Carl Mautner

I am an assistant professor at the University of California, Riverside.

I completed my Ph.D. in mathematics in May 2010 at UT Austin studying with David Ben-Zvi.


Current Teaching:

Spring 2016, Fields and Galois theory Math 201C.


I work with geometric methods in representation theory. More specifically, I am studying `modular' perverse sheaves - perverse sheaves on complex algebraic varieties with coefficients in a field of positive characteristic - and connections with the modular representation theory of groups and algebras from Lie theory.


Affine pavings and the enhanced nilpotent cone, submitted.

Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture, submitted.
(joint with S. Riche)

On the exotic t-structure in positive characteristic, to appear in International Mathematics Research Notices.
(joint with S. Riche)

Parity sheaves and tilting modules, to appear in Annales Scientifiques de l'Ecole Normale Supérieure.
(joint with D. Juteau and G. Williamson)

A geometric Schur functor, Selecta Math. (N.S.) 20 (2014), no. 4, 961-977. DOI: 10.1007/s00029-014-0147-9.

Sheaves on nilpotent cones, Fourier transform, and a geometric Ringel duality, to appear in Moscow Mathematical Journal.
(joint with P. Achar)

Parity Sheaves, J. Amer. Math. Soc. 27 (4), 1169-1212 (2014).
(joint with D. Juteau and G. Williamson)

Perverse sheaves and modular representation theory, Séminaires et Congrès 24-II (2012), 313-350.
(joint with D. Juteau and G. Williamson)

Past Teaching:

Winter 2016, Linear Algebra II Math 132.

Spring 2015, Modern Algebra Math 172.

Winter 2015, Linear Algebra II Math 132.

I have also taught courses on toric varieties (Spring 2013) and perverse sheaves (Fall 2011).

Some past activities:

I helped organize a workshop on Lie theory and representation theory here at UCR in February 2015.

In August 2010, Joel Kamnitzer and I organized a workshop on Ngo's proof of the Fundamental Lemma.

In Fall 2008 and Spring 2009, I co-organized a reading seminar on papers in algebra and geometry.

In Fall 2007, I organized a learning seminar on etale cohomology and the Weil conjectures.

Alex Kahle and I organized a graduate student workshop on knot theory and representations in January 2007.