February 3: Minghao Zhao, preprint seminar.
February 10: Charlie Wu, Toronto. Compact components of character varieties
Abstract: Relative character varieties of surface groups are varieties which parametrize representations of the fundamental group of a surface with prescribed behavior the punctures of the surface. In the 90s, Benedetto and Goldman discovered a surprising compact component of a (real) relative character variety, later generalized by the work of Deroin-Tholozan and Tholozan-Toulisse. We give a classification of all compact components of real relative character varieties in terms of Hodge theory. This is joint work with Daniel Litt.
February 17: Mattias Jonsson, Michigan. (JHU--UMD Complex Geometry Seminar, 2:00pm, Kirwan Hall 3206, UMD) On the Yau--Tian--Donaldson conjecture for extremal metrics
Abstract: Let X be a compact Kähler manifold. Calabi asked whether a given Kähler class on X contains a "canonical" Kähler metric, such as an extremal metric. Roughly speaking, the Yau-Tian-Donaldson conjecture states that if the Kähler class is the first Chern class of an ample line bundle, then the existence of an extremal metric should be governed by an algebro-geometric stability condition. I will present joint work with S. Boucksom, where we prove a version of this conjecture.
February 24: Kimoi Kemboi, Princeton. The Fano of lines and the Kuznetsov component of cubic fourfolds
Abstract: A smooth cubic fourfold gives rise to two kinds of hyperkähler fourfolds: one is classical --the variety of lines on the cubic; and the other is "non-commutative" --arising from the symmetric square of the Kuznetsov component. Galkin conjectured that these two objects should be derived equivalent. In this talk, I’ll explain a proof of this conjecture, which uses matrix factorizations and a wall-crossing derived equivalence for a particular 12-dimensional flop. This is joint work with Ed Segal.
March 3: Junsheng Zhang, NYU.
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March 10: Tamás Darvas, UMD.
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March 24: Benjamin Church, Stanford.
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March 31: Linquan Ma, Purdue/IAS.
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April 7: Ruijie Yang, University of Kansas.
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April 14: Matthew Hase-Liu, Columbia.
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April 21: Daniil Serebrennikov, preprint seminar