**Homepage of Dr. David Gepner**

Dr. David Gepner

D-93040 Regensburg

Germany

Office: 206

Phone: +49-(0)941-943-2761

Email:
david(dot)gepner(at)mathematik(dot)uni-regensburg(dot)de

Homotopy theory (in all its guises: stable, parametrized, motivic, equivariant, etc.) and interactions with algebraic K-theory and algebraic geometry

Winter semester 2012/2013: Algebraic K-theory of
schemes.

Summer semester 2012: Algebraic K-theory of spaces.

Summer semester 2011: Introduction to stable homotopy theory

Winter semester 2010: Twisted cohomology (joint with Ulrich Bunke), Topology I (exercises)

(with M. Ando and A.J. Blumberg) Equivariant units and orientations. In progress.

(with T. Lawson) Brauer groups and Galois cohomology of commutative S-algebras. In progress.

(with J. Kock) Polynomial functors and homotopical
species. In progress.

(with U. Bunke) Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory. 2011. In progress.

(with J. Greenlees) Comparison of rational circle-equivariant elliptic cohomology theories. 2011. In progress.

(with Rune Haugseng) Enriched
infinity categories. 2012.

(with B. Antieau) Brauer groups and étale
cohomology in derived algebraic geometry. 2012. Submitted.

(with J. Kock) Univalence
in locally cartesian closed infinity-categories. 2012.
Submitted.

(with M. Ando and A.J. Blumberg) Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map. 2011. Submitted.

(with B. Antieau and J. Gómez) Actions of Eilenberg-MacLane spaces on K-theory spectra and uniqueness of twisted K-theory. 2011. To appear in Transactions of the American Mathematical Society.

(with A.J. Blumberg and G. Tabuada) Uniqueness of the multiplicative cyclotomic trace. 2011. Submitted.

(with M. Ando and A.J. Blumberg) Twists of
K-theory and TMF. *Superstrings, geometry,
topology, and C*-algebras*, 27-63, Proc. Sympos. Pure Math.,
81. 2010.

(with A.J. Blumberg and G. Tabuada) A universal characterization of higher algebraic K-theory. 2010. To appear in Geometry and Topology.

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

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

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

(with A. Henriques) Homotopy theory of orbispaces. 2007. Submitted.

Equivariant elliptic cohomology and homotopy topoi.
Ph.D. Thesis, 2006. Available upon request.