Speaker: Dr. Fei Si (Peking Univ)
Time: 10:00-11:30 October 17, 2023 (Tuesday)
Place: MCM410
Title: Birational Geometry of Moduli Spaces of Del Pezzo Surface Pairs
Abstract: A K3 surfaces with an anti-symplectic involution is equivalent to a del pezzo surface pair (X, C) where X is a del pezzo surface and C is a curve on X so that C~-2KX. Their moduli spaces have many compactifications cations from different perspectives like GIT, Hodge theory and K-stability theory. It is natural to ask what is the precise relations of these compatifications? In this talk, I will provide a solution by viewing these compatifications as log canonical models of Baily-Borel compatification for degree 8 pairs. It is now known as Hassett-Keel-Looijenga program as initiated by Laza-O'Grady in the case of quartic K3 surfaces. Via this viewpoint, we can also obtain the K-moduli walls from an arithmetic stratification. This is based on joint work with Long Pan and Haoyu Wu.
Speaker: Prof. Thomas J. Haines (University of Maryland)
Time: 10:30-11:30am, October 17, 2023 (Tuesday)
Place: MCM110
Title: Cellular pavings for convolution morphisms and applications
Abstract: The recent work of Cass-van den Hove-Scholbach on the Geometric Satake Equivalence for Integral Motives required cellular pavings of fibers of convolution morphisms for affine Grassmannians over $\bbZ$. In this talk, I will explain that cellular pavings exist for all convolution morphisms attached to any partial affine flag varieties of Chevalley groups. I will explain the proof by a reduction to the full affine flag varieties, using some properties of "negative parahoric loop groups". Then I will mention some applications, such as a direct proof of Frobenius semisimplicity results for intersection cohomology groups of affine Schubert varieties over finite fields, and the "rationality over the base field" of the BBD decomposition theorem in related situations.
Speaker: Prof. Quansen Jiu (Capital Normal University)
Time: 16:00-17:00 October 17, 2023 (Tuesday)
Place: MCM110
Title: An extension of Calderon-Zygmund type singular integral
Abstract: In this talk, we will present a kind of singular integral which can be viewed as an extension of the classical Calderon-Zygmund type singular integral. We establish an estimate of the singular integral in the $L^q$ space for $1<q<\infty$. In particular, the Calderon-Zygmund estimate can be recovered from our obtained estimate. The proof of our main result is via the so called "geometric approach". We will also present an application of this type singular integral in the approximation of surface quasi-geostrophic (SQG) equation.
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