Department of Mathematics

Purdue University

West Lafayette, IN 47907

USA

Fax: (765) 494-0548

Email: dgepner@purdue.edu

Url: http://www.math.purdue.edu/~dgepner

Homotopy theory, algebraic
K-theory, derived algebraic geometry, higher category theory

Office Hours: Tuesday 4:30-5:30, Wednesday 2:00-3:00, Thursday 12:30-1:30, and by appointment

Fall 2015: MATH 69700, Homotopy Theory

Homotopy theory of orbispaces, with A. Henriques, 2007.

On the motivic spectra representing algebraic cobordism and algebraic K-theory, with V. Snaith. Documenta Mathematica, Vol. 14 (2009), 359-396.

An infinity-categorical approach to R-line bundles, R-module Thom spectra, and twisted R-homology, with M. Ando, A. Blumberg, M.J. Hopkins and C. Rezk, 2009. Journal of Topology (2013).

Units of ring spectra, Thom spectra, and orientations via rigid infinite loop space theory, with M. Ando, A. Blumberg, M.J. Hopkins and C. Rezk, 2009. Journal of Topology (2014).

A universal characterization of higher algebraic K-theory, with A. Blumberg and G. Tabuada. Geometry and Topology 17 (2013), 733-838.

Twists of K-theory and TMF, with M. Ando and A. Blumberg, in ``Superstrings, Geometry, Topology, and C*-algebras'', Proceedings of Symposia in Pure Mathematics, Vol. 81, AMS, Providence, 2010.

Uniqueness of the multiplicative cyclotomic trace, with A. Blumberg and G. Tabuada. Advances in Mathematics 260 (2014), 191-232.

Actions of Eilenberg-MacLane spaces on K-theory spectra and uniquess of twisted K-theory, with B. Antieau and J. G\'omez. Trans. Amer. Math. Soc. 366 (2014), no. 7, 3631-3648.

Brauer groups and etale cohomology in derived algebraic geometry, with B. Antieau. Geometry and Topology 18 (2014), no. 2, 1149-1244.

K-theory of endomorphisms via noncommutative motives, with A. Blumberg and G. Tabuada. To appear in Trans. Amer. Math. Soc.

Universality of multiplicative infinite loop space machines, with M. Groth and T. Nikolaus, submitted for publication.

Parametrized spectra, multiplicative Thom spectra, and the twisted umkehr map, with M. Ando and A. Blumberg, submitted for publication.

Univalence in locally cartesian closed infinity-categories, with J. Kock. Preprint, 2012, submitted for publication.

Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory, with U. Bunke. Preprint, 2013, submitted for publication.

Enriched infinity-categories via nonsymmetric infinity-operads, with R. Haugseng. Preprint, 2014. Advances in Mathematics 279 (2015) 575-671

Lax colimits and free fibrations in infinity-categories, with R. Haugseng and T. Nikolaus, submitted for publication.

Comparison of rational circle-equivariant elliptic cohomology theories, with J. Greenlees, in preparation.

Polynomial functors and homotopical species, with J. Kock, in preparation.

Galois cohomology of commutative ring spectra and obstruction theory spectral sequences, with Tyler Lawson, in preparation.

Integral representation theorems for deformation quantization modules, with F. Petit, in preparation.