Calendar
Posted January 19, 2025
1:00 pm – 4:00 pm Lockett 232Qualifier Exam in Algebra
Posted January 19, 2025
1:00 pm – 4:00 pm Lockett 232Qualifier Exam in Applied Math
Posted August 2, 2025
Last modified August 20, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Joseph DiCapua, Louisiana State University
Lubin–Tate Formal Group Laws
In this expository talk, we introduce Lubin–Tate formal group laws. The torsion points of a Lubin–Tate formal group law are defined, and we discuss the endomorphism ring of such a formal group law. Certain torsion points are used to define Coleman's trace operator, an important tool in Iwasawa theory. We briefly mention how Lubin–Tate formal group laws are used in one construction of the maximal abelian extension of a finite extension of the $p$-adics.
Posted August 18, 2025
Discussion and Training in Combinatorics
3:30 pm Lockett Hall 233
Gyaneshwar Agrahari, LSU
Emmanuel Astante, Louisiana State University
Organizational Meeting of DTC Seminar
The first meeting of the Discussion and Combinatorics Seminar will be held on this day and time. In this meeting, we will introduce everyone and give the details of how the seminar will be run.
Posted August 16, 2025
Last modified August 21, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Moisés Gómez-Solís, Louisiana State University
Laura Kurtz, Louisiana State University
Organizational Meeting
Posted July 21, 2025
Last modified August 17, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
Matthew Lemoine, Louisiana State University
Organizational Meeting
Please join us for the Informal Geometry and Topology Seminar. This seminar is an opportunity for grad students to get experience talking in front of an audience and practicing giving talks. In this first meeting, we will decide which topic/book/paper that we will follow for our discussion during the Fall semester. We will also have opportunities for individual talks. For more information, feel free to contact Matthew Lemoine or Krishnendu Kar.
Posted August 23, 2025
Last modified August 26, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Alex Olshevsky, Boston University
AFOSR YIP and NSF CAREER Awardee
The Connection Between Reinforcement Learning and Gradient Descent
Temporal difference (TD) learning with linear function approximation is one of the earliest methods in reinforcement learning and the basis of many modern methods. We revisit the analysis of TD learning through a new lens and show that TD may be viewed as a modification of gradient descent. This leads not only to a better explanation of what TD does but also improved convergence times guarantees. We discuss applications of this result to more involved reinforcement learning methods, such as actor-critic and neural-network based methods.
Posted August 25, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lcokett 233 or click to to attend on Zoom
Yiwei Ge, Louisiana State University
Unavoidable cc-minors in large 2-connected graphs
A cycle-contraction minor (or cc-minor) of a graph is obtained by iteratively contracting cycles. These minors interact in interesting ways with other graph relations, such as induced subgraphs and minors. In this talk, we will introduce the notion of cc-minors and explain the motivation for studying them from both graphic and matroidal perspectives. A 2023 paper of Allred, Ding, and Oporowski identified a set of unavoidable induced subgraphs in sufficiently large 2-connected graphs. We present a dual version of this theorem by focusing on unavoidable cc-minors of large 2-connected graphs. This talk is based on joint work with James Oxley.
Posted August 2, 2025
Last modified August 20, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Joseph DiCapua, Louisiana State University
Parametrization of Formal Norm Compatible Sequences
We give a classification of power series parametrizing Lubin–Tate trace compatible sequences. This proof answers a question posed in the literature by Berger and Fourquaux. Lubin–Tate trace compatible sequences are a generalization of norm compatible sequences, which arise in Iwasawa theory and local class field theory. The result we prove generalizes the interpolation theorem proved by Coleman in the classical norm compatible sequence case. We also, jointly with Victor Kolyvagin, give a method for finding such series explicitly in certain special cases.
Posted August 30, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Hari Narayanan, Louisiana State University
Introduction to Spectral Theory and Schrödinger Operators
This talk concentrates on the spectral theory of Schrödinger operators with a view toward modern research. The huge literature in this field was spawned by non-relativistic quan- tum mechanics and has led to rich advances in pure spectral theory and applications. After a brief review of finite dimensions, the talk first develops abstract spectral theory of self-adjoint operators in Hilbert space with some emphasis on classical ideas of harmonic analysis, namely spectral resolutions induced by symmetry groups. Then we introduce continuous and discrete Schrödinger operators with electric and magnetic potentials and some of the standard theorems. We treat periodic, quasi-periodic, and ergodic operators, in decreasing detail. The treatment of periodic operators will emphasize the connections to commutative algebra centering around the Fermi and Bloch algebraic or analytic varieties. This is followed by analysis in physical, momen- tum (dual), configuration, and reciprocal space; and a brief look at ergodic and quasi-periodic operators.
Posted September 1, 2025
Discussion and Training in Combinatorics
3:30 pm Lockett Hall 233Week 2: Review of Topology
This week, our speaker, Sayani Mukherjee, will kick off our discussion on the applications of the Borsuk-Ulam Theorem. Ms. Mukherjee is a second-year PhD student in our department. She will review the first two sections of the textbook: "Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry"
Posted August 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Rachel Meyers, Louisiana State University
TBD
TBD
Posted August 28, 2025
5:00 pm Kessler 3rd Floor Lounge (Lockett Hall)ASA First Fall Meeting
Come meet other interested Actuaries as the Actuarial Student Association has it's first Fall semester meeting. Pizza will be served!
Posted August 11, 2025
Last modified September 2, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Gabriela Gonzalez, Louisiana State University
Member, US National Academy of Sciences
Feedback Loops in the LIGO Gravitational Wave Detectors
The Laser Interferometric Gravitational-wave Observatory (LIGO) operates two detectors in Livingston, LA and Hanford, WA to detect perturbations of space time produced by astrophysical events like the collision of black holes. The detectors have an amazing sensitivity, using laser beams traveling in vacuum detecting differences in two 4km long arms smaller than a thousandth of a proton diameter in a frequency band between 10 Hz and 5 kHz. To achieve this sensitivity, a large number of feedback control systems are used to damp suspended mirrors, to reduce the effect of ground motion, to keep optical cavities resonant, and much more. I will briefly describe these systems and the challenges for current and future detectors.
Posted September 3, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Zoom (click here to join)
Dylan King, California Institute of Technology
Lagrangians, Palettes, and Uniform Turan Densities
The Turan density of a forbidden hypergraph F is the largest edge density a large hypergraph H can have without containing any copy of F, and determining this number for various F is a notoriously difficult problem. One on-ramp to this question (from Erdos and Sos) is to furthermore require that the hyperedges of H are distributed nearly uniformly across the vertices, giving the uniform Turan density of F. All known examples of such uniformly dense H avoiding some F follow the so-called “palette” construction of Rodl. In this talk we will introduce each of these notions before discussing our main result, that any palette can be obtained as an extremal construction for some finite family of forbidden subgraph F, which will require the tools of hypergraph regularity and Lagrangians. Based on joint work with Simon Piga, Marcelo Sales, and Bjarne Schuelke.
Posted September 1, 2025
Last modified September 10, 2025
Geometry and Topology Seminar Seminar website
3:30 am Lockett 233
Kyle Binder, Louisiana State University
Cohomology of Toric Varieties Associated with Matroids
The Chow ring of a matroid is an important tool in studying the combinatorics of matroids through geometric techniques, and it played a central role in the Adiprasito, Huh, and Katz proof of the Rota—Heron—Welsh conjecture for matroids. This ring is defined to be the Chow ring of the smooth, quasi-projective toric variety associated with the Bergman fan of the matroid, and, remarkably, it enjoys many of the Hodge-theoretic properties of Chow rings of smooth, projective varieties. In this talk, we will extend the Chow ring of these toric varieties to the larger (singular) cohomology ring, compute the top-graded piece of cohomology in terms of the associated matroid, and describe how to compute all of the Betti numbers in the case of uniform matroids.
Posted August 27, 2025
Last modified September 10, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Sayani Mukherjee, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology, follow Melissa Zhang's notes.
Posted September 8, 2025
Combinatorics Seminar Questions or comments?
8:30 am – 9:30 am Zoom (click here to join)
Tony Huynh, Institute for Basic Science (IBS)
Rainbow triangles and the Erdős-Hajnal problem in projective geometries
We formulate a geometric version of the Erdős-Hajnal conjecture that applies to finite projective geometries rather than graphs. In fact, we give a natural extension of the 'multicoloured' version of the Erdős-Hajnal conjecture. Roughly, our conjecture states that every colouring of the points of a finite projective geometry of dimension $n$ not containing a fixed colouring of a fixed projective geometry $H$ must contain a subspace of dimension polynomial in $n$ avoiding some colour. When $H$ is a 'triangle', there are three different colourings, all of which we resolve. We handle the case that $H$ is a 'rainbow' triangle by proving that rainbow-triangle-free colourings of projective geometries are exactly those that admit a certain decomposition into two-coloured pieces. This is closely analogous to a theorem of Gallai on rainbow-triangle-free coloured complete graphs. The two non-rainbow colourings of $H$ are handled via a recent breakthrough result in additive combinatorics due to Kelley and Meka. This is joint work with Carolyn Chun, James Dylan Douthitt, Wayne Ge, Matthew E. Kroeker, and Peter Nelson.
Posted August 2, 2025
Last modified September 10, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Hang Xue, The University of Arizona
Fourier–Jacobi periods on unitary groups
We explain what Fourier–Jacobi periods on unitary groups are and prove the global Gan–Gross–Prasad conjecture about them. We also give an application to the Tate conjecture of product of unitary Shimura varieties.
Posted September 10, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Shalini Shalini, LSU
Gowri Priya Sunkara, LSU
The Elvis Problem with Convex Bifunctions/The Minimal Time Function Under More General Assumptions
The Elvis problem models a time optimal control problem across two regions having a common interface Sigma, each with a constant convex velocity set. We generalized this framework by introducing convex bifunctions of the form F_i(r, v) which are convex, lower semicontinuous, and proper. The minimization problem is min [ F_0(r_0, y - x_0) + F_1(r_1, x_1 - y) ], over r_0 > 0, r_1 > 0 and y in Sigma. The bifunctions F_i are jointly convex in (r, v) and convex analysis is used to derive optimality conditions. Under general assumptions on the target set S and the system dynamics, we show that the minimal time function is a proximal solution to a pair of Hamilton–Jacobi inequalities. Uniqueness is established via two distinct types of boundary conditions. We also introduce a new propagation result, which characterizes proximal sub gradients of the minimal time function in terms of normal cones and a boundary inequality condition. Furthermore, we provide necessary and sufficient conditions for the Lipschitz continuity of the minimal time function near S. In particular, a Petrov-type modulus condition is shown to guarantee such continuity. Our results extend earlier results to a broader class of time dynamics, even within non-Euclidean settings.
Posted September 15, 2025
5:30 pm Kessler Lounge (3rd Floord Lockett Hall)ASA Meeting
Brief Presentation about the basics of becoming a credentialed actuary. Additional Tips about studying for exams/resumes Pizza will be served!
Posted September 1, 2025
Last modified September 15, 2025
Geometry and Topology Seminar Seminar website
3:30 am Lockett 233
Kevin Schreve, Louisiana State University
L^2-homology of right-angled Coxeter groups
A flag triangulation of an (n-1)-dimensional sphere determines a right-angled Coxeter group and a closed n-manifold which is a K(G,1) for the commutator subgroup. The Singer Conjecture predicts that the L^2-homology of the universal cover is only nonzero in dimension n/2. We will show the Singer conjecture holds if 1) L is the barycentric subdivision of the boundary of a simplex, 2) L is the barycentric subdivision of a triangulation of an odd-dimensional sphere Based on joint work with Grigori Avramidi and Boris Okun.
Posted August 27, 2025
Last modified September 14, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Anurakti Gupta, Louisiana State University
Continuing our Discussion of Khovanov Homology
We are continuing our discussion of Khovanov Homology following Melissa Zhang's notes. (https://arxiv.org/abs/2501.03115)
Posted September 15, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Zoom (click here to attend on Zoom)
Rose McCarty, Georgia Institute of Technology
Neighborhood complexity and matroids
Abstract: We will discuss neighborhood complexity in graphs and some of its many applications. We will touch on applications to graph coloring, discrete geometry, and first-order logic. However, our main focus will be using neighborhood complexity to find the "unavoidable" GF(q)-representable cosimple matroids of large girth. This talk is based on joint work with James Davies, Meike Hatzel, Kolja Knauer, and Torsten Ueckerdt.