Journal of Homotopy and Related Structures, № 10: 565–622. doi: 10.1007/s40062-014-0077-4.
- Nikolaus, T, Schreiber, U, and Stevenson, D. . “Principal infinity-bundles - General theory.” Journal of Homotopy and Related Structures, № 10: 749–801. doi: 10.1007/s40062-014-0083-6.
- Nikolaus, T. . “Algebraic K-Theory of ∞-Operads.” Journal of K-Theory, № 14 (3): 614–641. doi: 10.1017/is014008019jkt277.
- Bašić, M, and Nikolaus, T. . “Dendroidal sets as models for connective spectra.” Journal of K-Theory, № 14 (3): 387–421. doi: 10.1017/is014005003jkt265.
- Nikolaus, T, and Waldorf, K. . “Four equivalent versions of nonabelian gerbes.” Pacific Journal of Mathematics, № 264 (2): 355–420. doi: 10.2140/pjm.2013.264.355.
- Nikolaus, T, and Waldorf, K. . “Lifting problems and transgression for non-abelian gerbes.” Advances in Mathematics, № 242: 50–79. doi: 10.1016/j.aim.2013.03.022.
- Nikolaus, T, and Schweigert, C. . “Bicategories in field theoriesan - invitation.” in Strings, gauge fields, and the geometry behind. The legacy of Maximilian Kreuzer, edited by Anton Rebhan, Ludmil Katzarkov, Johanna Knapp, Radoslav Rashkov and Emanuel Scheidegger. Singapore: World Scientific Publishing. doi: 10.1142/8561.
- Nikolaus, T, Sachse, C, and Wockel, C. . “A smooth model for the string group.” International Mathematics Research Notices, № 16 (16): 3678–3721. doi: 10.1093/imrn/rns154.
- Maier, J, Nikolaus, T, and Schweigert, C. . “Strictification of weakly equivariant Hopf algebras.” Bulletin of the Belgian Mathematical Society - Simon Stevin, № 20 (2): 269–285. doi: 10.48550/arXiv.1109.0236.
- Maier, J, Nikolaus, T, and Schweigert, C. . “Equivariant Modular Categories via Dijkgraaf-Witten Theory.” Advances in Theoretical and Mathematical Physics, № 16 (1): 289–358. doi: 10.48550/arXiv.1103.2963.
- Nikolaus, T, and Schweigert, C. . “Equivariance in higher geometry.” Advances in Mathematics, № 226 (4): 3367–3408. doi: 10.1016/j.aim.2010.10.016.
- Nikolaus, T. . “Algebraic models for higher categories.” Indagationes Mathematicae, № 21 (1-2): 52–75. doi: 10.1016/j.indag.2010.12.004.
- Nikolaus, Thomas. . “Higher Categorical Structures in Geometry - General Theory and Applications to Quantum Field Theory.” Dissertation thesis, Universität Hamburg.
- Nikolaus, Thomas. . Äquivariante Gerben und Abstieg (Diplomarbeit),
- Fuchs, J, Nikolaus, T, Schweigert, C, and Waldorf, K. . “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/?.