Welcome to the
homepage of David Gepner
Department of Mathematics
West Lafayette, IN 47907
Phone: (765) 494-1956
Fax: (765) 494-0548
Homotopy theory, algebraic
K-theory, derived algebraic geometry, higher category theory
Office: MATH 740
Office Hours: Tuesday 4:30-5:30, Wednesday 2:00-3:00, Thursday
12:30-1:30, and by appointment
Fall 2015: MATH 35100, Linear Algebra
(Practice Exams: 1a, solutions, 1b; 2a,
2b, solutions; 3a, solutions, 3b)
Fall 2015: MATH 69700, Homotopy Theory
Publications and preprints
cohomology and homotopy topoi, Ph.D. thesis, 2006.
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),
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,
Uniqueness of the multiplicative cyclotomic trace, with A.
Blumberg and G. Tabuada. Advances in Mathematics 260 (2014),
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,
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.
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
Univalence in locally cartesian closed infinity-categories, with
J. Kock. Preprint, 2012, submitted for publication.
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
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
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.