Reading seminar in algebraic geometry.
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.

Tentative Schedule

9/9. Organizational meeting.

9/16 Paul Hacking. What is mirror symmetry?

9/23 Charles Ouyang. Higgs bundles and SYZ geometry

9/30 No seminar due to BATMOBILE conference.

10/7 Postponed due to illness.

10/14 Wendelin Lutz. Mirror symmetry for toric Fano manifolds.

10/21 Eyal Markman. Mukai's SL(2,Z) action on the derived category of an abelian variety.

10/28 Paul Hacking. Mirror symmetry for Fano manifolds. Abstract.

11/4 Cristian Rodriguez.

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

11/18 Ethan Zhou.

11/25 No seminar (Thanksgiving).

12/2 Chunlin Shao.

12/9 Arthur Wang.

12/16a Joe Foster.

12/16b Yuxuan Yang.

Some references

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

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