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)
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)
In 2016, I organized and attended a reading course on quantum cohomology supervised by Davesh Maulik. A list of references is available here.
In 2012-2013, I ran a learning seminar for graduate students on interacting particle systems. A list of references and talks is available here.