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.
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
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.
|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|
|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|