Posted September 6, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm - 2:30 pm Lockett 233
Nilangshu Bhattacharyya, Louisiana State University

Characteristic Classes - Lecture 3

Posted September 6, 2023

Last modified September 22, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Ana Bălibanu, Louisiana State University

Moment maps and multiplicative reduction

Symplectic reduction is a process that eliminates the symmetries of a Poisson manifold equipped with a Hamiltonian group action. Many algebraic varieties which are of interest to representation theory arise as reductions of symplectic spaces associated to algebraic groups. We introduce several new reduction procedures, some of which are multiplicative analogues of ”classical” examples of symplectic reduction. This is joint work with Maxence Mayrand.

Posted August 30, 2023

Last modified September 1, 2023

Xiaoqi Huang, Louisiana State University

Curvature and growth rates of log-quasimodes on compact manifolds

We will discuss the relation between curvature and L^q norm estimates of spectral projection operators on compact manifolds. We will present a new way that one can hear the shape of a connected compact manifold of constant sectional curvatures, if the shape refers to curvature, and the radios used are the L^q norm of quasimodes. This is based on ongoing work with Christopher Sogge.

Posted August 30, 2023

Last modified September 18, 2023

Xiaoqi Huang, Louisiana State University

Curvature and growth rates of log-quasimodes on compact manifolds

We will discuss the relation between curvature and L^q norm estimates of spectral projection operators on compact manifolds. We will present a new way that one can hear the shape of a connected compact manifold of constant sectional curvatures, if the shape refers to curvature, and the radios used are the L^q norm of quasimodes. This is based on ongoing work with Christopher Sogge.

Posted September 18, 2023

Colloquium Questions or comments?

3:30 pm - 4:20 pm Lockett 232
Wilhelm Schlag, Yale University

Lyapunov exponents, Schrödinger cocycles, and Avila’s global theory

In the 1950s Phil Anderson made a prediction about the effect of random impurities on the conductivity properties of a crystal. Mathematically, these questions amount to the study of solutions of differential or difference equations and the associated spectral theory of self-adjoint operators obtained from an ergodic process. With the arrival of quasicrystals, in addition to random models, nonrandom lattice models such as those generated by irrational rotations or skew-rotations on tori have been studied over the past 30 years. By now, an extensive mathematical theory has developed around Anderson’s predictions, with several questions remaining open. This talk will attempt to survey certain aspects of the field, with an emphasis on the theory of SL(2,R) cocycles with an irrational or Diophantine rotation on the circle as base dynamics. In this setting, Artur Avila discovered about a decade ago that the Lyapunov exponent is piecewise affine in the imaginary direction after complexification of the circle. In fact, the slopes of these affine functions are integer valued. This is easy to see in the uniformly hyperbolic case, which is equivalent to energies falling into the gaps of the spectrum, due to the winding number of the complexified Lyapunov exponent. Remarkably, this property persists also in the non-uniformly hyperbolic case, i.e., on the spectrum of the Schrödinger operator. This requires a delicate continuity property of the Lyapunov exponent in both energy and frequency. Avila built his global theory (Acta Math. 2015) on this quantization property. I will present some recent results with Rui HAN connecting Avila’s notion of acceleration (the slope of the complexified Lyapunov exponent in the imaginary direction) to the number of zeros of the determinants of finite volume Hamiltonians relative to the complex toral variable. This connection allows one to answer questions arising in the supercritical case of Avila’s global theory concerning the measure of the second stratum, Anderson localization on this stratum, as well as settle a conjecture on the Hölder regularity of the integrated density of states.

Posted August 18, 2023

Last modified September 11, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Cristina Pignotti, Università degli Studi dell'Aquila

Consensus Results for Hegselmann-Krause Type Models with Time Delay

We study Hegselmann-Krause (HK) opinion formation models in the presence of time delay effects. The influence coefficients among the agents are nonnegative, as usual, but they can also degenerate. This includes, e.g., the case of on-off influence, namely the agents do not communicate over some time intervals. We give sufficient conditions ensuring that consensus is achieved for all initial configurations. Moreover, we analyze the continuity type equation obtained as the mean-field limit of the particle model when the number of agents goes to infinity. Finally, we analyze a control problem for a delayed HK model with leadership and design a simple control strategy steering all agents to any fixed target opinion.

Posted September 25, 2023

Combinatorics Seminar Questions or comments?

2:30 pm - 3:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)
Xiaonan Liu, Vanderbilt University

Counting Hamiltonian cycles in planar triangulations

Whitney showed that every planar triangulation without separating triangles is Hamiltonian. This result was extended to all $4$-connected planar graphs by Tutte. Hakimi, Schmeichel, and Thomassen showed the first lower bound $\log _2 n$ for the number of Hamiltonian cycles in every $n$-vertex $4$-connected planar triangulation and, in the same paper, they conjectured that this number is at least $2(n-2)(n-4)$, with equality if and only if $G$ is a double wheel. We show that every $4$-connected planar triangulation on $n$ vertices has $\Omega(n^2)$ Hamiltonian cycles. Moreover, we show that if $G$ is a $4$-connected planar triangulation on $n$ vertices and the distance between any two vertices of degree $4$ in $G$ is at least $3$, then $G$ has $2^{\Omega(n^{1/4})}$ Hamiltonian cycles. Joint work with Zhiyu Wang and Xingxing Yu.

Posted September 24, 2023

Algebra and Number Theory Seminar Questions or comments?

3:20 pm - 4:10 pm Lockett 233 or click here to attend on Zoom
Cheng Chen, University of Minnesota

TBA

Posted September 6, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm - 2:30 pm Lockett 233
Colton Sandvick, Louisiana State University

Characteristic Classes - Lecture 4

Posted August 23, 2023

Last modified September 25, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Yuan Yao, Sorbonne University

Morse-Bott theory and embedded contact homology

I will give an overview of embedded contact homology as a Floer theory that counts pseudo-holomorphic curves asymptotic to Reeb orbits. Then I shall explain how to compute this homology theory in the Morse-Bott setting, via an enumeration of J-holomorphic cascades

Posted September 26, 2023

Probability Seminar Questions or comments?

3:30 am Lockett 232
Jing Wang, Purdue University

TBA

Posted September 25, 2023

Applied Analysis Seminar Questions or comments?

9:00 am Zoom (email dmassatt@lsu.edu for link)TBA

Posted September 24, 2023

Algebra and Number Theory Seminar Questions or comments?

3:20 pm - 4:10 pm Lockett 233 or click here to attend on Zoom
Tewodros Amdeberhan, Tulane University

TBA

Posted September 6, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm - 2:30 pm Lockett 233
Krishnendu Kar, Louisiana State University

TBA

Posted August 20, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Wenyuan Li, Northwestern University

TBA

Posted September 12, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Melvin Leok, University of California, San Diego

TBA

Posted August 14, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm - 3:20 pm Lockett 233
Konstantin Aleshkin, Columbia University

TBA

Posted September 5, 2023

Applied Analysis Seminar Questions or comments?

3:30 pm Zoom
Camil Muscalu, Cornell University

TBA

Posted September 11, 2023

3:30 pm TBA
Allison Miller, Swarthmore

TBA

Posted September 4, 2023

Algebra and Number Theory Seminar Questions or comments?

2:30 pm - 3:20 pm Lockett 233 or click here to attend on Zoom
Tong Liu, Purdue University

TBA

Posted September 11, 2023

3:30 pm TBA
Allison Miller, Swarthmore

TBA

Posted September 6, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm - 2:30 pm Lockett 233
Megan Fairchild, Louisiana State University

TBA

Posted August 17, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Laura Wakelin, Imperial College London

TBA

Posted August 22, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Eduardo Cerpa, Pontificia Universidad Católica de Chile
SIAM Activity Group on Control and Systems Theory Prize Recipient

Control and System Theory Methods in Neurostimulation

Electrical stimulation therapies are used to treat the symptoms of a variety of nervous system disorders. Recently, the use of high frequency signals has received increased attention due to its varied effects on tissues and cells. In this talk, we will see how some methods from Control and System Theory can be useful to address relevant questions in this framework when the FitzHugh-Nagumo model of a neuron is considered. Here, the stimulation is through the source term of an ODE and the level of neuron activation is associated with the existence of action potentials which are solutions with a particular profile. A first question concerns the effectiveness of a recent technique called interferential currents, which combines two signals of similar kilohertz frequencies intended to activate deeply positioned cells. The second question is about how to avoid the onset of undesirable action potentials originated when signals that produce conduction block are turned on. We will show theoretical and computational results based on methods such as averaging, Lyapunov analysis, quasi-static steering, and others.

Posted August 16, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm - 3:20 pm Lockett 233
Kendric Schefers, UC Berkeley

TBA

Posted December 9, 2022

Last modified September 5, 2023

Applied Analysis Seminar Questions or comments?

3:30 pm Lockett Hall 233 and Zoom
Nicolas Meunier, LaMME, Universite Evry Val D'Essonne

TBA

Posted September 4, 2023

Algebra and Number Theory Seminar Questions or comments?

3:20 pm - 4:10 pm Lockett 233 or click here to attend on Zoom
Micah Milinovich, University of Mississippi

TBA

Posted September 25, 2023

Probability Seminar Questions or comments?

3:30 pm Lockett 232
Chuntian Wang, University of Alabama

On the impact of spatially heterogeneous human behavioral factors on 2D dynamics of infectious diseases

It is well observed that human natural and social behavior have non-negligible impacts on spread of contagious disease. For example, large scaling gathering and high level of mobility of population could lead to accelerated disease transmission, while public behavioral changes in response to pandemics may reduce infectious contacts. In order to understand spatial characteristics of epidemic outbreaks like clustering, we formulate a stochastic-statistical epidemic environment-human-interaction dynamic system, which will be called as SEEDS. In particular, a 2D agent-based biased-random-walk model with SEAIHR compartments set on a two-dimensional lattice is constructed. Two environment variables are taken into consideration to capture human natural and social behavioral factors, including population crowding effects, and public preventive measures in the presence of contagious transmissions. These two variables are assumed to guide and bias agent movement in a combined way. Numerical investigations imply that controlling mass mobility or promoting disease awareness can impede a global-scale spatial population aggregation to form, and consequently suppress disease outbreaks. Importance of coordinated public-health interventions and public compliance to these measures are explicitly demonstrated. A mechanistic interpretation of spatial geometric traits in progression of epidemic transmissions is provided through these findings, which may be useful for quantitative evaluations of a variety of public-health policies.

Posted September 6, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm - 2:30 pm Lockett 233
Jake Murphy, LSU

TBA

Posted August 20, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Amanda Wilkens, University of Texas

TBA

Posted August 22, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Philip E. Paré, Purdue University

Modeling, Estimation, and Analysis of Epidemics over Networks

We present and analyze mathematical models for network-dependent spread. We use the analysis to validate a SIS (susceptible-infected-susceptible) model employing John Snow’s classical work on cholera epidemics in London in the 1850’s. Given the demonstrated validity of the model, we discuss control strategies for mitigating spread, and formulate a tractable antidote administration problem that significantly reduces spread. Then we formulate a parameter estimation problem for an SIR (susceptible-infected-recovered) networked model, where costs are incurred by measuring different nodes' states and the goal is to minimize the total cost spent on collecting measurements or to optimize the parameter estimates while remaining within a measurement budget. We show that these problems are NP-hard to solve in general and propose approximation algorithms with performance guarantees. We conclude by discussing an ongoing project where we are developing online parameter estimation techniques for noisy data and time-varying epidemics.

Posted August 11, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm - 3:20 pm 233 Lockett
Yan Zhou, Northeastern University

TBA

Posted September 1, 2023

Applied Analysis Seminar Questions or comments?

3:30 pm Zoom
Amir Sagiv, Technion Israel Institute of Technology

TBA

Posted August 22, 2023

Last modified September 24, 2023

Algebra and Number Theory Seminar Questions or comments?

3:20 pm - 4:10 pm Lockett 233 or click here to attend on Zoom
Kalani Thalagoda, Tulane University

Bianchi Modular Forms over $\mathbb{Q}(\sqrt{-17})$

Bianchi modular form are a generalization of classical modular forms defined over imaginary quadratic fields. A theory of modular symbols exists for computing Bianchi modular forms as Hecke eigensystems. However, when the class group of the imaginary quadratic field is nontrivial, modular symbol techniques only compute the principal part of the eigensystem. In this talk, I will explain how to extract a Hecke eigensystem for $\mathbb{Q}(\sqrt{-17})$, which has a class group of order $4$.

Posted September 25, 2023

Probability Seminar Questions or comments?

3:30 pm Zoom (Click “Questions or Comments?” to request a Zoom link)
Qi Feng, Florida State University

TBA

Posted September 6, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm - 2:30 pm Lockett 233
Amit Kumar, Louisiana State University

TBA

Posted August 23, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Mustafa Hajij, University of San Francisco

TBA

Posted September 7, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm - 3:20 pm Lockett 233
Daniil Klyuev, MIT

TBA

Posted September 20, 2023

Applied Analysis Seminar Questions or comments?

3:30 pm Lockett Hall 233
Burak Hatinoglu, Michigan State University

TBA on spectral theory of quantum graphs

(Host: Stephen Shipman)

Posted September 24, 2023

Algebra and Number Theory Seminar Questions or comments?

3:20 pm - 4:10 pm Lockett 233 or click here to attend on Zoom
Hui Xue, Clemson University

TBA

Posted September 6, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm - 2:30 pm Lockett 233
Archisman Bhattacharjee, Louisiana State University

TBA

Posted August 27, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Biji Wong, Duke University

TBA

Posted January 18, 2023

Last modified August 22, 2023

Control and Optimization Seminar Questions or comments?

Time and Location To Be Announced
Maruthi Akella, University of Texas
Fellow of AIAA, IEEE, and AAS

Sub-Modularity Measures for Learning and Robust Perception in Aerospace Autonomy

Onboard learning and robust perception can be generally viewed to characterize autonomy as overarching system-level properties. The complex interplay between autonomy and onboard decision support systems introduces new vulnerabilities that are extremely hard to predict with most existing guidance and control tools. In this seminar, we review some recent advances in learning-oriented and information-aware path- planning, and sub-modularity metrics for non-myopic sensor scheduling for “plug-and- play” systems. The concept of “learning-oriented” path-planning is realized through certain new classes of exploration inducing distance metrics. These technical foundations will be highlighted through aerospace applications with active learning inside dynamic and uncertain environments.

Posted August 12, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm - 3:20 pm Lockett 233
Jonathan Gruber, University of York

TBA

Posted September 6, 2023

Applied Analysis Seminar Questions or comments?

3:30 pm - 4:30 pm Zoom
Ivan Veselić, Technical University of Dortmund

TBA

Posted September 4, 2023

Algebra and Number Theory Seminar Questions or comments?

3:20 pm - 4:10 pm Lockett 233 or click here to attend on Zoom
Jason Gaddis, Miami University

TBA

Posted September 6, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm - 2:30 pm Lockett 233
Saumya Jain, Louisiana State University

TBA

Posted September 6, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Federico Salmoiraghi, Queen's University

TBA

Posted September 2, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Sean Meyn, University of Florida
Robert C. Pittman Eminent Scholar Chair, IEEE Fellow, IEEE CSS Distinguished Lecturer

TBA

Posted September 3, 2023

Applied Analysis Seminar Questions or comments?

3:30 pm - 4:30 pm Zoom
Yannick Sire, Johns Hopkins University

TBA

Posted September 3, 2023

Applied Analysis Seminar Questions or comments?

3:30 pm - 4:30 pm ZoomTBA

Posted September 22, 2023

Applied Analysis Seminar Questions or comments?

3:30 pm Lockett 232
Eduard-Wilhelm Kirr, University of Illinois Urbana-Champagne

TBA

Posted September 24, 2023

Algebra and Number Theory Seminar Questions or comments?

3:20 pm - 4:10 pm Lockett 233 or click here to attend on Zoom
Hongdi Huang, Rice University

TBA

Posted September 6, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm - 2:30 pm Lockett 233
Gurleen Nanda, Louisiana State University

TBA

Posted September 4, 2023

Applied Analysis Seminar Questions or comments?

3:30 pm - 4:30 pm Zoom
Piermarco Cannarsa, Università degli studi di Roma "Tor Vergata"

Generalised characteristics of Hamilton-Jacobi equations, propagation of singularities, and long-time behaviour

A generalised characteristic (GC) is a solution of certain differential inclusions that play a crucial role for propagation of singularities of solutions to Hamilton-Jacobi equations $H(x,u(x),Du(x))=0$. GC's were introduced in (D1977), in the context of hyperbolic conservation laws and then adapted to Hamilton-Jacobi equations in (AC2002) and (CY2009). In this talk, we will discuss several topics related to GC's including restricted classes of characteristics introduced in (KS2016), uniqueness issues, continuation properties in connection with propagation of singularities (CC2017). Then, for mechanical systems on the torus, that is, \begin{equation*} \frac 12|Du(x)|^2+V(x)=\alpha \\end{equation*} we will study the long time behaviour of GC's. By using limiting occupational measures, we will show that the critical set of $u$ is an approximate attractor for the GC flow. We will also give a criterion to decide whether, asymptotically, a GC is almost surely either singular or arbitrarily close to the regular critical set of $u$. \bigskip {\bf\large References} \medskip \begin{itemize} \item[(AC2002)] Albano, P., Cannarsa, P.: Propagation of singularities for solutions of nonlinear first order partial differential equations. Arch. Ration. Mech. Anal. 162(1), 1-23 (2002) \item[(CC2017)] Cannarsa, P., Cheng, W.: Generalized characteristics and Lax-Oleinik operators: global theory. Calc. Var. Partial Differ. Equ. 56(5), 31 (2017) \item[(CY2009)] Cannarsa, P., Yifeng, Yu.: Singular dynamics for semiconcave functions. J. Eur. Math. Soc. (JEMS) 11(5), 999-1024 (2009) \item[(D1977)] Dafermos, C.M.: Generalized characteristics and the structure of solutions of hyperbolic conservation laws. Indiana Univ. Math. J. 26(6), 1097-1119 (1977) \item[(KS2016)] Khanin, K., Sobolevski, A.: On dynamics of Lagrangian trajectories for Hamilton-Jacobi equations. Arch. Ration. Mech. Anal. 219(2), 861-885 (2016) \end{itemize}

Posted September 8, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Meeko Oishi, University of New Mexico
NSF BRITE Fellow

TBA

Posted September 24, 2023

Algebra and Number Theory Seminar Questions or comments?

3:20 pm - 4:10 pm Lockett 233 or click here to attend on Zoom
Rena Chu, Duke University

TBA

Posted September 24, 2023

Algebra and Number Theory Seminar Questions or comments?

3:20 pm - 4:10 pm Lockett 233 or click here to attend on Zoom
Ana Bălibanu, Louisiana State University

TBA