Chunyi Li (University of Warwick). Bridgeland stability conditions on projective varieties. Friday 1st May, 1:30-2:30pm. Huxley 130.

Abstract: Slope stability for vector bundles on curves was introduced by Mumford in the 1960s, providing a rigorous foundation for the construction of moduli spaces. In higher dimensions, the notion of stability splits into slope stability and Gieseker stability. While both retain many of the desirable properties as in the curve case, each also presents subtle technical limitations.
The Bridgeland stability condition can be viewed as a generalized slope stability on curves to higher-dimensional varieties in a more unified and robust way, combining advantages of both slope and Gieseker stability. A central question in the theory has been to determine which varieties admit Bridgeland stability conditions. In this talk, I will discuss recent progress on the existence of stability conditions on all projective varieties.

Matthew Habermann (Imperial). Dubrovin’s conjectures in the Landau—Ginzburg setting. Friday 8th May, 1:30-2:30pm. Huxley 130.

Abstract: Landau–Ginzburg (LG) models are the natural mirror candidates to Fano manifolds and have an enumerative theory analogous to quantum cohomology, known as FJRW theory. In this talk, I will begin by giving an overview of these ideas, keeping a running comparison to quantum cohomology in order to explain some of the similarities and subtleties. I will then briefly explain the notion of Frobenius manifolds, how they arise in FJRW theory and how Dubrovin’s conjectures for Fano varieties lead to natural analogues in this LG setting. Finally, I would like to discuss work-in-progress in collaboration with Yefeng Shen and Weiqiang He. 

Qaasim Shafi (Heidelberg University). Friday 15th May, 1:30-2:30pm. Huxley 130.

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Aline Zanardini (EPFL). Friday 5th June, 1:30-2:30pm. Huxley 130.

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Sebastian Opper (Charles University, Prague). Friday 19th June, 1:30-2:30pm. Huxley 130.

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Holly Krieger (Cambridge). Friday 26th June, 1:30-2:30pm. Huxley 130.

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