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
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)