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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 |

## 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