GTM seminar

Speaker: Artan Sheshmani (Ohio State university/ Kavli IPMU)
Title: On the proof of the S-duality modularity conjecture for the quintic threefold
Date (JST): Thu, Oct 01, 2015, 15:30 - 17:00
Place: Seminar Room A
Abstract: I will talk about recent joint works with Amin Gholampour, Richard Thomas and Yukinobu Toda, on an algebraic-geometric proof of the S-duality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold. Our strategy is to first use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over relative Hilbert scheme of points on surfaces and then prove modularity; More precisely, together with Gholampour we have proven that the generating series, associated to the top intersection numbers of the Hibert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson for absolute Hilbert schemes. These intersection numbers, together with the generating series of Noether-Lefschetz numbers, will provide the ingredients to prove modularity of the above DT invariants over the quintic threefold.