## expository articles

Longer expository writings. None of the material presented is original.

**Perverse sheaves and the Kazhdan-Lusztig conjectures**, 2011. (pdf)

We sketch a proof of the Kazhdan-Lusztig conjectures via perverse
sheaves and intersection cohomology on Schubert varieties. Written
for a course on perverse sheaves taught by Carl Mautner at Harvard in Fall 2011.

**D-modules and representation theory**, Part III Essay, University of
Cambridge, 2011. (pdf)

We give an introduction to the theory of algebraic
D-modules. As an application, we prove the Beilinson-Bernstein
correspondence. Advisor: Ian Grojnowski

**Frobenius splitting for Schubert varieties**, Senior Thesis, Harvard University, 2010. (pdf)

We introduce the theory of Frobenius
splitting and apply it to show that Schubert and Bott-Samelson
varieties are Frobenius split. As applications, we show that Schubert
varieties are normal, Cohen-Macaulay, and have rational resolutions
and obtain a geometric proof of the Demazure character
formula. Advisor: Dennis Gaitsgory

## seminar notes

Short notes for talks at learning seminars. These have not
been carefully proofread.

**Introduction to rational Cherednik algebras**, Spring 2015. (pdf)

**Schur-Weyl duality for quantum groups**, Fall 2014. (pdf)

**The trigonometric Casimir connection**, Spring 2014. (pdf)

**Quantum Hamiltonian reduction**, Spring
2014. (pdf 1) (pdf 2)

**Grothendieck's simultaneous resolution and the Springer correspondence**, Fall
2013. (pdf 1)
(pdf 2)
(pdf 3)

## learning seminar

In 2012-2013, I ran a learning seminar for graduate students on interacting particle
systems. A list of references and talks is available

here.