## 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.

CV

**Current Teaching:**

** **

**
**
Spring 2016, Fields and Galois theory Math 201C.

**Research:**

** **

**
**
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.

**Papers:**

** **

**
**
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.