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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: 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.

**DMS Colloquium: Gregory Puleo**

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

Speaker: **Gregory Puleo**

Title: A story about graph saturation

Abstract: The classical extremal problem in graph theory asks: given some graph \(H\), what is the largest number of edges in an \(n\)-vertex graph with no subgraph isomorphic to \(H\)? In this talk, we will discuss the saturation problem in graph theory, a variant on the classical extremal problem. In contrast to the extremal problem, for which powerful general results are known, relatively little is known about graph saturation. While general upper bounds on the saturation number are known, a nontrivial lower bound has been elusive. Recently, Alex Cameron and I succeeded at proving a lower bound on the saturation number that is asymptotically sharp on a large class of graphs. I will discuss both the mathematical details of this result and the story of how it came to be.

**DMS Colloquium: Thi-Thao-Phuong Hoang**

**Feb 12, 2021 04:00 PM**

Speaker: **Thi-Thao-Phuong Hoang**

Title: Efficient time-stepping methods for nonlinear evolution problems

Abstract: Numerical modeling of geophysical flows is challenging due to the presence of various coupled processes that occur at different spatial and temporal scales. It is critical for the numerical schemes to efficiently capture such a wide range of scales in both space and time to produce accurate and robust simulations over long time horizons. In this talk, I will present advanced time-stepping methods for the rotating shallow water equations discretized on spatial meshes with variable resolutions. Two different approaches will be considered, and both allow spatially dependent time step sizes to be used for time integration in different regions of the computational domain. The first approach is a fully explicit local time-stepping algorithm based on strong stability preserving Runge-Kutta schemes. The second approach, namely the localized exponential time differencing method, is based on spatial domain decomposition and exponential time integrators, which makes possible the use of much larger time step sizes compared to explicit schemes and avoids solving nonlinear systems. Numerical results on various test cases are presented to demonstrate the performance of the proposed methods.

**DMS Colloquium: W. James Lewis**

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

Speaker: **W. James "Jim" Lewis** (University of Nebraska-Lincoln)

Title: The Role of the Mathematics Department in the Mathematical Education of Teachers

Abstract: The AMS publication *Towards Excellence: Leading a Doctoral Mathematics Department in the 21st Century* opens with the sentence, “We have a simple message: To ensure their institution’s commitment to excellence in mathematics research, doctoral departments must pursue excellence in their instructional programs.” The CBMS publication *The Mathematical Education of Teachers II* recommends that at institutions that prepare teachers, teacher education should be “an important part of a mathematics department’s mission.”

In this talk, we will report on work at the University of Nebraska-Lincoln to improve the mathematical education of teachers as well as efforts to improve how we teach mathematics to freshmen.

**Zoom link: aub.ie/lewis (835 7247 0290)**

**Brief BIO**:

Last Updated: 09/11/2015