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# Departmental 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 Parker Hall, Room 250 (unless otherwise advertised) with refreshments preceding at 3:30pm in Parker Hall, Room 244.

**DMS Colloquium: Mark Walker**

**Dec 03, 2021 04:00 PM**

Speaker: **Mark Walker** (Willa Cather Professor, University of Nebraska--Lincoln)

Title: The Total and Toral Rank Conjectures

Abstract: Assume \(X\) is a nice topological space (a compact \(CW\) complex) that admits a fixed-point free action by a \(d\)-dimensional torus \(T\). For example, \(X\) could be \(T\) acting on itself in the canonical way. The Toral Rank Conjecture, due to Halperin, predicts that the sum of the (topological) Betti numbers of \(X\) must be at least \(2^d\). Put more crudely, this conjecture predicts that it takes at least \(2^d\) cells to build such a space \(X\) by gluing them together.

Now suppose \(M\) is a module over the polynomial ring \(k[x_1, \dots, x_d]\) that is finite dimensional as a \(k\)-vector space. The Total Rank Conjecture, due to Avramov, predicts that the sum of (algebraic) Betti numbers of \(M\) must be at least \(2^d\). Here, the algebraic Betti numbers refer to the ranks of the free modules occurring in the minimal free resolution of \(M\).

In this talk, I will discuss the relationship between these conjectures and recent progress toward settling them.

Faculty host: Michael Brown

**DMS Colloquium: Dr. Xuyu Wang**

**Nov 05, 2021 04:00 PM**

Speaker: **Dr. Xuyu Wang** (Assistant Professor at California State University, Sacramento)

Title: Artificial Intelligence of Things for Robust Wireless Sensing Systems

Abstract: With the development of Internet of Things (IoT) and wireless techniques, several wireless signals (e.g., Wi-Fi, RFID, Acoustic, Radar, and LoRa) can be exploited for wireless sensing applications. Artificial Intelligence of Things (AIoT) is an integrative technology, which could leverage artificial intelligence (e.g., deep learning) to develop data-driven IoT applications. To address some fundamental challenges (e.g., black-box model, limited labeled data, different data domains) in deep learning-driven wireless sensing systems, in this talk, I will mainly discuss three robust wireless sensing systems (i.e., deep Gaussian processes for indoor localization, recurrent variational autoencoder for human health monitoring, and meta-learning for human pose estimation) using different wireless IoT devices.

Faculty host: Guanqun Cao

**DMS Colloquium: Hanwen Huang**

**Oct 22, 2021 04:00 PM**

Speaker: **Hanwen Huang** (College of Public Health, University of Georgia)

Title: LASSO risk and phase transition under dependence

For general covariance matrix, we derive the asymptotic risk of LASSO in the limit of both sample size n and dimension p going to infinity with fixed ratio n/p. A phase boundary is precisely established in the phase space. Above this boundary, LASSO perfectly recovers the signals with high probability. Below this boundary, LASSO fails to recover the signals with high probability. While the values of the non-zero elements of the signals do not have any effect on the phase transition curve, our analysis shows that the curve does depend on the signed pattern of the nonzero values of the signal for non-i.i.d. covariance matrix. Underlying our formalism is a recently developed efficient algorithm called approximate message passing (AMP) algorithm. We generalize the state evolution of AMP from i.i.d. case to general case. Extensive computational experiments confirm that our theoretical predictions are consistent with simulation results on moderate size system.

Faculty host: Peng Zeng

**DMS Colloquium: Ivan Yotov**

**Mar 26, 2021 04:00 PM**

Speaker: **Ivan Yotov** (University of Pittsburgh, http://www.math.pitt.edu/~yotov/)

Title: Stokes-Biot modeling of fluid-poroelastic structure interaction

Abstract: We study mathematical models and their finite element approximations for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic material. Applications of interest include flows in fractured poroelastic media, coupling of surface and subsurface flows, and arterial flows. The free fluid flow is governed by the Navier-Stokes or Stokes/Brinkman equations, while the poroelastic material is modeled using the Biot system of poroelasticity. The two regions are coupled via dynamic and kinematic interface conditions, including balance of forces, continuity of normal velocity, and no-slip or slip with friction tangential velocity condition. Well-posedness of the weak formulations is established using techniques from semigroup theory for evolution PDEs with monotone operators. Mixed finite element methods are employed for the numerical approximation. Solvability, stability, and accuracy of the methods are analyzed with the use of suitable discrete inf-sup conditions. Numerical results will be presented to illustrate the performance of the methods, including their flexibility and robustness for several applications of interest.

Brief Bio:

Dr. Ivan Yotov is a Professor in the Department of Mathematics at the University of Pittsburgh. He received his Ph.D. in 1996 from Rice University. Dr. Yotov’s research interests are in the numerical analysis and solution of partial differential equations and large scale scientific computing with applications to fluid flow and transport. His current research focus is on the design and analysis of accurate multiscale adaptive discretization techniques (mixed finite elements, finite volumes, finite differences) and efficient linear and nonlinear iterative solvers (domain decomposition, multigrid, Newton-Krylov methods) for massively parallel simulations of coupled multiphase porous media and surface flows. Other areas of research interest include estimation of uncertainty in stochastic systems and mathematical and computational modeling for biomedical applications. Dr. Yotov is also an adjunct faculty at the McGowan Institute for Regenerative Medicine.

Faculty host: Thi-Thao-Phuong Hoang

Zoom link: https://auburn.zoom.us/j/84763379682

**DMS Colloquium: Dr. Shan Yu**

**Mar 19, 2021 04:00 PM**

**Dr. Shan Yu**(University of Virginia)

Title: Sparse Modeling of Functional Linear Regression via Fused Lasso with Application to Genotype-by-Environment Interaction Studies

Abstract: The estimator of coefficient functions in a functional linear model (FLM) based on a small number of subjects is often inefficient. To address this challenge, we propose an FLM based on fused learning. This talk will describe a sparse multi-group FLM to simultaneously estimate multiple coefficient functions and identify groups such that coefficient functions are identical within groups and distinct across groups. By borrowing information from relevant subgroups of subjects, our method enhances estimation efficiency while preserving heterogeneity in model parameters and coefficient functions. We use an adaptive fused lasso penalty to shrink coefficient estimates to a common value within each group. To enhance computation efficiency and incorporate neighborhood information, we propose to use a graph-constrained adaptive lasso with a highly efficient algorithm. This talk will use two real data examples to illustrate the applications of the proposed method on genotype-by-environment interaction studies.

This talk features joint work with Aaron Kusmec, Lily Wang, and Dan Nettleton.

Brief Bio:

Dr. Shan Yu is an Assistant Professor in the Department of Statistics at the University of Virginia. Her research interests include Non-/Semi-Parametric Regression Methods, Functional Data Analysis, Spatial/Spatiotemporal Data Analysis, Statistical Methods for Neuroimaging Data, and Variable Selection for High Dimensional Data. Shan's research has appeared in such journals as the *Journal of the American Statistical Association* and *Statistica Sinica*. She earned a Ph.D. in Statistics from Iowa State University in 2020. She joined the University of Virginia in 2020.

Host: Guanqun Cao

Zoom link: https://auburn.zoom.us/j/4026989542

**DMS Colloquium: Aris Winger**

**Feb 26, 2021 04:00 PM**

Speaker: **Aris Winger** (Georgia Gwinnett College)

Title: Equity and Advocating in the Mathematics Classrooms and Departments

Abstract: How do we create mathematical spaces within our classroom that validate and value all students? What are the steps that we can personally take that will transform the mathematical experience in our classroom for marginalized students? In this talk, participants will engage in an interactive conversation about the challenges presented when we start to radically imagine different mathematical spaces from one where, for too long, have been marginalizing for too many people.

Dr. Winger also has a **new book out** about **advocating for students of color in mathematics**. Here is the link for this book : https://www.amazon.com/dp/B08QC3SHFG/ref=cm_sw_em_r_mt_dp_cD37FbHZ6ZRJD in case you would like to pick up the book.

Zoom link: https://auburn.zoom.us/j/83289004804

Zoom host: Nedret Billor

Note from host: As you may already know that we have an ongoing collaborative NSF project led by CU Denver, University of Memphis, and AU (led by Rodger, Stone, Merchant, and Billor), titled **Promoting Success in Undergraduate Mathematics through Graduate Teacher Training** (PSUM-GTT) since 2019 in our department. As a part of this project, we have scheduled several Auburn critical issues seminar series which would be beneficial for all of us in our department. The first Zoom seminar will be given by Dr. Aris Winger from Georgia Gwinnett College.

Last Updated: 09/11/2015