Calendar

1:00 pm – 4:00 pm Lockett 232

Qualifier Exam in Topology

Monday, August 18, 2025

Posted January 19, 2025

1:00 pm – 4:00 pm Lockett 232

Qualifier Exam in Analysis

Wednesday, August 20, 2025

Posted January 19, 2025

1:00 pm – 4:00 pm Lockett 232

Qualifier Exam in Algebra

Friday, August 22, 2025

Posted January 19, 2025

Algebra and Number Theory Seminar Questions or comments?

1:00 pm – 4:00 pm Lockett 232

Qualifier Exam in Applied Math

Tuesday, August 26, 2025

Posted August 2, 2025
Last modified August 20, 2025

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 Geometry and Topology 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

Wednesday, August 27, 2025

Posted July 21, 2025
Last modified August 17, 2025

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.

Friday, August 29, 2025

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

Algebra and Number Theory 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.

Tuesday, September 2, 2025

Posted August 2, 2025
Last modified August 20, 2025

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

Discussion and Training in Combinatorics

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

3:30 pm Lockett Hall 233

Week 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"

Wednesday, September 3, 2025

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

Actuarial Student Association

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!

Friday, September 5, 2025

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

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.

Wednesday, September 10, 2025

Posted September 1, 2025
Last modified September 10, 2025

Informal Geometry and Topology Seminar Questions or comments?

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

1:30 pm Lockett Hall 233

Sayani Mukherjee, Louisiana State University
Khovanov Homology

Continuing our discussion of Khovanov Homology, follow Melissa Zhang's notes.

Friday, September 12, 2025

Posted September 8, 2025

Algebra and Number Theory 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.

Tuesday, September 16, 2025

Posted August 2, 2025
Last modified September 10, 2025

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

Actuarial Student Association

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!

Wednesday, September 17, 2025

Posted September 1, 2025
Last modified September 15, 2025

Informal Geometry and Topology Seminar Questions or comments?

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

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)

Today, Friday, September 19, 2025

Posted September 15, 2025

Algebra and Number Theory 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.

Tuesday, September 23, 2025

Posted August 2, 2025
Last modified September 10, 2025

2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom

Andreas Mono, Vanderbilt University
A modular framework for generalized Hurwitz class numbers

We discover a neat linear relation between the mock modular generating functions of the level $1$ and level $N$ Hurwitz class numbers. This relation gives rise to a holomorphic modular form of weight $\frac{3}{2}$ and level $4N$ for $N > 1$ odd and square-free. This follows from a more general inspection of the weight $\frac{1}{2}$ Maass–Eisenstein series of level $4N$v at its spectral point $s = \frac{3}{4}$. This idea goes back to Duke, Imamoğlu and Tóth in level $4$ and relies on the theory of so-called sesquiharmonic Maass forms. Furthermore, we connect the aforementioned results to a regularized Siegel theta lift as well as a regularized Kudla–Millson theta lift for odd prime levels, which builds on earlier work by Bruinier, Funke and Imamoğlu. This is joint work with Olivia Beckwith. We conclude by presenting the situation in higher weights as well, which is sole work.

Posted September 18, 2025

3:30 pm – 4:30 pm Lockett 136

Matthew McCoy, Louisiana State University
Introduction to Ergodic Theory, Chebyshev Polynomial Expansions, and Schur Complements

This talk will serve as an introductory talk to Ken Beard's talk on 9/30: Momentum Space Algorithm for Electronic Structure of Double-Incommensurate Trilayer Graphene. We will introduce relevant concepts in spectral theory.

Event contact: Laura Kurtz

Wednesday, September 24, 2025

Posted September 1, 2025
Last modified September 18, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 am Lockett 233

Robin Koytcheff, University of Louisiana, Lafayette
Milnor invariants and thickness of spherical links

Various authors have studied the question of how long a rope of a given thickness is needed to tie a given isotopy class of knot or link. In joint work with Rafal Komendarczyk and Fedya Manin, we generalize this work to spherical links in arbitrary dimensions. In more detail, we study their Milnor invariants in terms of Massey products and prove asymptotically optimal upper bounds on Milnor invariants in terms of embedding thickness. Interestingly, there is a dichotomy between polynomial and exponential bounds, depending on the dimensions of the spheres. We apply our results to answer a question of Freedman and Krushkal about exponentially thin 2-complexes in 4-space.

Posted August 27, 2025

1:30 pm Lockett Hall 233

Gargi Patil, Louisiana State University
TBD

TBD

Tuesday, September 30, 2025

Posted September 18, 2025

3:30 pm – 4:30 pm Lockett 136

Ken Beard, LSU
Momentum Space Algorithm for Electronic Structure of Double-Incommensurate Trilayer Graphene

Although recent experimental results seem to indicate the existence of flat bands for twisted trilayer graphene (TTG), at present there is no convergent algorithm for approximating the density of states (or other desirable observables). We attempt to address this by using kernel polynomial approximation with an ab initio momentum-space tight-binding model. The unique challenge in the case of TTG is the lack of a periodic moir\'{e} supercell. This is addressed by modifying the truncation to account for more complex Umklapp scattering.

Event contact: Laura Kurtz

Wednesday, October 1, 2025

Posted September 10, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 am Lockett 233

Colin Crowley, University of Oregon
TBA

TBA

Posted August 27, 2025

1:30 pm Lockett Hall 233

Saumya Jain, Louisiana State University
TBD

TBD (Independent Talk)

Friday, October 3, 2025

Posted August 14, 2025

Control and Optimization Seminar Questions or comments?

10:30 am – 11:20 am Zoom (click here to join)

Xin Zhang, New York University
TBA

Posted September 19, 2025

Student Colloquium

1:30 pm Lockett Hall ---

Jason Cantarella, University of Georgia
How and why to teach a computer to untangle knots

Unknot recognition is a classical 'hard problem' in computational topology. At the moment, the leading candidate for a full solution is Lackenby's quasi-polynomial algorithm which has theoretical complexity 2^(O(log n)^3). So far, this hasn't led to a really efficient practical method for knot identification. A different idea for knot simplification (knot energies) goes back to Freedman (and before). In this method, we try to put some energy function on a test curve such as a repulsive charge and then follow the evolution of the curve, hoping that it will lead to a recognizable configuration. This has proved to be computationally intractable for numerical reasons. In this talk, we describe a hybrid approach which alternates between using powerful diagrammatic simplifications and a new semigeometric energy defined on diagrams. We'll give results on benchmark sets of hard unknots and then discuss how this method allowed us to give strong new evidence supporting the 'knot entropy conjecture' for random knots in self-avoiding walks. This has consequences for knots in polymer chemistry and (perhaps) for knots in DNA and other biopolymers. The talk will include various animations and demonstrations, a couple of puzzles, and some open questions. It should be fairly accessible to undergraduates.

Posted March 28, 2025
Last modified September 15, 2025

3:30 pm TBA

Wenxiong Chen , Yeshiva University
TBA

Event contact: Jiuyi Zhu

Monday, October 6, 2025

Posted March 16, 2025
Last modified September 15, 2025

2:30 pm TBA

Nicola Garofalo, Arizona State University Charles Wexler Professor in Mathematics,
TBA

Event contact: Jiuyi Zhu

Posted August 3, 2025
Last modified September 15, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm TBA

Donatella Danielli, Arizona State University School Director and Foundation Professor
TBA

Event contact: Jiuyi Zhu

Wednesday, October 8, 2025

Posted August 27, 2025

1:30 pm Lockett Hall 233

Krishnendu Kar, Louisiana State University
TBD

TBD

Friday, October 10, 2025

Posted August 1, 2025

Control and Optimization Seminar Questions or comments?

10:30 am – 11:20 am Zoom (click here to join)

Felix Schwenninger, University of Twente, The Netherlands
TBA

Tuesday, October 14, 2025

Posted August 2, 2025

Algebra and Number Theory Seminar Questions or comments?

2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom

Kenz Kallal, Princeton University
TBA

Wednesday, October 15, 2025

Posted August 27, 2025

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett Hall 233

Adithyan Pandikkadan, Louisiana State University
TBD

TBD

Posted September 10, 2025

Harmonic Analysis Seminar

3:30 pm – 4:30 pm Lockett 138

Bruno Poggi, University of Pittsburgh
TBA

Monday, October 20, 2025

Posted August 27, 2025
Last modified September 12, 2025

Algebra and Number Theory Seminar Questions or comments?

3:30 pm Lockett Hall 233

Xuenan Li, Columbia University
TBA: Something on 2D electronic materials

Event contact: Stephen Shipman

Tuesday, October 21, 2025

Posted September 2, 2025

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.

Wednesday, October 22, 2025

Posted September 1, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 am Lockett 233

Matthew Haulmark, UT Rio Grande Valley
TBA

TBA

Posted August 27, 2025

1:30 pm Lockett Hall 233

Remi Mandal, Louisiana State University
TBD

TBD

Friday, October 24, 2025

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.

Tuesday, October 28, 2025

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.

Wednesday, October 29, 2025

Posted September 1, 2025
Last modified September 2, 2025

Informal Geometry and Topology Seminar Questions or comments?

3:30 am Lockett 233

Chen Zhang, Stony Brook University
TBA

TBA

Posted August 27, 2025

1:30 pm Lockett Hall 233

Nilangshu Bhattacharyya, Louisiana State University
TBD

TBD

Wednesday, November 5, 2025

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

Colloquium Questions or comments?

3:30 pm Lockett 233

Matthew Zaremsky, University at Albany (SUNY)
TBD

Thursday, November 6, 2025

Posted August 19, 2025

3:30 pm Lockett 232

David Roberts, University of Minnesota, Morris
TBA

Friday, November 7, 2025

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.

Monday, November 10, 2025

Posted August 21, 2025
Last modified September 13, 2025

3:30 pm Lockett Hall 233

Roy Goodman, New Jersey Institute of Technology
TBA: Something on Hamiltonian systems

Event contact: Stephen Shipman

Wednesday, November 12, 2025

Posted September 1, 2025