Posted March 21, 2025
Last modified March 25, 2025
Control and Optimization Seminar Questions or comments?
9:30 am – 10:20 am Note the Special Earlier Seminar Time For Only This Week. This is a Zoom Seminar. Zoom (click here to join)
Denis Dochain, Université Catholique de Louvain
IEEE Fellow, IFAC Fellow
Automatic Control and Biological Systems
This talk aims to give an overview of more than 40 years of research activities in the field of modelling and control of biological systems. It will cover different aspects of modelling, analysis, monitoring and control of bio-systems, and will be illustrated by a large variety of biological systems, from environmental systems to biomedical applications via food processes or plant growth.
Posted March 21, 2025
Combinatorics Seminar Questions or comments?
11:30 am – 12:30 pm Zoom Link
Jorn van der Pol, University of Twente
Turán densities for matroid basis hypergraph
What is the maximum number of bases of an n-element, rank-r matroid without a given uniform matroid U as a minor? This question arises in the problem of determining the Turán density of daisy-hypergraphs. Ellis, Ivan, and Leader recently showed that this density is positive, thus disproving a conjecture by Bollobás, Leader, and Malvenuto. Their construction is a matroid basis hypergraph, and we show that their construction is best-possible within the class of matroid basis hypergraphs. This is joint work with Zach Walsh and Michael C. Wigal.
Posted September 19, 2024
Last modified October 25, 2024
Colloquium Questions or comments?
3:30 pm Lockett 232
Bogdan Suceava, California State University Fullerton
TBD
Posted March 16, 2025
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Justin Lanier, University of Sydney
TBA
TBA
Posted February 3, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Adithyan Pandikkadan, Louisiana State University
TBD
Posted March 8, 2025
Last modified March 9, 2025
Tomoyuki Kakehi, University of Tsukuba
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation
In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and call the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows. {\bf Theorem.} We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution. We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
Posted March 9, 2025
3:30 pm – 4:30 pm TBA
Tomoyuki Kakehi, University of Tsukuba
Inversion formulas for Radon transforms and mean value operators on the sphere
This talk consists of two parts. In the first part, we explain the Radon transfrom associated with a double fibration briefly and then we introduce several inversion formulas. In the second part, we deal with the mean value operator $M^r$ on the sphere. Here we define $M^r: C^{\infty} (\mathbb{S}^n) \to C^{\infty} (\mathbb{S}^n)$ by $$ M^r f (x) = \frac{1}{\mathrm{Vol} (S_r (x))} \int_{y \in S_r (x)} f(y) d\mu(y), \qquad f \in C^{\infty} (\mathbb{S}^n), $$ where $S_r (x)$ is the geodesic sphere with radius $r$ and center $x$ and $d\mu$ is the measure on $S_r (x)$ induced from the canonical measure on $\mathbb{S}^n$. We will give conditions on $r$ for $M^r$ being injective or surjective. For example, in the case $n=3$, $M^r$ is injective but not surjective if and only if $r/\pi$ is a Liouville number. We will also give some related results on Gegenbauer polynomials. This is a joint work with J. Christensen, F. Gonzalez, and J. Wang.
Posted November 7, 2024
Last modified March 13, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Irena Lasiecka, University of Memphis
AACC Bellman Control Heritage Awardee, AMS Fellow, SIAM Fellow, and SIAM Reid Prize Awardee
Mathematical Theory of Flow-Structure Interactions
Flow-structure interactions are ubiquitous in nature and in everyday life. Flow or fluid interacting with structural elements can lead to oscillations, hence impacting stability or even safety. Thus problems such as attenuation of turbulence or flutter in an oscillating structure (e.g., the Tacoma bridge), flutter in tall buildings, fluid flows in flexible pipes, nuclear engineering flows about fuel elements, and heat exchanger vanes are just a few prime examples of relevant applications which place themselves at the frontier of interests in applied mathematics. In this lecture, we shall describe mathematical models describing the phenomena. They are based on a 3D linearized Euler equation around unstable equilibria coupled to a nonlinear dynamic elasticity on a 2D manifold. Strong interface coupling between the two media is at the center of the analysis. This provides for a rich mathematical structure, opening the door to several unresolved problems in the area of nonlinear PDEs, dynamical systems, related harmonic analysis, and differential geometry. This talk provides a brief overview of recent developments in the area, with a presentation of some new methodology addressing the issues of control and stability of such structures. Part of this talk is based on recent work with D. Bonheur, F. Gazzola and J. Webster (in Annales de L’Institute Henri Poincare Analyse from 2022), work with A. Balakrishna and J. Webster (in M3AS in 2024), and also work completed while the author was a member of the MSRI program "Mathematical problem in fluid dynamics" at the University of California Berkeley (sponsored by NSF DMS -1928930).
Posted January 21, 2025
Combinatorics Seminar Questions or comments?
3:30 pm – 4:30 pm Zoom Link
Joseph Bonin, George Washington University
Results on positroids from the perspective of structural matroid theory
A matroid of rank $r$ on $n$ elements is a positroid if it has a representation by an $r$ by $n$ matrix over $\mathbb{R}$ with the property that the determinant of each $r$ by $r$ submatrix is nonnegative. Positroids are commonly studied through the lens of algebraic combinatorics, where a fixed linear order on the ground set is regarded as part of the positroid. We focus on the matroid structure per se, without a priori fixing a linear order on the ground set. A number of earlier characterizations of positroids involve connected flats and non-crossing partitions; we provide a new characterization of a similar flavor and discuss some of its applications. One application is finding conditions under which two positroids can be glued together along a common restriction, in the freest way possible, to yield another positroid: for instance, if $M$ and $N$ are positroids and the intersection of their ground sets is an independent set and a set of clones in both $M$ and $N$, then the free amalgam of $M$ and $N$ is a positroid (that encompasses parallel connections and much more). Also, the class of positroids is minor-closed, and we identify many multi-parameter infinite families of excluded minors for this class, while more excluded minors remain to be discovered.
Posted February 21, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
John Jairo Lopez, Tulane University
Title TBA
Abstract TBA (Host: Stephen Shipman)
Posted January 26, 2025
Last modified February 12, 2025
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Kairi Black, Duke University
TBA
Posted February 3, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Matthew Lemoine, Louisiana State University
TBD
Posted February 4, 2025
Last modified February 10, 2025
Geometry and Topology Seminar Seminar website
Lockett 233
Matthew Haulmark, Cornell University
TBA
Posted February 10, 2025
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Joshua Mundinger, University of Wisconsin
TBA
Posted March 25, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm – 4:20 pm Lockett 232
Robert Lipton, Mathematics Department, LSU
Dynamic Fast Crack Growth
Nonlocal modeleling for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. The material displacement field is uniquely determined by the initial boundary value problem. The theory naturally satisfies energy balance, with positive energy dissipation rate in accord with the Clausius-Duhem inequality. Notably, these properties are not imposed but follow directly from the constitutive law and evolution equation. The limit of vanishing non-locality is analized using simple arguments from geometric measure theory to identify the limit damage energy and weak convergence methods of pde to identify the limit solution. The limiting energy is the Grifith fracture energy. The limit evolution is seen to be a weak solution for the wave equation on a time dependent domain. The exsistence theory for such solutions was recently developed in Dal Maso and Toader, J. Differ. Equ. 266, 3209–3246 (2019).
Posted February 3, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Nilangshu Bhattacharyya, Louisiana State University
TBD
Posted January 27, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Galen Dorpalen-Barry, Texas A&M
TBA
Posted January 10, 2025
Last modified March 26, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Carolyn Beck, University of Illinois Urbana-Champaign
IEEE Fellow
Discrete State System Identification: An Overview and Error Bounds
Classic system identification methods focus on identifying continuous-valued dynamical systems from input-output data, where the main analysis of such approaches largely focuses on asymptotic convergence of the estimated models to the true models, i.e., consistency properties. More recent identification approaches have focused on sample complexity properties, i.e., how much data is needed to achieve an acceptable model approximation. In this talk I will give a brief overview of classical methods and then discuss more recent data-driven methods for modeling continuous-valued linear systems and discrete-valued dynamical systems evolving over networks. Examples of the latter systems include the spread of viruses and diseases over human contact networks, the propagation of ideas and misinformation over social networks, and the spread of financial default risk between banking and economic institutions. In many of these systems, data may be widely available, but approaches to identify relevant mathematical models, including underlying network topologies, are not widely established or agreed upon. We will discuss the problem of modeling discrete-valued, discrete-time dynamical systems evolving over networks, and outline analysis results under maximum likelihood identification approaches that guarantee consistency conditions and sample complexity bounds. Applications to the aforementioned examples will be further discussed as time allows.
Posted December 10, 2024
Last modified January 5, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett
Yuanzhen Shao, University of Alabama
Some recent developments in the study of magnetoviscoelastic fluids
In this talk, we consider the motion of a magnetoviscoelastic fluid in a nonisothermal environment. When the deformation tensor field is governed by a regularized transport equation, the motion of the fluid can be described by a quasilinear parabolic system. We will establish the local existence and uniqueness of a strong solution. Then it will be shown that a solution initially close to a constant equilibrium exists globally and converges to a (possibly different) constant equilibrium. Further, we will show that that every solution that is eventually bounded in the topology of the natural state space exists globally and converges to the set of equilibria. If time permits, we will discuss some recent advancements regarding the scenario where the deformation tensor is modeled by a transport equation. In particular, we will discuss the local existence and uniqueness of a strong solution as well as global existence for small initial data.
Posted January 23, 2025
Last modified January 27, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Annette Karrer, The Ohio State University
TBA
Posted January 12, 2025
Last modified January 16, 2025
Zi Li Lim, UCLA
TBA
Posted January 16, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Bahman Gharesifard, Queen's University
TBA
Posted February 19, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Nina Amini, Laboratory of Signals and Systems, CentraleSupélec
TBA
Posted March 16, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm TBATBA