I work primarily in representation theory, with a bias towards topological and geometric methods.

I am not associated with any institution (a euphemism for unemployed).

**Preprints**

- Chow groups and equivariant geometry,

very preliminary and unstable; standard health warnings apply. - Tate classes, equivariant geometry and purity of fibres

**Publications**

- On Euler-Poincare characteristics,

Comptes Rendus**353**, Issue 5 (2015), 449-453. - Some geometric facets of the Langlands correspondence for real groups,

Bull. London Math. Soc.**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.

**Miscellaneous articles**

- Graded tensoring and crystals
- On Hall-Littlewood polynomials
- On the geometric Hecke algebra,

Enveloping Algebras and Geometric Representation theory, Oberwolfach Reports**9**, Issue 1 (2012). - A note on Hecke patterns in Category O
- A remark on some bases in the Hecke algebra
- Derived equivalences and category O,

PhD thesis, UW-Madison, 2011.

**Incomplete/scratch work**

- 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 the preprint `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**

- Proudfoot Talbot (Oregon, 2012)
- Geometric Langlands (Freiburg, 2012)
- Enveloping algebras and geometric representation theory (Oberwolfach, 2012)
- Algebraic Lie theory (Newton Institute, 2009)

**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: 26 July, 2015*