### BIMSA一周学术报告预告 11.28-12.02

2022-11-28 Mon

The Extended Persistent Homology Transform for Manifolds with Boundary

AMSS-YMSC-BIMSA Joint Seminar on Progress of Topology and Its ApplicationsSpeaker: Vanessa Robins Australian National University

Time: 11:00-12:30

Venue: Online

Zoom: 787 662 9899（PW: BIMSA）

Abstract

The Persistent Homology Transform (PHT) is a topological transform introduced by Turner, Mukherjee and Boyer in 2014. Its input is a shape embedded in Euclidean space; then to each unit vector the transform assigns the persistence module ofthe height function over that shape with respect to that direction. The PHT is injective on piecewise-linear subsets of Euclidean space, and it has been demonstrably useful in diverse applications as it provides a landmark-free method for quantifying the distance between shapes. One shortcoming is that shapes with different essential homology (i.e., Betti numbers) have an infinite distance between them. The theory of extended persistence for Morse functions on a manifold was developed by Cohen-Steiner, Edelsbrunner and Harer in 2009 to quantify the support of the essential homology classes. By using extended persistence modules of height functionsover a shape, we obtain the extended persistent homology transform (XPHT) which provides a finite distance between shapes even when they have different Betti numbers. It may seem that the XPHT requires significant additional computational effort, but recent work by Katharine Turner and myself shows that when A is a compact manifold with boundary X, embedded in Euclidean space, the XPHT of A can be derivedfrom the PHT of X. James Morgan has implemented the required algorithms for 2-dimensional binary images as an R-package. This talk will provide an outline of our results and an illustration of their application to shape clustering.

Speaker Intro

Vanessa Robins is an associate professor in the Research School of Physics at the Australian National University. She develops theory and algorithmsfor the quantification of shape in data. Her major contributions include fundamental mathematical results for persistent homology, algorithm and software development for computing topological information from digital images, and their application to the characterisationof porous and granular materials.

Organizers：

Jie Wu, Guo-Wei Wei, Stephen Shing-Toung Yau, Haibao Duan, Yong Lin, Jianzhong Pan, Fei Han, Kelin Xia, Chao Zhou

2022-11-28 Mon

Local theta correspondence via C*-agebras of groups

Automorphic Theory SeminarSpeaker: Haluk Sengun University of Sheffield

Time: 19:00-20:30

Venue: Online

Zoom: 293 812 9202（PW: BIMSA）

Abstract

Local theta correspondence sets up a bijection between certain sets of admissible irreps of a pair of reductive groups G,H which sit as each others' centralizers in a larger symplectic group. The local correspondences then bundle up to set up a bijection between certain sets of automorphic representations of G and H. As a result, local theta correspondence is of importance in both representation theory and in the theory of automorphic forms. In joint work with Bram Mesland (Leiden), we have used Rieffel's theory of induction for representations of C*-algebras to prove that in many cases, local theta lifting is functorial and is continuous with respect to weak containment. In the talk, I will explain our approach and time permitting, will discuss further applications. Some of the results I will discuss can be found in the preprint arXiv:2207.13484.

Speaker Intro

Haluk Sengun is a number theorist based at the University of Sheffield, UK. He obtained his PhD at the University of Wisconsin-Madison and has held postdoctoral positions in Essen, Bonn, Barcelona and Warwick. He is interested arithmetic aspects of automorphic forms, cohomology of arithmetic groups and computational approaches. His recent work focuses on bringing in tools from the theory of C*-algebras and noncommutative geometry to his areas of interest listed above.

Organizers：Taiwang Deng, Bin Xu, Jun Yu

2022-11-29 Tue

Opinion Dynamics on Sheaves

AMSS-YMSC-BIMSA Joint Seminar on Progress of Topology and Its ApplicationsSpeaker: Robert Ghrist

Time: 09:00-10:30

Venue: Online

Zoom: 787 662 9899（PW: BIMSA）

Abstract

There is a long history of networked dynamical systems that models the spread of opinions over social networks, with the graph Laplacian playing a lead role. One of the difficulties in modelling opinion dynamics is the presence of polarization: not everyone comes to consensus. This talk will describe work with Jakob Hansen introducing a new model for opinion dynamics using sheaves of vector spaces over social networks. The graph Laplacian is enriched to a Hodge Laplacian, and the resulting dynamics on discourse sheaves can lead to some very interesting and perhaps more realistic outcomes. Extensions of these ideas to sheaves of lattices (in joint work with Hans Riess) will also be surveyed.

Speaker Intro

Robert Ghrist is the Andrea Mitchell PIK Professor of Mathematics and Electrical & Systems Engineering at the University of Pennsylvania. After earning a BS in Mechanical Engineering (University of Toledo, 1991), and the MS and PhD in Applied Mathematics (Cornell University, 1994, 1995), he held positions in Mathematics departments at the University of Texas (Austin), Georgia Tech, and the University of Illinois (Urbana-Champaign). He has been at Penn since 2008. Ghrist is a recognized leader in the field of Applied Algebraic Topology, with publications detailing topological methods for sensor networks, robotics, signal processing, data analysis, optimization, and more. He is the author of a leading textbook on the subject (Elementary Applied Topology, 2014), and has managed numerous large DoD grants from AFOSR, ASDRE, DARPA, and ONR. His research has been recognized with the NSF CAREER, NSF PECASE, SciAm50, and Vannevar Bush Faculty Fellow awards. Ghrist has been an invited speaker at two International Congresses of Mathematicians: once (Madrid 2006) for research and once (Seoul, 2014) for education. Ghrist is a dedicated expositor and communicator of Mathematics, with teaching awards that include the MAA James Crawford Prize, Penn's Lindback Award, and the S. Reid Warren award in Engineering at Penn. Ghrist is the author, designer, and animator of popular YouTube video texts (featureing the Calculus BLUE Project), as well as an online course on Coursera featured in the New York Times, BoingBoing, and Gizmodo.

Organizers：

Jie Wu, Guo-Wei Wei, Stephen Shing-Toung Yau, Haibao Duan, Yong Lin, Jianzhong Pan, Fei Han, Kelin Xia, Chao Zhou

2022-11-29 Tue

Symmetric Mass Generation

Category and Topological Order SeminarSpeaker: Yizhuang You UCSD

Time: 09:30-11:00

Venue: Online

Tencent: 607 3645 0351

Abstract

Symmetric mass generation (SMG) is a novel mechanism for massless fermions to acquire a mass via a strong-coupling non-perturbative interaction effect. In contrast to the conventional Higgs mechanism for fermion mass generation, the SMG mechanism does not condense any fermion bilinear coupling and preserves the full symmetry. It is connected to a broad range of topics, including anomaly cancellation, topological phase classification, and chiral fermion regularization. In this talk, I will introduce SMG through toy models, and review the current understanding of the SMG transition. I will also mention recent numerical efforts to investigate the SMG phenomenon. I will conclude the talk with remarks on future directions.

Speaker Intro

Organizers：Hao Zheng

2022-11-29 Tue

A proof of Kudla-Rapoport conjecture for Kramer models at ramified primes

BIMSA-YMSC Tsinghua Number Theory SeminarSpeaker: Qiao He University of Wisconsin-Madison

Time: 10:30-11:30

Venue: Online

Zoom: 293 812 9202（PW: BIMSA）

Abstract

n this talk, I will first talk about the Kudla-Rapoport conjecture, which suggests a precise identity between arithmetic intersection numbers of special cycles on Rapoport-Zink space and derived local densities of hermitian forms. Then I will discuss how to modify the original conjecture over ramified primes and how to prove the modified conjecture. On the geometric side, we completely avoid explicit calculation of intersection number and the use of Tate’s conjecture. On the analytic side, the key input is a surprisingly simple formula for derived primitive local density. This talk is based on joint work with Chao Li, Yousheng Shi and Tonghai Yang.

Organizers：Hansheng Diao, Yueke Hu, Emmanuel Lecouturier, Cezar Lupu

2022-11-30 Wed

The Loop Hecke Algebra and Charge Conserving Yang–Baxter Operators

BIMSA-Tsinghua Quantum Symmetry SeminarSpeaker: Eric Rowell Texas A&M University

Time: 09:30-11:00

Venue: Online

Zoom: 537 192 5549（PW: BIMSA）

Abstract

The Loop Braid Group 𝐿𝐵𝑛 is the motion group of 𝑛 free loops in 𝑆3, with generators the “leapfrog” motions and the symmetric exchanges. In recent work with Celeste Damiani and Paul Martin, we defined a family of finite dimensional quotients 𝐿𝐻𝑛 of 𝐿𝐵𝑛 via certain quadratic relations. The structure of these (non-semisimple) Loop Hecke Algebras is partially understood through (conjecturally faithful) representations obtained from a loop braided vector space, i.e. a pair (𝑆, 𝑅) of Yang–Baxter operators satisfying the appropriate mixed relations. One salient feature of the matrix 𝑅 is that it is charge conserving. This begs the question: can we classify charge conserving Yang–Baxter operators? Recently with Martin, we have found such a classification with a concise combinatorial description. In this talk, I will give an overview of these two projects. Time permitting we will circle back to the question of 𝐿𝐵𝑛 representations.

Organizers：Zhengwei Liu, Sebastien Palcoux, Yilong Wang, Jinsong Wu

2022-11-30 Wed

Differential calculus in vector bundles: a (graded) algebraic approach

BIMSA-BIT Differential Geometry SeminarSpeaker: Jacob Kryczka BIMSA

Time: 15:15-16:30

Venue: Online

Zoom: 559 700 6085（PW: BIMSA）

Abstract

We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras. In particular we will describe a special class of short exact sequences of such functors and discuss how they may be interpreted as higher order Atiyah sequences. Time permitting, we will interpret the corresponding notion of the Atiyah class in this setting.

Organizers：Kotaro Kawai, Sebastian Heller, Lynn Heller, Chao Qian

2022-11-30 Wed

A number theory problem arising in quantum information theory

Geometry and Gravitation SeminarSpeaker: Ingemar Bengtsson University of Stockholm

Time: 17:15-18:30

Venue: Online

Zoom: 839 2831 2262（PW: BIMSA）

Abstract

A maximal regular simplex inscribed in the set of quantum states has some engineering applications --- if it exists. Attempts to prove that it does, in all finite dimensional Hilbert spaces, have revealed an unexpected connection to an open problem in algebraic number theory. The whole story is quite new, and it it may have ramifications that we have not thought of yet.

Speaker Intro

"My name is Ingemar Bengtsson, and I have been a lecturer at Fysikum in Stockholm since '93 (and a professor since '00). My previous 'career' was at Chalmers, CERN and Imperial College. The research areas that I like the best usually have something to do with geometry. General relativity is a favourite. Most of my work there is on black holes. My strongest prejudice is that the world has four dimensions; this is the direction in which I look for clues about quantum gravity. Then I work on quantum information theory, since the geometry of the space of quantum states is wonderful and rather mysterious. What I find fascinating about relativity and quantum mechanics---as it happens, the two deepest theories we have---is that their basic equations have been around for a century, and yet they keep springing conceptual surprises on us. I am looking for the next surprise there, but I do keep a weather eye open on other subjects as well."

2022-12-01 Thu

BIMSA-Tsinghua Seminar on Machine Learning and Differential EquationsSpeaker: Jianwei Ma Peking University

Time: 10:00-11:30

Venue: Online

Zoom: 537 192 5549（PW: BIMSA）

Speaker Intro

Organizers：Fansheng Xiong, Wuyue Yang, Wen-An Yong, Yi Zhu

2022-12-01 Thu

Maximum entropy model and its application

Internal Seminar on Machine Learning and Differential EquationsSpeaker: Wuyue Yang BIMSA

Time: 14:00-16:00

Venue: Online

Zoom: 537 192 5549（PW: BIMSA）

Abstract

Entropy is an important concept in thermodynamics and statistical mechanics. Maximum entropy model (MaxEnt) is a method for solving probabilistic models. In this talk, I will introduce Maximum Entropy models and its applications in biology and other fields.

Speaker Intro

Organizers：Wuyue Yang, Fansheng Xiong, Xiaopei Jiao

2022-12-02 Fri

Mathematics of topological quantum computing

YMSC-BIMSA Quantum Information SeminarSpeaker: Xingshan Cui Purdue University

Time: 09:30-11:00

Venue: 清华大学近春园西楼一层报告厅

Tencent: 337 8937 1456

Abstract

Topological quantum computing (TQC) is among the best approaches to building a large-scale fault-tolerant quantum computer. The quantum media for TQC are topological phases of matter that harbor non-Abelian anyons and quantum gates are implemented by braiding of anyons. The mathematics of topological phases of matter is described by modular tensor categories or equivalently by topological quantum field theories. We give a review on the rich interactions between TQC and the various subjects mentioned above. We illustrate the concept of TQC with an important class of anyons, namely, metaplectic anyons, and show that braidings of anyons assisted by certain topologically protected measurements is universal for quantum computing. The interest in metaplectic anyons arises from the potential physical realization in fractional quantum Hall systems. Some related questions on universality of anyons will also be addressed.

Organizers：Zhengwei Liu

2022-12-02 Fri

Suspension Homotopy of 4-manifolds And the Second 2-local Cohomotopy Sets

Math and Biology SeminarSpeaker: Pengcheng Li Southern University of Science and Technology

Time: 10:30-11:30

Venue: Online

Zoom: 293 812 9202（PW: BIMSA）

Abstract

In this talk we study the homotopy type of the (double) suspension of an orientable, closed, connected $4$-manifold $M$, whose integral homology can have $2$-torsion. This gives a complete solution to a prior research problem of So and Theriault. Moreover, the decomposition results are applied to give a characterization of the second $2$-local cohomotopy set $\pi^2(M;\mathbb{Z}_{(2)})$, which is the set of homotopy classes of based maps from $M$ into the $2$-local sphere $S^2_{(2)}$.

Organizers：Jie Wu, Jingyan Li, Xiang Liu, Fedor Pavutnitskiy

• ### BIMSA一周学术报告预告 11.21-11.25

2022-11-21 MonThe $Delta$-twisted homology and fiber bundle structure of twisted simplicial setsBIMSA Topology SeminarSpeaker: Mengmeng Zhang Hebei Normal University and BIMSATime: 15:30-17:00 Venue: 1129B Zoom: 537 192 5549（PW: BIMSA）AbstractIn this talk, I will give a brief introduction for simplicial set theory. Then I will report our recent progress for unifying $delta$-homology, introduc...

• ### BIMSA一周学术报告预告 11.7-11.11

2022-11-07A Geometric Model for the Module Category of a Skew-gentle AlgebraBIMSA Topology Seminar报告人 何平 BIMSA时 间 15:30-17:00 Mon地 点 1129BZoom 537 192 5549（PW: BIMSA）摘要The main object of this report is to give a geometric model for the module category of a skew-gentle algebra via a partial ideal/tagged triangulation on a puncture marked surface. On the one hand, by using this model...