## Mirror Symmetry

### News

Please Note: If you wish to receive credit points for this class, please let us know soon which module this would be for you. The physics "Pflichtseminar" requires a written summary of your talk.

A organizational meeting will be held on Monday, July 22, at 2pm, in SR 00.200 MATHEMATIKON.

First meeting on October 15.

### Organization

Each session will be devoted to a fairly broad topic that should be split among two (or more) responsible speakers. Each team will be tutored by one of the organizers. The current distribution of topics and speakers is here. There are still a few open slots, please contact us or come to the first meeting for further information.

Meeting time and place: Tuesday 2:30p.m., MATHEMATIKON SR 2

### Instructors

Dr. Ingmar Saberi, saberi@mathi.uni-heidelberg.de
Prof. Dr. J. Walcher, walcher@uni-heidelberg.de

### Description

Mirror symmetry is one of the oldest and best understood dualities that have emerged from string theory and has had a profound impact in certain areas of pure mathematics. The original statements, motivated by Conformal Field Theory, concerned certain enumerative questions in algebraic geometry and their solution in terms of Hodge theory. Soon after, two mathematical formulations were put forward: Kontsevich's Homological Mirror Symmetry inteprets the duality as an equivalence of symplectic and algebraic categories. The study of torus fibrations initiated by Strominger, Yau and Zaslow gives an explicit geometric correspondence. Today, mirror symmetry remains an extremely active research field, reaching in influence far beyond its original formulation as a duality between Calabi-Yau manifolds, to such subjects as representation theory, singularity theory, and knot theory. This seminar will trace mirror symmetry from its origins to some modern developments. One of our main goals will be to understand Nick Sheridan's 2011 proof of homological mirror symmetry for the quintic threefold.

Prerequisites: The seminar is aimed at Masters students in mathematics and mathematical physics. Participants should have a solid background in at least one of symplectic geometry, algebraic geometry or quantum field and string theory, with nodding acquaintance of the other two.

### Schedule of Talks

Schedule still subject to change.

Date Speakers TitleAbstractNotes
October 15 Fabian, Benjamin T-duality
October 22 Levin, Sebastian Kähler geometry
October 29 Tristan, Aarya Mirror symmetry for $T^2$
November 5 Tobias, David 2d $\mathcal N=(2,2)$ SuSy
November 12 Niklas Toric geometry
November 19 Lukas, Michael Hori-Vafa mirror symmetry
November 26 N.N. T.B.A.
December 3 Ingmar, Johannes D-branes
December 10 Fabio, N.N. Derived categories
December 17 Menelaos, N.N. Fukaya categories
January 7 Johanna, Steffen HMS for elliptic curve
January 14 Adnan, N.N. HMS for projective space
January 21 N.N., N.N. HMS for quintic