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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 |
References
- Overviews on mirror symmetry:
Kentaro Hori, Mirror symmetry. 2003.
Paul S. Aspinwall, et al., Dirichlet branes and mirror symmetry. 2009.
- Derived category of coherent sheaves on varieties:
Daniel Huybrechts, Fourier–Mukai transforms in Algebraic Geometry. 2006.
Ravi Vakil, The Rising Sea: Foundations of Algebraic Geometry. Online.
- Fukaya categories:
Paul Seidel, Fukaya Categories and Picard–Lefschetz Theory. 2008.
Denis Auroux, A beginner’s introduction to Fukaya categories. math.SG/1301.7056.
- Mathematical proofs of homological mirror symmetry:
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