Joint Harvard-CUHK-YMSC Differential Geometry Seminar

Beginning immediately, until at least December 31, all seminars will take place virtually, through Zoom.

During the Fall 2020 semester, the Differential Geometry Seminar will take place on Tuesday’s at 8:00am ET. This seminar is a joint event between Harvard CMSA and Tsinghua University’s Yau Mathematical Science Center. To learn how to attend, please contact Yun Shi (yshi@cmsa.fas.harvard.edu) and Rongxiao Mi (rongxiao@cmsa.fas.harvard.edu).

DateSpeakerTitle/Abstract
9/29/2020Tristan Collins (MIT)Title: SYZ mirror symmetry for del Pezzo surfaces and rational elliptic surfaces

Abstract:  I will discuss some aspects of SYZ mirror symmetry for pairs (X,D) where X is a del Pezzo surface or a rational elliptic surface and D is an anti-canonical divisor which is either smooth or a wheel of rational curves.  In particular I will explain the existence of special Lagrangian fibrations and mirror symmetry for (suitably interpreted) Hodge numbers. If time permits, I will describe a proof of SYZ mirror symmetry for del Pezzo surfaces.  This is joint work with A. Jacob and Y.-S. Lin.
8/6/2020Lutian Zhao (UIUC)Title: The Gopakumar-Vafa invariants for local P2.
 
Abstract: In this talk, I will introduce the Gopakumar-Vafa(GV) invariant and show one calculation on the nonreduced cycle. The GV invariant is an integral invariant predicted by physicists that counts the number of curves inside a given Calabi-Yau threefold. The definition has been conjectured by Maulik-Toda in 2016 in terms of perverse sheaf. I’ll use this definition on the total space of the canonical bundle of P2 and compute the associated invariants. This verifies a physical formula based on the work of Katz-Klemm-Vafa in 1997.
10/13/2020
8:00pm ET
Siu-Cheong Lau (Boston University)Title: Kaehler quiver geometry in application to machine learning
 
Abstract: Quiver theory and machine learning share a common ground, namely, they both concern about linear representations of directed graphs.  The main difference arises from the crucial use of non-linearity in machine learning to approximate arbitrary functions; on the other hand, quiver theory has been focused on fiberwise-linear operations on universal bundles over the quiver moduli.
Compared to flat spaces that have been widely used in machine learning, a quiver moduli has the advantages that it is compact, has interesting topology, and enjoys extra symmetry coming from framing.  In this talk, I will explain how fiberwise non-linearity can be naturally introduced by using Kaehler geometry of the quiver moduli.
10/20/2020Henry Liu (Columbia University)Title: Self-duality in quantum K-theory
 
Abstract: When we upgrade from equivariant cohomology to equivariant K-theory, many important algebraic/geometric tools such as dimensional vanishing become inapplicable in general. I will explain some nice conditions we can impose on K-theory classes to restore some of these tools. These conditions hold for many types of curve-counting theories (e.g. quasimaps) and are crucial for the development of those flavors of quantum K-theory, but they notably are not present in Gromov-Witten theory. I will describe an attempt to twist GW theory to fulfill these
conditions.

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