I am an assistant professor at the University of California, Riverside. At the moment I am on leave from Riverside and visiting Dartmouth College.
I completed my Ph.D. in mathematics in May 2010 at UT Austin studying with David Ben-Zvi.
Peter Samuelson and I are organizing a mini-conference at UCR in December (2019).
Research:
I study symmetry in algebra and geometry. More specifically, my research is in geometric representation theory, a field that lies at the crossroads of algebra, topology, algebraic geometry and combinatorics. Much of my work so far has been motivated by problems in modular representation theory, meaning representation theory over fields of positive characteristic.
Papers:
(joint with T. Braden) Ringel duality for perverse sheaves on hypertoric varieties.
Advances in Mathematics, 344 (2019), 35-98.
(joint with T. Braden) Matroidal Schur algebras.
J. Algebraic Combin., 46 (2017), no. 1, 51-75.
Affine pavings and the enhanced nilpotent cone.
Proc. Amer. Math. Soc., 145 (2017), no. 4, 1393-1398.
(joint with S. Riche) Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture.
J. Eur. Math. Soc., 20 (2018), no. 9, 2259-2332.
(joint with S. Riche) On the exotic t-structure in positive characteristic
Int. Math. Res. Not. 2016, no. 18, 5727-5774.
(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.
Some past activities:
In October 2018, I was an organizer of the first annual Riverside Mathematics Workshop for Excellence and Diversity
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.
Past Teaching:
Spring 2019, Linear Algebra I, Math 131.
Spring 2019, Representation Theory of Finite Groups, Math 260 021.
Winter 2019, Algebraic Analysis, Math 226.
Fall 2018, Linear Algebra I, Math 131.
Spring 2018, Algebraic Topology II, Math 246B.
Winter 2018, Algebraic Topology I, Math 246A.
Fall 2017, First-Year Calculus, Math 9A.
Winter 2017, Topology II, Math 205B.
Winter 2017, Algebraic Geometry I, Math 243A.
Fall 2016, First-Year Calculus, Math 9A.
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).