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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="author" content="Reading Course on Quantum Cohomology">
<meta name="keywords" content="Reading Course on Quantum Cohomology">
<meta name="description" content="Reading Course on Quantum Cohomology">
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<title>Reading Course on Quantum Cohomology (Spring 2016)</title>
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<link href="css/qc-style.css" rel="stylesheet">
</head>
<body>
<div class="container">
<div class="page-header">
<h1>Reading Course on Quantum Cohomology (Spring 2016)</h1>
<p>Supervisor: Davesh Maulik</p>
<p>Friday 9:00am at 2-346</p>
</div>
<h2>Schedule</h2>
<table class="table">
<thead>
<th width=5%>Week</th>
<th width=10%>Date</th>
<th width=15%>Speaker</th>
<th width=50%>Topic</th>
<th width=20%>References</th>
</thead>
<tbody>
<tr>
<td>1</td>
<td>February 15</td>
<td>Yi</td>
<td>Equivariant Localization</td>
<td>[AB], [Clay]</td>
</tr>
<tr>
<td>2</td>
<td>February 22</td>
<td>David</td>
<td>Moduli space and deformation theory of stable maps</td>
<td>[Clay] Chapters 23-24</td>
</tr>
<tr>
<td>3</td>
<td>March 4</td>
<td>Dorin</td>
<td>GIT, stability, semi-stability</td>
<td>[Gin]</td>
</tr>
<tr>
<td>4</td>
<td>March 11</td>
<td>Sid</td>
<td>Constructions and computations with Nakajima quiver varieties</td>
<td>[Gin]</td>
</tr>
<tr>
<td>5</td>
<td>March 18</td>
<td>Yi</td>
<td>GW invariants, reduced / virtual fundamental class; Example: Small quantum cohomology for P^1</td>
<td>[Clay], [MS2], [Giv], [Kim]</td>
</tr>
<tr>
<td>6</td>
<td>April 1</td>
<td>David</td>
<td>Equivariant quantum cohomology, quantum connection, descendant GW invariants, example of P^n</td>
<td>[Clay]</td>
</tr>
<tr>
<td>7</td>
<td>April 8</td>
<td>Dorin</td>
<td>[BMO]: Proof of main result / Toda limits</td>
<td>[BMO]</td>
</tr>
<tr>
<td>8</td>
<td>April 15</td>
<td>Sid</td>
<td>[MO]: Stable envelopes and R-matrices</td>
<td>[MO]</td>
</tr>
<tr>
<td>9</td>
<td>April 22</td>
<td>Yi</td>
<td>[MO]: Definition of the geometric Yangian</td>
<td>[MO]</td>
</tr>
<tr>
<td>10</td>
<td>April 29</td>
<td>David</td>
<td>[MO]: Stable basis</td>
<td>[MO]</td>
</tr>
<tr>
<td>11</td>
<td>May 6</td>
<td>Dorin</td>
<td>[MO]: Identification of the quantum connection with the trigonometric Casimir connection</td>
<td>[MO]</td>
</tr>
<tr>
<td>12</td>
<td>May 13</td>
<td>Sid</td>
<td>[She]: Definition / applications of stable envelope and stable basis</td>
<td>[She]</td>
</tr>
</tbody>
</table>
<h2>References</h2>
<table class="table">
<thead>
<th width=20%>Abbreviation</th>
<th width=60%>Source</th>
<th width=20%>Link</th>
</thead>
<tbody>
<tr>
<td>[AB]</td>
<td>Atiyah-Bott. The moment map and equivariant cohomology</td>
</tr>
<tr>
<td>[BMO]</td>
<td>Braverman Maulik Okounkov -- Quantum cohomology of the Springer resolution</td>
</tr>
<tr>
<td>[Clay]</td>
<td>Clay volume on mirror symmetry</td>
<td><a href="http://www.claymath.org/library/monographs/cmim01.pdf">Link</a></td>
</tr>
<tr>
<td>[CK]</td>
<td> D. Cox and S. Katz, Mirror Symmetry and Algebraic
Geometry, AMS, 1999</td>
</tr>
<tr>
<td>[FP]</td>
<td>Fulton-Pandharipande</td>
<td><a href="http://arxiv.org/abs/alg-geom/9608011">Link</a></td>
</tr>
<tr>
<td>[Gin]</td>
<td>V. Ginzburg, Lectures on Nakajima’s Quiver
Varieties</td>
<td>arXiv:0905.0686</td>
</tr>
<tr>
<td>[Giv]</td>
<td>Alexander Givental. Stationary Phase Integrals, Quantum Toda
Lattices, Flag Manifolds and the Mirror Conjecture.</td>
<td><a href="http://front.math.ucdavis.edu/9612.5001">Link</a></td>
</tr>
<tr>
<td>[Kim]</td>
<td>Bumsig Kim. Quantum cohomology of flag manifolds G/B and
quantum Toda lattices</td>
</tr>
<tr>
<td>[KM]</td>
<td>Kontsevich-Manin</td>
<td><a href="http://www.ihes.fr/~maxim/TEXTS/WithManinCohFT.pdf">Link</a></td>
</tr>
<tr>
<td>[Mau]</td>
<td>Maulik. PCMI Notes</td>
</tr>
<tr>
<td>[MO]</td>
<td>Maulik Okounkov -- Quantum Groups and Quantum
Cohomology.</td>
</tr>
<tr>
<td>[Mc]</td>
<td>McBreen -- Quantum Cohomology of Hypertoric Varieties
and Geometric Representations of Yangians</td>
</tr>
<tr>
<td>[MS]</td>
<td>McBreen Shenfeld -- Quantum Cohomology of Hypertoric
Varieties</td>
</tr>
<tr>
<td>[MS2]</td>
<td>McDuff-Salamon, J-holomorphic curves and quantum
cohomology, Chapter 11</td>
</tr>
<tr>
<td>[Neg]</td>
<td>Quantum Algebras and Cyclic Quiver Varieties</td>
</tr>
<tr>
<td>[Oko]</td>
<td>Okounkov -- PCMI Notes</td>
</tr>
<tr>
<td>[She]</td>
<td>Shenfeld -- Abelianization of stable envelopes in
symplectic resolutions</td>
</tr>
<tr>
<td>[Su]</td>
<td>Su -- Equivariant quantum cohomology of cotangent bundle
of G/P</td>
</tr>
</tbody>
</table>
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