Calendar
Posted September 2, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm Lockett 233 or click here to attend on Zoom
Guanyu Li, Cornell University
Derived Commuting Schemes, Representation Homology, and Cohomology of Lie Algebras
The commuting schemes of an algebraic group or a Lie algebra play important roles in many areas of mathematics. They can be viewed as special cases of representation schemes, which are often highly singular. Derived algebraic geometry provides tools to remedy the deficiency. In particular, the derived representation scheme, together with its associated algebraic invariant known as representation homology, offers deeper insights into the structure of representation schemes. While the representation homology of reductive groups and reductive Lie algebras has been studied in the literature, it is natural to ask about the behavior of these objects and their relationships in the non-reductive setting. In this talk, I will discuss the derived commuting scheme of a maximal unipotent subgroup of a semisimple group scheme, as well as the derived commuting scheme of its Lie algebra. First, the higher structure of the derived commuting scheme detects whether the underlying commuting scheme is a complete intersection. Unlike the reductive case, the derived commuting scheme of a unipotent subgroup is equivalent to that of its Lie algebra. Using an analogue of the trace map, most of the homology classes can be explained in terms of the classical cohomology of a maximal nilpotent Lie algebra, described via the root system of the semisimple Lie algebra. This could be interpreted that the singularities of the commuting scheme of a maximal nilpotent subalgebra are largely determined by root system data. If time permits, I will also discuss a possible nilpotent analogue of the Macdonald identity, together with an interpretation in terms of representation homology.
Posted October 19, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Laura Kurtz, Louisiana State University
Stochastic Homogenization
In this talk, we develop tools of stochastic homogenization of elliptic operators. We focus mainly on the periodic case and discuss the implications of the stochastic case.
Event contact: Moises Gomez-Solis
Posted October 6, 2025
Last modified October 8, 2025
Paul Kirk, Indiana University
The SU(2) character variety "Functor" from the bordism category of 2+1 manifolds to the Weinstein symplectic "category"
Around 1990, Atiyah-Floer made a "conjecture" advocating for the study of 3-manifolds by using the symplectic properties of the SU(2) character varieties of 2 and 3-manifolds. This conjecture and surrounding philosophy has had a profound influence on the development of low dimensional topology ever since (with its most powerful consequences the construction of Heegard-Floer theory and the growth of symplectic topology). I'll explain what all these words mean in down to earth terms, and why there are "scare quotes" everywhere, and discuss history and related areas of mathematics. Tip: To help you get something out of the talk, spend a few minutes looking at: (a) the definition of the fundamental group of a space, and the Seifert-Van Kampen theorem, (b) the definition of the quaternions, and in particular the unit quaternions=SU(2), and (c) the definition of a symplectic manifold and a Lagrangian submanifold.
Posted August 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Remi Mandal, Louisiana State University
TBD
TBD
Posted September 1, 2025
Last modified October 9, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Matthew Haulmark, UT Rio Grande Valley
Cubes from Divisions
Actions on CAT(0) cube complexes have played an important role in advances in low-dimensional topology. Most notably, they are central to Wise's Quasiconvex Hierarchy Theorem and Agol's proof of the Virtual Haken Conjecture. In group theory, one way of obtaining an action on a cube complex is via the Sageev construction. Given a group G and a collection of codimension-1 subgroups of G, Sageev's construction gives an isometric action on a CAT(0) cube complex. In recent work with Jason Manning, we give an alternate route to the Sageev construction, which is potentially applicable to new situations. Much of this talk will be spent on background. We will introduce the notion of a wall space, as well as the cube complex dual to a wallspace. We will then construct an action on a CAT(0) cube complex given a group action on a sufficiently nice topological space and a system of divisions of that space.
Posted October 6, 2025
Last modified October 13, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Paul Kirk, Indiana University
On the SU(2) character variety of a closed oriented genus 2 surface
A celebrated theorem of Narasimhan-Ramanan asserts that the singular variety $X(F_2)=Hom(\pi_1(F_2),SU(2))/Conjugation$ is homeomorphic to $CP^3$. The proof passes through the (mysterious) Narasimhan-Seshadri correspondence. I'll outline an elementary differential topology proof that $X(F_2)$ is a manifold, homeomorphic to CP^3, and discuss how 3-manifolds with genus 2 boundary determine embedded lagrangians in $X(F_2)$. If time permits, I'll end the talk with a discussion of context, particularly with a program known as the Atiyah-Floer conjecture.
Posted September 5, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Naira Hovakimyan, University of Illinois Urbana-Champaign
Fellow of AIAA, ASME, IEEE, and IFAC
Safe Learning in Autonomous Systems
Learning-based control paradigms have seen many success stories with autonomous systems and robots in recent years. However, as these robots prepare to enter the real world, operating safely in the presence of imperfect model knowledge and external disturbances is going to be vital to ensure mission success. We introduce a class of distributionally robust adaptive control architectures that ensure robustness to distribution shifts and enable the development of certificates for validation and verification of learning-enabled systems. An overview of different projects at our lab that build upon this framework will be demonstrated to show different applications.
Posted October 17, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 click here to attend on Zoom
Christine Cho, Louisiana State University
The symmetric strong circuit elimination property
A set $\mathcal{C}$ of incomparable non-empty subsets of a finite set $E$ is the set of circuits of a matroid on $E$ when $\mathcal{C}$ satisfies either the weak circuit elimination axiom or the strong circuit elimination axiom. The strong circuit elimination axiom is inherently asymmetric. In this talk, we will present the symmetric strong circuit elimination property (SSCE) and characterize the class of connected matroids that possess this property. We will also explore the notion of skew circuits in a matroid, both in relation to the class of matroids satisfying SSCE and beyond. This talk is based on joint work with James Oxley and Suijie Wang.
Posted September 9, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Kalani Thalagoda, Tulane University
A summation formula for Hurwitz class numbers
The Hurwitz class numbers, $H(n)$, count ${\rm SL}(2,\mathbb{Z})$-classes of binary quadratic forms inversely weighted by stabilizer size. They are famously connected to the sum of three squares problem and to class numbers of imaginary quadratic fields. The work of Zagier in 1975 showed that their generating functions are related to a weight $3/2$ Harmonic Maass form. In this talk, I will discuss a summation formula for mock modular forms of moderate growth, with an emphasis on its application to Hurwitz class numbers. This is joint work with Olivia Beckwith, Nicholas Diamantis, Rajat Gupta, and Larry Rolen.
Posted August 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
TBD
TBD
Posted September 1, 2025
Last modified September 23, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Chen Zhang, Stony Brook University
TBA
TBA
Posted October 7, 2025
Last modified October 9, 2025
Control and Optimization Seminar Questions or comments?
9:30 am – 10:20 am Note: First of 2 Seminars for 10/31. Zoom (click here to join)
Alexandre Mauroy, Université de Namur
Dual Koopman Operator Formulation in Reproducing Kernel Hilbert Spaces for State Estimation
The Koopman operator acts on observable functions defined over the state space of a dynamical system, thereby providing a linear global description of the system dynamics. A pointwise description of the system is recovered through a weak formulation, i.e. via the pointwise evaluation of observables at specific states. In this context, the use of reproducing kernel Hilbert spaces (RKHS) is of interest since the above evaluation can be represented as the duality pairing between the observables and bounded evaluation functionals. This representation emphasizes the relevance of a dual formulation for the Koopman operator, where a dual Koopman system governs the evolution of linear evaluation functionals. In this talk, we will leverage the dual formulation to build a Luenberger observer that estimates the (infinite-dimensional) state of the Koopman dual system, and equivalently the (finite-dimensional) state of the nonlinear dynamics. The method will be complemented with theoretical convergence results that support numerical Koopman operator-based estimation techniques known from the literature. Finally, we will extend the framework to a probabilistic approach by solving the problem of moments in the RKHS setting.
Posted October 8, 2025
Last modified October 9, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Note: Second of 2 Seminars for 10/31. Zoom (click here to join)
Umesh Vaidya, Clemson University
TBA
Posted October 21, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Michael Lacey, Georgia Institute of Technology
TBA
Posted August 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Evan Short, Louisiana State University
TBD
TBD
Posted August 21, 2025
Last modified October 9, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Matthew Zaremsky, University at Albany (SUNY)
On the Sigma-invariants of pure symmetric automorphism groups
An automorphism of the free group F_n is "pure symmetric" if it sends each generator to a conjugate of itself. The group of all pure symmetric automorphisms of F_n, sometimes called the "McCool group" of F_n, is an interesting and important group with connections to braid groups, motion planning, and mathematical physics. The "Sigma-invariants" of a group are a family of geometric invariants due to Bieri, Neumann, Strebel, and Renz, which are notoriously difficult to compute in general, but reveal a wealth of information about the group and its fibering properties. In recent joint work with Mikhail Ershov, we compute large parts of the Sigma-invariants of the McCool groups, and in particular prove that they are always either empty or dense in the relevant character sphere. One key tool to highlight is an underutilized criterion due to Meinert, which seems likely to have additional future applications.
Posted August 19, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
David Roberts, University of Minnesota, Morris
TBA
Posted July 26, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Rami Katz, Università degli Studi di Trento, Italy
Oscillations in Strongly 2-Cooperative Systems and their Applications in Systems Biology
The emergence of sustained oscillations (via convergence to periodic orbits) in high-dimensional nonlinear dynamical systems is a non-trivial question with important applications in control of biological systems, including the design of synthetic bio-molecular oscillators and the understanding of circadian rhythms governing hormone secretion, body temperature and metabolic functions. In systems biology, the mechanism underlying such widespread oscillatory biological motifs is still not fully understood. From a mathematical perspective, the study of sustained oscillations is comprised of two parts: (i) showing that at least one periodic orbit exists and (ii) studying the stability of periodic orbits and/or characterizing the initial conditions which yield solutions that converge to periodic trajectories. In this talk, we focus on a specific class of nonlinear dynamical systems that are strongly 2-cooperative. Using the theory of cones of rank k, the spectral theory of totally positive matrices and Perron-Frobenius theory, we will show that strongly 2-cooperative systems admit an explicit set of initial conditions of positive measure, such that every solution emanating from this set converges to a periodic orbit. We further demonstrate our results using the n-dimensional Goodwin oscillator and a 4-dimensional biological oscillator based on RNA–mediated regulation.
Posted August 21, 2025
Last modified September 13, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett Hall 233
Roy Goodman, New Jersey Institute of Technology
TBA: Something on Hamiltonian systems
Event contact: Stephen Shipman
Posted August 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Matthew Lemoine, Louisiana State University
TBD
TBD (Independent Talk)
Posted September 1, 2025
Last modified September 23, 2025
Geometry and Topology Seminar Seminar website
3:30 pm TBA
Jayden Wang, University of Michigan
TBA
TBA
Posted August 1, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Thinh Doan, University of Texas at Austin
AFOSR YIP and NSF CAREER Awardee
TBA
Posted October 15, 2025
Last modified October 16, 2025
Mathematical Physics and Representation Theory Seminar
1:30 pm – 2:20 pm Lockett 233
Paul Sobaje, Georgia Southern University
A Geometric Model For Steinberg Quotients
Let G be a reductive algebraic group over a field of characteristic p > 0. Over the last decade, the longstanding search for a character formula for simple G-modules has been replaced (subsumed even) by the same problem for characters of tilting G-modules. In recent years I began studying "Steinberg quotients" of certain tilting characters. These are formal characters with good combinatorial properties straightforwardly derived from the representation theory of G. In some ways they are also the best candidates to be described by a characteristic p version of Weyl's famous formula. In joint work with P. Achar, we prove that these formal characters are in fact actual characters of a natural class of objects coming from geometric representation theory.
Posted August 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
TBD
TBD
Posted July 13, 2025
Last modified July 18, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Dimitra Panagou, University of Michigan
AFOSR YIP, NASA Early Career Faculty, and NSF CAREER Awardee
TBA
Posted August 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Huong Vo, Louisiana State University
TBD
TBD (Independent Talk)
Posted August 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
TBD
TBD
Posted September 10, 2025
Last modified September 23, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Corey Bregman, Tufts University
TBA
TBA
Posted July 22, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Javad Velni, Clemson University
TBA
Posted August 18, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Zequn Zheng, Louisiana State University
TBA