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.