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# Colloquia

Our department is proud to host weekly colloquium talks featuring research by leading mathematicians from around the world. Most colloquia are held on Fridays at 4pm in ACLC, Room 010 (unless otherwise advertised) with refreshments preceding at 3:15pm in Parker Hall, Room 244.

**DMS Colloquium: Prof. Guillaume Bal**

**Dec 02, 2022 04:00 PM**

Speaker:** Prof. Guillaume Bal** (University of Chicago)

Title: Asymmetric transport and topological invariants

Abstract: The field of topological (acoustic, electromagnetic, electronic, mechanical) insulators analyzes asymmetric transport phenomena observed along interfaces that separate insulating bulks. It finds applications in many areas of physical and materials sciences. The topological nature of the asymmetric transport ensures that it persists in the presence of perturbations of the underlying model, which forms its main practical appeal.

A physical observable taking the form of an edge conductivity models the asymmetric transport of a system's Hamiltonian. To simplify the computation of this observable, we associate a natural Fredholm operator to the (partial differential) Hamiltonian and compute its topological charge by means of a Fedosov-H\"ormander formula, which implements in Euclidean space an Atiyah-Singer index theorem. We then relate the index of the Fredholm operator to a bulk-difference invariant, a Chern number, that is readily computable for a large class of problems. The main remaining difficulty is to equate the physical observable to the aforementioned index. The talk will present such a bulk-edge correspondence for a large class of Hamiltonians and sketch its derivation.

We then use the correspondence to compute the asymmetry in several settings, with applications in graphene-based regular and Floquet topological insulators as well as topological properties of twisted bilayer graphene. Time permitting, we will contrast the above spectral properties with the practically relevant temporal picture, in particular the propagation of semi-classical wavepackets along curved interfaces.

Faculty host: Junshan Lin

**DMS Colloquium: Dr. Matthew R. Ballard**

**Nov 04, 2022 04:00 PM**

Speaker: Dr. Matthew R. Ballard (University of South Carolina)

Title: How complex are modules over quotients of polynomial rings?

Abstract: From linear algebra, we know that a single number captures (most) everything about a finite-dimensional vector space. Adding the structure of commuting operators on top of the scalar action enriches the situation a good deal. In particular, building a module from the analogs of vector spaces (free modules) can be done with a finite amount of data but determining that data can be very complicated.

Faculty host: Michael Brown

**Brief Bio**: Matt is a professor at the University of South Carolina. He studies algebraic geometry, with a specific focus on mirror symmetry. Before starting at South Carolina, Matt obtained his Ph.D. at the University of Washington and was a post doc at the University of Pennsylvania, the University of Wisconsin, and the University of Vienna.

**DMS Colloquium: CANCELED**

**Sep 30, 2022 04:00 PM**

Speaker: **Dr. Dana Bartosova** (University of Florida)

Title: Model Theory in Ramsey Theory

Abstract: Classical finite Ramsey theorem states that for any natural number (m\leq n\) and a number of colours \(k\geq 2\), there is a natural number \(N\) such that whenever we colour \(m\)-tuples of \(\{1,2,\ldots, N\}\) by \(k\) colours, there is an \(n\)-element subset \(Y\) of \(\{1,2,\ldots, N\}\) whose all \(m\)-element subsets received the same colour. This theorem has generalizations in possibly every area of mathematics. In this talk, we will focus on structural Ramsey theory, which in place of finite sets speaks about finite structures in some first-order language, such as finite graphs, finite Boolean algebras, or finite vector spaces over finite fields.

I will talk about recent research in model-theoretic transfer principles of Ramsey properties between classes of finite structure (join work with Lynn Scow) and from classes of finite structures to their ultraproducts (AIMSQuaREs project with Mirna Dzamonja, Rehana Patel, and Lynn Scow).

**Bio**: Dana Bartosova obtained her undergraduate and master’s degree from the Charles University in Prague, as well as a master’s degree from the Free University of Amsterdam. She went on completing her Ph.D. degree at the University of Toronto in 2013. Dana had postdocs at a semester program at HIM institute in Bonn, University of Sao Paulo and Carnegie-Mellon University, and since 2018 she has been an assistant professor at the University of Florida. Her research is supported by an individual NSF grant and an NSF CAREER grant. She is also the co-founder of Math Parents Coffee and the director of UF Math Circle.

**DMS Colloquium: Dr. Henry Adams**

**Sep 23, 2022 04:00 PM**

Speaker: **Dr. Henry Adams** (Colorado State University)

Title: What are Gromov-Hausdorff distances?

Abstract: The Gromov-Hausdorff distance is a notion of dissimilarity between two datasets or between two metric spaces. It is an important tool in geometry, but notoriously difficult to compute. In the first part of my talk, I will give an introduction to Gromov-Hausdorff distances. Then, in the second part of my talk, I will use tools from applied topology to give (potentially tight) lower bounds on the Gromov-Hausdorff distance between unit spheres of different dimensions. This is joint work in a polymath-style project with many people who are currently or formerly at Colorado State, Ohio State, Carnegie Mellon, or Freie Universität Berlin.

Faculty host: Dr. Ziqin Feng

**DMS Colloquium: Dr. Junshan Lin**

**Sep 16, 2022 04:00 PM**

Speaker: **Dr. Junshan Lin** (Auburn)

Abstract: The advance in fabrication technology allows for the manipulation of electromagnetic waves at various scales by novel materials and devices. The applications of these materials and devices in physics and engineering have driven the need for mathematical studies to guide their experimental designs. In particular, rigorous mathematical theories need to be established to understand new types of wave-matter interactions; efficient computational methods need to be developed for the modeling of wave phenomena in complex media and solving related inverse problems for their applications.

In this talk, I will first give an overview of my research along this direction. Then I will exemplify how mathematical research contributes to these aspects by using one specific project on resonant wave scattering in subwavelength structures (structures with features much smaller than the operating wavelength). I will present quantitative mathematical theories for various resonance phenomena arising in different subwavelength structures and fast numerical methods for their computational modeling. I will also introduce the mathematical framework for the application of resonances in biosensing and imaging.

**DMS Colloquium: Dr. Guanqun Cao**

**Sep 09, 2022 04:00 PM**

Speaker: **Dr. Guanqun Cao** (Auburn)

Title: Statistical Learning for Next-Generation Complex Data Analysis

Abstract: In the era of big data, advancements of modern technology have enabled the collection of sophisticated and ultra-high dimensional data sets, such as spatial data, 2D/3D images, and other objects. Most existing approaches, such as standard nonparametric smoothing, empirical likelihood, and quadratic discriminant analysis, perform well only under relatively simple data structure framework and strong assumptions. In this talk, I overview my recent research on the statistical learning for complex data analysis from three fundamental areas: regression, inference, and classification. In particular, newly developed varying coefficient Geo models, deep learning based multi-dimensional functional data regression, and classification methods will be presented.

Last Updated: 09/06/2022