## 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:**

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Fall 2016, First-Year Calculus Math 9A.

**Research:**

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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:**

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(joint with T. Braden) Matroidal Schur algebras.

Submitted.
Affine pavings and the enhanced nilpotent cone.

*Proc. Amer. Math. Soc.* (to appear)
(joint with S. Riche) Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture.

*J. Eur. Math. Soc.* (to appear)
(joint with S. Riche) On the exotic t-structure in positive characteristic

*Int. Math. Res. Not.* (to appear)
(joint with D. Juteau and G. Williamson) Parity sheaves and tilting modules,

*Ann. Sci. Éc. Norm. Supér.* (4) 49 (2016), no. 2, 257-275.
A geometric Schur functor,

*Selecta Math. (N.S.)* 20 (2014), no. 4, 961-977. DOI: 10.1007/s00029-014-0147-9.
(joint with P. Achar) Sheaves on nilpotent cones, Fourier transform, and a geometric Ringel duality.

*Mosc. Math. J.* 15 (2015), no. 3, 407-423, 604.
(joint with D. Juteau and G. Williamson) 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.

**Past Teaching:**

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Spring 2016, Fields and Galois theory Math 201C.

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:**

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In March 2016, Pramod Achar and I organized an workshop on Sheaves and Modular Representations of Reductive Groups at the American Institute of Mathematics.

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.