Fall 2022: Mirror symmetry

This semester the reading seminar will study mirror symmetry.

The seminar will consist of talks by faculty followed by talks by graduate students. We will attempt to make the seminar accessible to everyone.

The seminar will meet on Fridays, 2:30PM--3:30PM, in LGRT 1322.

9/9. Organizational meeting.

9/16 Paul Hacking.

9/23 Charles Ouyang.

9/30 Wendelin Lutz.

10/7 Eyal Markman.

10/14 Kristin DeVleming.

10/21 Cristian Rodriguez.

10/28 Ethan Zhou.

11/4 Chunlin Shao.

11/11 No seminar (Veteran's day).

11/18 Arthur Wang.

11/25 No seminar (Thanksgiving).

12/2 Joe Foster.

12/9 Yuxuan Yang.

Homological algebra of mirror symmetry, by M. Kontsevich arxiv.

Mirror symmetry is T-duality, by A. Strominger, S-T. Yau, and E. Zaslow arxiv.

The moduli space of special Lagrangian submanifolds, by N. Hitchin arxiv.

Special Lagrangian fibrations I: Topology and II: Geometry, by M. Gross arxiv I and arxiv II.

Examples of special Lagrangian fibrations, by M. Gross arxiv.

Mirror symmetry and T-duality in the complement of an anticanonical divisor, by D. Auroux arxiv.

Special Lagrangian fibrations, wall-crossing, and mirror symmetry, by D. Auroux arxiv.

Categorical Mirror Symmetry: The Elliptic Curve, by A. Polishchuk and E. Zaslow arxiv.

Mirror symmetry for abelian varieties, by V. Golyshev, V. Lunts, and D. Orlov arxiv.

Abelian varieties, theta functions, and the Fourier--Mukai transform, by A. Polishchuk, C.U.P. 2002, Chapter 6.

Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves, by D. Auroux, L. Katzarkov, and D. Orlov arxiv.

Homological Mirror Symmetry for log Calabi--Yau surfaces, by P. Hacking and A. Keating arxiv.

A beginner's introduction to Fukaya categories, by D. Auroux arxiv.

Four dimensions from two in symplectic topology, by M. Symington arxiv.

Links to the seminar from previous semesters.

Birational geometry and the minimal model program, Spring 2022

Fano varieties, Fall 2021

Mirror symmetry, Spring 2020

K3 surfaces, Fall 2019

The minimal model program, Spring 2019

Non-commutative K3 surfaces, Fall 2018

Topics in algebraic geometry, Spring 2018

Surface singularities, Fall 2017

Birational geometry, Spring 2017.

Algebraic surfaces, Fall 2016.

Fano varieties, Fall 2015

The Hitchin system, character varieties, and related topics, Spring 2015

Holomorphic symplectic varieties and Hyperkahler manifolds, Fall 2014

Syzygies, Spring 2014

Toric varieties, Fall 2013

Derived categories in algebraic geometry, Spring 2013

Deformation theory, Fall 2012

Curves, K3 surfaces, and Fano 3-folds, Spring 2012

Topics in algebraic geometry, Fall 2011

Surfaces of general type, Spring 2011

Algebraic surfaces, Fall 2010.

Stability conditions on derived categories and wall crossing, Spring 2010

Mirror symmetry and tropical geometry, Fall 2009

Deformation theory, Fall 2008

Green's Conjectures, Spring 2008

Bridgeland Stability, Fall 2007.

Minimal Model Program, Spring 2007

Commutative Algebra and Polyhedra Seminar, Spring 2006.

Geometry and Algebra of Polyhedra Seminar, Fall 2005.

Commutative Algebra Seminar, 2004-2005