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<!DOCTYPE html>
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<li><a href="research.html">research</a></li>
<li><a href="notes.html">exposition</a></li>
<li><a href="teaching.html">teaching</a></li>
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<h2>expository articles</h2>
<p>
Longer expository writings. None of the material presented is original.
</p>
<p><b>Perverse sheaves and the Kazhdan-Lusztig conjectures</b>, 2011. (<a href="notes/klconj.pdf">pdf</a>)
<span class="abs-non"><br/>
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.
</span></p>
<p><b>D-modules and representation theory</b>, Part III Essay, University of
Cambridge, 2011. (<a href="notes/dmod.pdf">pdf</a>)
<span class="abs-non"><br/>
We give an introduction to the theory of algebraic
D-modules. As an application, we prove the Beilinson-Bernstein
correspondence. Advisor: Ian Grojnowski
</span></p>
<p><b>Frobenius splitting for Schubert varieties</b>, Senior Thesis, Harvard University, 2010. (<a href="notes/frobsplit.pdf">pdf</a>)
<span class="abs-non"><br/>
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
</span></p>
<h2>seminar notes</h2>
<p>
Short notes for talks at learning seminars. These have not
been carefully proofread.
</p>
<p><b>Introduction to rational Cherednik algebras</b>, Spring 2015. (<a href="notes/rca.pdf">pdf</a>)
<span class="abs-non"><br/>
</span></p>
<p><b>Schur-Weyl duality for quantum groups</b>, Fall 2014. (<a href="notes/swd.pdf">pdf</a>)
<span class="abs-non"><br/>
</span></p>
<p><b>The trigonometric Casimir connection</b>, Spring 2014. (<a href="notes/tcc.pdf">pdf</a>)
<span class="abs-non"><br/>
</span></p>
<p><b>Quantum Hamiltonian reduction</b>, Spring
2014. (<a href="notes/qham1.pdf">pdf 1</a>) (<a href="notes/qham2.pdf">pdf 2</a>)
<span class="abs-non"><br/>
</span></p>
<p><b>Grothendieck's simultaneous resolution and the Springer correspondence</b>, Fall
2013. (<a href="notes/springer.pdf">pdf 1</a>)
(<a href="notes/springer2.pdf">pdf 2</a>)
(<a href="notes/springer3.pdf">pdf 3</a>)
<span class="abs-non"><br/>
</span></p>
<h2>learning seminars</h2>
<p>In 2016, I organized and attended a reading course on quantum cohomology supervised by Davesh Maulik. A list of references is available <a href="qc.html">here</a>.</p>
<p>In 2012-2013, I ran a learning seminar for graduate students on interacting particle
systems. A list of references and talks is available <a href="ips/ipsseminar.html">here</a>.</p>
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