Homological mirror symmetry is a mysterious relationship between symplectic and algebraic geometry. It has its origins in string theory, but it turns out to be extraordinarily mathematically useful. Although it can be formulated as a precise conjecture in some settings, and the conjecture can sometimes be proved, that's not necessarily the most productive way to approach it. Rather, it turns out to be very useful as a `philosophy', and as such has motivated key developments in symplectic and algebraic geometry (and other areas). So our approach will not be to cover the technical background necessary to make precise statements, nor to cover some of the mathematics it has motivated; rather, we will try to get a feel for what HMS really `is', by working through as many explicit examples as possible.
All are welcome to attend. If you wish to be kept informed please contact Nick Sheridan to be added to the mailing list.
Please email Nick if you would like to claim a talk, or if there is a topic you'd like to talk about which is not listed here.
Fantastic reference: Auroux' Topics course on mirror symmetry (videos and typed notes here).
Wed 18/9, 11-12: Introduction, Nick Sheridan, JCMB 4319A, Notes, References
Fri 23/9, 11-12, Intro to the Fukaya category, Nick Sheridan, JCMB 5323, Notes, References
Fri 30/9, 11-12, Intro to the Fukaya category (cont'd); Intro to the derived category, Nick Sheridan, Matt Booth, JCMB 5323, Nick's outline, Matt's notes
Fri 7/10, 11-12, Intro to the derived category (cont'd), Matt Booth, JCMB 5323, Nick's outline, Matt's notes
Fri 18/10, 12-1, The cylinder, Augustinas Jacovskis, JCMB 5323, Outline, Augustinas' notes
Fri 25/10, 12-1, The affine line, the projective line, Sebastian Schlegel Mejia, JCMB 5323, Outline, Sebastian's notes
Fri 1/11, 12-1, The projective plane, Qingyuan Jiang, JCMB 5323, Outline, Qingyuan's notes
Fri 8/11, 12-1, Cancelled (EDGE days)
Fri 15/11, 12-1, The elliptic curve, Dougal Davis, JCMB 5323, Outline, Dougal's notes
Fri 22/11, 12-1, The SYZ conjecture, Kai Hugtenburg, *JCMB 6206*, Outline, Kai's notes, relevant notes
Fri 24/1, 12-1, The Fukaya category of a Fano variety, Kai Hugtenburg, JCMB 5327, Outline
The other direction for the projective line, Francesca Carocci, Outline
Fri 7/2, 12-1, Singular SYZ fibrations, Outline