Interesting talks

These are talks I attended which I find very intereting.

Walking AG Seminar, Purdue

-October 17th, 2012: Derived equivalence of irregular varieties, Luigi Lombardi.
The speaker studies the question about derived invariants. Suppose that X and Y are two smooth complex projective varieties with derived equivalence D(X)=D(Y). It is known that dimension, canonical ring, and irregularity are derived equivalence. Kontsevich's Homological Mirror Symmetry indicates Hodge numbers h^{p,q}(X) are also derived invariants. Popa's conjecture asks if the cohomological jumping loci V^i(K_X) are derived invariants. The speaker considers a weaker conjecture aobut derived invariance of the connected component V^i(K_X)_0 which suffices for many application. The study of V^i(K_X) dates back to Green and Lazarsfeld. The theory is developed by Popa-Pareschi to GV-sheaves and Chen-Hacon for varieties of maximal Albanese dimension. The theories of Foruier Mukai transforms and Hochschild cohomology are critically in the study.

-September 6th, 2012: History of resolution of singularities, Shreeram S Abhyankar

-August 22th, 2012: The Bicategory of Landau-Ginzburg Models, Daniel Murfet.
Abstract: The speaker explains how bicategories naturally arise in the study of two-dimensional topological field theories with defect lines, and howworking with a simple diagrammatic language for these bicategories can simplify difficult proofs in pure mathematics. An interesting example isthe bicategory whose objects are isolated hypersurface singularities and whose 1-morphisms are matrix factorisations; the speaker discuss a result about adjoints in this bicategory worked out in recent joint work with Nils Carqueville. Apply their method to different bicategories would recover HHR and other well-known results.