I work primarily in representation theory, with a bias for topological and geometric methods.
- On Euler-Poincare characteristics,
Comptes Rendus 353, Issue 5 (2015), 449-453.
- Some geometric facets of the Langlands correspondence for real groups,
Bull. LMS 47 (2) (2015), 225-232.
- A remark on braid group actions on coherent sheaves,
Osaka J. of Math. 51 (2014), 719-728.
- Affine and degenerate affine BMW algebras: actions on tensor space,
with Z. Daugherty and A. Ram, Selecta Math. 19 (2013), 611-653.
- Affine and degenerate affine BMW algebras: the center,
with Z. Daugherty and A. Ram, Osaka J. of Math. 51 (2014), 257-283.
- Derived equivalences and sl2 categorifications for Uq(gln),
J. of Algebra 346 (2011), 82-100.
(not intended for `official' publication)
The Hodge conjecture is trivial in equivariant geometry
Some silliness related to the preprint `Chow groups and equivariant geometry'.
Basic observation: alternate proof
Sheaf theoretic Kunneth
Summands of Bott-Samelson motives
Cohomology of homogeneous varieties is Tate
Equivariant nearby cycles [unstable]
Misc. discussion around smooth base change and induction equivalence
Discussion around smooth morphisms and the equivariant derived category
This is related to the equivariant part of `On Euler-Poincare characteristics' above.
Discussion around the cohomology of the complement of a normal crossings divisor
Notes on motivic models for category O
Some geometric facets of the Langlands correspondence for real groups
This is an ugly version of its namesake above. The primary difference is that appropriate changes (technical and linguistic) are made so that the arguments work both in the setting of mixed Hodge modules and mixed l-adic sheaves. There are some interesting questions (related to `Frobenius semisimplicity') that arise in the l-adic setting. There is no discussion of convolution, the Hecke algebra, or formality in this version.
Projective functors and free pro-unipotent sheaves
Computing extensions between sheaves (a la Beilinson-Ginzburg-Soergel)
Notes from conferences/workshops
Notes from various talks
- Rook placements and Jordan forms (Martha at CU-Boulder, 2013)
- Satake isomorphisms and affine Beilinson-Bernstein localization (Masoud at Freiburg, 2012)
- F to C ala [BBD] (Soergel at Freiburg, 2012)
- Cotangent complexes of moduli spaces and symplectic structures (Z. Zhang at Freiburg, 2012)
- Geometric Langlands for GL_1 (Oliver at Freiburg, 2012)
- Geometric Langlands and Physics (E. Scheidegger at Freiburg, 2012)
- Generic vanishing fails for singular varieties in characteristic p (S. Kovacs at CSU, 2012)
- Kazhdan-Lusztig cells and Calegoro-Moser space (Rouquier at UC-Riverside, 2012)
- Geometric realizations of quantum groups (Yiqiang Li at NCSU, 2012)
- The Hodge theorem as a derived self intersection (Andrei at Buchweitz's birthday conference, 2012)
- Index theory for elliptic operators (E. Van Erp at CU-Boulder, 2012)
- Tensor triangulated geometry (P. Balmer at ANU, 2009)
Notes for/from courses
Some notes that I wrote as a student (graduate and undergraduate) can be found here.
Last updated: 09 August, 2015