We build GBU Topology to store talks, seminars, workshops about geometry and topology given in School of Sciences, Great Bay University. One can find the source code here.
Hao Zhao (South China Normal University), May 11, 23’, Thursday, 15:00-16:00; TencentMeeting: 423681872.
In order to study the double suspension $E^2:S^{2n-1}\to \Omega^2 S^{2n+1}$ when localized at a prime $p$, Selick filtered $\Omega^2 S^{2n+1}$ by some H-spaces which geometrically realize a natural Hopf algebra filtration of the cohomology $H^\ast (\Omega^2 S^{2n+1};\mathbb{Z}/p)$. Later, Gray showed that the fiber $W_n$ of $E^2$ has an integral classifying space $BW_n$.
In this talk I will introduce how to correspondingly filter $BW_n$ in a manner which is compatible with Selick’s filtration and the homotopy fibration $S^{2n-1}\to \Omega^2 S^{2n+1}\to BW_n$. Furthermore, I will talk about our results on the multiplicative properties and homotopy exponents of the spaces in the filtrations.Feifei Fan (South China Normal University), May 5, 23’, Friday, 15:00-16:00; TencentMeeting: 105432114.
This talk is toward the applications of toric topology in algebraic combinatorics, especially the face enumeration problems for triangulated spheres and further for triangulated manifolds. A motivational problem is the celebrated g-conjecture in the theory of face enumeration. First, we survey how the g-conjecture came about and how it relates to the topology of a class of toric spaces, which can be viewed as a generalization of toric varieties. Using the theory of toric topology, we give a topological interpretation for several fundamental results in algebraic combinatorics.
Qi Guo (Remin University of China), Dec. 7, 23’, Thursday, 15:00-16:00; TencentMeeting: 597930348.
In this talk, I will discuss some recent works on spectral gap of Dirac operator and its applications. First, I will go over the background of Dirac operator on Spin manifold. Then I will show three main theorems on spectrum of Dirac operator. At last, I will explain how these works can be applied to nonlinear problems. The key ingredient is the Clifford multiplication which comes from the representation of Clifford algebra.
Yang Ming (Hubei Polytechnic University), Dec. 7, 23’, Thursday, 16:10-17:20; TencentMeeting: 597930348.
Computational lithography is the set of mathematical and algorithmic approaches designed to improve the resolution attainable through photolithography. Computational lithography has become instrumental in further shrinking the design nodes and topology of semiconductor transistor manufacturing. In this talk, I will introduce the basic concepts and ideas in the patterning flow and explain how to use kernel methods to accelerate the numerical calculation.
Yang Shen (Fudan University), Dec. 8, 23’, Friday, 15:00-16:00; TencentMeeting: 276191606.
Let $M_{g,n(g)}$ be the moduli space of hyperbolic surfaces of genus $g$ with $n(g)$ punctures endowed with the Weil-Petersson metric. In this talk, we discuss the asymptotic behavior of the Cheeger constants and spectral gaps of random hyperbolic surfaces in $M_{g,n(g)}$ when $n(g)$ grows slower than $g$ as $g\to\infty$. This is a joint work with Yunhui Wu.
Xiang Liu (Nankai University), Dec. 8, 23’, Friday, 16:10-17:20; TencentMeeting: 276191606.
Artificial intelligence (AI) based drug design has demonstrated great potential to fundamentally change the pharmaceutical industries. However, a key issue in all AI-based drug design models is efficient molecular representation and featurization. In this talk, I will introduce our recently proposed persistent models for molecular representation and featurization. In our persistent models, molecular interactions and structures are characterized by various topological objects, including simplicial complex and hypergraph. Then mathematical invariants can be calculated to give quantitative featurization of the molecules. These persistent functions are used as molecular descriptors for the machine learning models. The state-of-art results can be obtained by these persistent function based machine learning models.