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Mirror Symmetry seminar

A learning seminar on the mathematical aspects of 2D Mirror Symmetry, particularly the Homological Mirror Symmetry (HMS) conjecture. We will meet on Tuesdays from 14:00-17:00 in the QM Seminar Room. It is also registered as the course Advanced topics in geometry and topology as a PhD course in SDU.

Anyone is welcome to attend and/or give talks. Graduate students are required to give a talk to receive credit. If you want to join, please contact me directly. A rough outline of the schedule of the talks is given below. This schedule may be subject to change.

# Date Topics Speaker Reference
Talk 1 07/09 An overview of Mirror Symmetry Bingyu [Aspinwall]
Talk 2 14/09 An overview of Mirror Symmetry II Bingyu [Aspinwall]
Talk 2 29/09 Coherent sheaves Adrian [Vakil]
Talk 3 06/10 Derived category of coherent sheaves Joël [Huybrechts]
Talk 4 12/10 Beilinsen theorem for $D^b\mathrm{Coh}(\mathbb{P}^n)$ Yuki [Huybrechts]
Talk 5 26/10 Floer homology Alyosha [Auroux]
Talk 6 02/11 Fukaya Category Siva [Auroux]
Talk 7 09/11 HMS of elliptic curve Shomrik [Polishchuk-Zaslow]
Talk 8 23/11 HMS of $\mathbb{P}^2$ Matthias  
Talk 9 31/11 TBD    
Talk 10 07/11 TBD    
Talk 11 14/12 TBD    
Talk 12 TBD TBD    
Talk 13 TBD TBD    
Talk 14 TBD TBD    
Talk 15 TBD TBD    


Kentaro Hori, Mirror symmetry. 2003.

Paul S. Aspinwall, et al., Dirichlet branes and mirror symmetry. 2009.

Daniel Huybrechts, Fourier–Mukai transforms in Algebraic Geometry. 2006.

Ravi Vakil, The Rising Sea: Foundations of Algebraic Geometry. Online.

Paul Seidel, Fukaya Categories and Picard–Lefschetz Theory. 2008.

Denis Auroux, A beginner’s introduction to Fukaya categories. math.SG/1301.7056.

Alexander Polishchuk, Eric Zaslow, Categorical Mirror Symmetry: The Elliptic Curve. math.AG/9801119

Paul Seidel, Homological mirror symmetry for the quartic surface. 2006.

Denis Auroux, Ludmil Katzarkov and Dmitri Orlov, Mirror symmetry for weighted projective planes and their noncommutative deformations. 2008.

Nick Sheridan, Homological mirror symmetry for Calabi–Yau hypersurfaces in projective space. 2015.

Benjamin Gammage, Vivek Shende, Mirror symmetry for very affine hypersurfaces. 2017.

Vivek Shende, Toric mirror symmetry revisited. 2021.

Online resources:

Denis Auroux, Topics in Differential Geometry

Workshop: Homological Mirror Symmetry, 2015 at Hebrew University

James Pascaleff, Homological Mirror Symmetry