Research Interests

Research Interests

$\bullet$ Homotopy theory and Higher Algebra.
$\bullet$ Algebraic $K$-theory.
$\bullet$ Field theories and mathematical Physics.
$\bullet$ (topological) Hochschild homology and non-commutative geometry.

Selected Publications

Selected Publications of Thomas Nikolaus

$\bullet$ T. Nikolaus and S. Sagave. Presentably symmetric monoidal $\infty$-categories are represented by symmetric monoidal model categories. Algebr. Geom. Topol., 17(5):3189–3212, 2017.

$\bullet$ D. Gepner, R. Haugseng, and T. Nikolaus. Lax colimits and free fibrations in $\infty$-categories. Doc. Math., 22:1225–1266, 2017.

$\bullet$ U. Bunke, T. Nikolaus, and M. Völkl. Differential cohomology theories as sheaves of spectra. J. Homotopy Relat. Struct., 11(1):1–66, 2016.

$\bullet$ D. Gepner, M. Groth, and T. Nikolaus. Universality of multiplicative infinite loop space machines. Algebr. Geom. Topol., 15(6):3107–3153, 2015.

$\bullet$ U. Bunke and T. Nikolaus. $T$-duality via gerby geometry and reductions. Rev. Math. Phys., 27(5):1550013, 46 pp., 2015.

$\bullet$ T. Nikolaus. Algebraic K-theory of $\infty$-operads. J. K-Theory, 14(3):614–641, 2014.

$\bullet$ T. Nikolaus and K. Waldorf. Lifting problems and transgression for non-abelian gerbes. Adv. Math., 242:50–79, 2013.

$\bullet$ T. Nikolaus, C. Sachse, and C. Wockel. A smooth model for the string group. Int. Math. Res. Not. IMRN, (16):3678–3721, 2013.

$\bullet$ T. Nikolaus and C. Schweigert. Equivariance in higher geometry. Adv. Math., 226(4):3367–3408, 2011.

$\bullet$ T. Nikolaus. Algebraic models for higher categories. Indag. Math. (N.S.), 21(1-2):52–75, 2011.

Current Publications

$\bullet $ E. Dotto, A. Krause, T. Nikolaus, and I. Patchkoria. Witt vectors with coefficients and characteristic polynomials over non-commutative rings. arXiv e-prints, February 2020. arXiv:2002.01538v1.

$\bullet $ A. Krause and T. Nikolaus. Bökstedt periodicity and quotients of DVRs. arXiv e-prints, July 2019. arXiv:1907.03477.

$\bullet $ T. Barthel, M. Hausmann, N. Naumann, T. Nikolaus, J. Noel, and N. Stapleton. The Balmer spectrum of the equivariant homotopy category of a finite abelian group. Inventiones Mathematicae, 216(1):215–240, April 2019. URL: https://ui.adsabs.harvard.edu/abs/2019InMat.216..215B, doi:10.1007/s00222-018-0846-5.

$\bullet $ L. Hesselholt and T. Nikolaus. Algebraic $ K $-theory of planar cuspical curves. arXiv e-prints, March 2019. arXiv:1903.08295.

$\bullet $ B. Antieau and T. Nikolaus. Cartier modules and cyclotomic spectra. arXiv e-prints, September 2018. URL: https://ui.adsabs.harvard.edu/abs/2018arXiv180901714A, arXiv:1809.01714.