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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: 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.

Sep 23, 2022 04:00 PM

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.

DMS Colloquium: Dr. T. T. Phuong Hoang

Sep 02, 2022 04:00 PM

Speaker: Dr. T. T. Phuong Hoang (Auburn)

Title: Global-in-time domain decomposition methods for coupled problems in heterogeneous porous media

Abstract:  Global-in-time domain decomposition (DD) methods are iterative algorithms that solve time-dependent problems in the subdomains over the whole time interval and exchange data on the space-time interfaces between the subdomains. These methods can be seen as a combination of the classical waveform relaxation method (for a large system of ODEs) and standard DD algorithms for steady-state problems. The global-in-time DD approach is very well suited to multiscale multiphysics problems as it allows the use of local discretizations in both space and time in different regions of the computational domain.

In this talk, we introduce the mathematical concepts of DD methods for evolution equations and present our work on global-in-time DD for the coupling of surface and subsurface flows as well as flow in fractured porous media. Both mathematical analysis and numerical performance of the proposed methods with nonconforming time grids will be investigated.

DMS Colloquium: Dr. Ted Kilgore

Aug 26, 2022 04:00 PM

NOTE NEW LOCATION

Refreshments 244 Parker Hall at 3:15

Speaker: Dr. Theodore Kilgore (Auburn University)

Title: The weighted Weierstrass Theorem for continuous functions defined on$$[0,\infty)$$ or on $$(-\infty, \infty)$$, proved using Bernstein-Chlodovski operators

Abstract:  here

Last Updated: 09/06/2022