SYSU-CUHK Joint Online Workshop on Geometry and Physics (I)

Purpose:

Due to the corona, it becomes very difficult to have international visits nowadays. To contribute the academic commutation in mathematics between Sun Yat-sen Unversity (SYSU) and the Chinese University of Hong Kong (CUHK), we organize this joint online workshop. This is the first one on geometry and physics, and is fully supported by SYSU.

Organizers:

LEUNG, Naichung Conan        (The Chinese University of Hong Kong)

LI, Changzheng                     (Sun Yat-sen University)

CHAN, Kwok Wai                  (The Chinese University of Hong Kong)

Speakers: 

Kwok Wai Chan                (The Chinese University of Hong Kong)         

Siu-Cheong Lau                (Boston University)

Jae-Hyouk Lee                  (Ewha Womans University)

 Mao Sheng                      (University of Science and Technology of China)     

Zoom No.: 753 271 5869

Password: please emal  lichangzh AT mail.sysu.edu.cn

Program: (Beijing time)

 9:30-10:30         

 Speaker: Siu-Cheong Lau

 Title: Noncommutative geometry in application to machine learning

 Abstract: It is an interesting observation that neural network in machine learning shares the same starting point as quiver representation theory.  In this talk, I will build an algebro-geometric formulation of a `computing machine' which is well-defined over the moduli space of representations.  An important algebraic ingredient is extending the associative geometry of Connes, Cuntz-Quillen, Ginzburg to near-rings, in order to accommodate non-linear activation functions in neural network.  Furthermore, I will explain a uniformization between spherical, Euclidean and hyperbolic moduli spaces of framed quiver representations.

10:45-11:45         

Speaker: Jae-Hyouk Lee

Title: Polygon spaces and spin action

Abstract: In this talk, we discuss the geometry of the polygons in Euclidean spaces. We explain fundamental issues of chamber structures of polygon spaces according to moment maps and related polytopes, and introduce an approach with spin action to characterize polygons in 5-dimensional Euclidean space. This is a joint with Eunjeong Lee.

14:30-15:30

Speaker: Mao Sheng

Title: Tensor product theorem for semistable parabolic $\lambda$-connections

Abstract: Let $X$ be a smooth complex projective variety and $D\subset X$ a reduced effecitve normal crossing divisor. Fix an ample line bundle $L$ over $X$. We prove that the tensor product of $\mu_L$-semistable parabolic $\lambda$-connections over $(X,D)$ is again $\mu_L$-semistable. For empty $D$ and integrable $\lambda$-connections, the known proof is transcendental (by proving the existence of HYM metric on stable Higgs bundles). Our new method is first establishing a tensor product theorem in positive characteristic and then taking reduction by modulo p. This is a joint work with Jianping Wang.

15:45-16:45

Speaker: Kwok Wai Chan

Title: On Fukaya's approach to SYZ mirror symmetry

Abstract: The main theme of this talk is Fukaya's program on SYZ mirror symmetry. Let X be a Calabi-Yau manifold equipped with an SYZ fibration to a base manifold B. Then Fukaya's program relates holomorphic disks in X with boundaries on Lagrangian torus fibers with deformations of complex structures on the SYZ mirror, via Morse theory on the base B. I will explain joint works with Conan Leung and Ziming Ma where we proved modified versions of some of Fukaya's conjectures.

Contact information:

Prof. LI, Changzheng 
Email: lichangzh AT mail.sysu.edu.cn

Phone: +86-20-84111738 

School of Mathematics, Sun Yat-sen University, No. 135, Xingang Xi Road, Haizhu, Guangzhou, 510275, China 

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Remark: The second Joint Online Workshop on Geometry and Physics (II) will be held on July 19, 2021.