Also take a look at our interactive calendar:
Events of week
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Spring 2026 Math For All; April 10-11, 2026
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Girls in STEM at Tulane (GiST); Saturday, March 7, 2026
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Week of March 20 - March 16
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March 16, 2026
Algebra and Combinatorics
Topic: On Non-standard Graded Veronese Subalgebras
Speaker: Thai Thanh Nguyen - University of Dayton
Abstract: In a polynomial ring, the d-th Veronese subring is generated as a k-algebra by all monomials whose degree is a multiple of d. In a polynomial ring with standard grading (degree of each variable is 1), the Veronese subrings have many nice properties: they are normal, Cohen-Macaulay, and Koszul. Furthermore, their defining ideals are quadratic, binomial, and determinantal, generated by 2x2 minors of suitable matrices that also form a Groebner basis for the ideal. In this talk, we will discuss Veronese subrings of a non-standard graded polynomial ring. We will see that many of the nice properties are satisfied in two-variable case, but no longer hold in general in more variables. This is based on joint work with Bek Chase, Luca Fiorindo, Thiago de Holleben, Emanuela Marangone, Alexandra Seceleanu, and Srishti Singh.
Location: Gibson Hall 126 A
Time: 3:00 PM
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March 18, 2026
Algebra and Combinatorics
Topic: Resonance Sums, Shifted Convolutions, and Bounds towards the Square-Root Cancellation Hypothesis
Speaker: Praneel Samanta - University of Kentucky (Host): Kalani Thalagoda
Abstract: The square-root cancellation hypothesis, in its original form, concerns cancellation in certain GL(1) sums with applications to the distribution of zeros of L-functions associated with GL(2) cusp forms. Building on Ye’s work on a varying GL(2) cusp form and my work (jointly with Ye and Gillespie) on the Rankin Selberg convolution of two GL(2) cusp forms, both allowed to move, I will discuss a variant in which only one form is permitted to vary. This leads naturally to shifted convolution sums and new analytic challenges. I will outline my methods and preliminary results in this setup and discuss how these fit into the broader concept of the square root cancellation hypothesis.
Location: Gibson Hall, room 126
Time: 3:00 PM
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Week of March 13 - March 09
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March 12, 2026
Colloquium
Topic: D'Arcais Polynomials
Speaker: Bernhard Heim - Universitat Koln (Host): Olivia
Abstract: In this joint work with Markus Neuhauser, we investigate D'Arcais polynomials, which extend k-colored partitions and encompass all powers of the Dedekind eta function. We present new results on their zero distributions, examine their coefficients, and apply both analytic and algebraic number theoretic techniques, particularly excluding nontrivial roots of unity as zeros. I will also report on a joint work with Kathrin Bringmann and Olivia Beckwith on k-regular partitions.
Location: MA-200B
Time: 3:30 PM
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March 12, 2026
Geometry & Topology
Topic: Persistent Homology Learning Seminar (LSC)
Speaker: Rafal Komendarczyk - Tulane University
Abstract: We will move into the realm of the bottleneck distance and the Isometry Theorem.
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This learning seminar introduces the foundations of persistent homology, a key tool in topological data analysis for capturing multiscale topological features of general metric spaces. We will study persistence modules, barcodes, and distances such as the bottleneck and interleaving metrics, with a focus on their geometric meaning.
A central goal of the seminar is to understand and prove stability theorems for persistent homology, including bounds relating bottleneck distance to the Gromov–Hausdorff distance. Core examples will come from Morse theory and Vietoris–Rips filtrations of metric spaces.
The seminar is structured as a guided, collaborative reading course and is aimed at graduate students and faculty generally interested in this aspect of topology and geometry.
Location: Hebert 210
Time: 12:30 PM
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March 12, 2026
Mathematics Department Ph.D. Thesis Defense
Topic: Bayesian Phylogenetic Models with Scalable Inference
Speaker: Yuwei Bao - Tulane University
Abstract: Rapid growth in viral sequence data demands Bayesian phylogenetic methods that are both accurate and computationally efficient. However, the topological constraints, especially tight temporal bounds, construct a parameter space that is incompatible with vanilla Hamiltonian Monte Carlo (HMC) reparameterizations. Furthermore, piecewise-constant demographic priors introduce discontinuities, effectively precluding the use of gradient-based sampling in many genomic contexts.
Two developments address these bottlenecks. Reflective Hamiltonian Monte Carlo (rHMC) simulates trajectories directly on constrained node heights and enforces validity via reflections at constraint boundaries, improving robustness and mixing in outbreak-like settings and achieving substantial efficiency gains across three viral datasets. Smooth Skygrid replaces the piecewise-constant Skygrid with a continuously differentiable effective population size model, providing stable gradients and smooth posterior geometry for Hamiltonian methods. Together, these methods enable faster, more stable gradient-based phylogenetic inference and are implemented in the open-source Bayesian Evolutionary Analysis by Sampling Trees (BEAST) software.
Location: Norman Mayer Building MA-104,
Zoom: https://tulane.zoom.us/j/94309649742
Time: 1:00 PM
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March 11, 2026
Algebra and Combinatorics
Topic: Crepant resolutions via stacks
Speaker: Jeremy Usatine - Florida State University (Host): Kalina Mincheva
Abstract: Consider an invariant that behaves nicely for smooth varieties, such as Euler number, Betti numbers, or Hodge numbers. Suppose we want a version of this invariant for singular varieties that sees interesting information about the singularities. I will discuss how this naturally leads to the notion of crepant resolutions of singularities. However, crepant resolutions (by varieties) are rare in practice. I will discuss joint work with M. Satriano in which we show that crepant resolutions actually exist in broad generality, as long as one is willing to consider algebraic stacks. Specifically, any variety with log-terminal singularities admits a crepant resolution by a smooth algebraic stack. As one consequence, in joint work with J. Huang and M. Satriano, we obtained a cohomological interpretation for Batyrev's stringy Hodge numbers. This talk will not assume familiarity with stacks.
Location: Gibson Hall 126
Time: 3:00 PM
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March 10, 2026
Graduate Student Colloquium
Topic: $F$-volumes for sequences of filtrations and $p$-families
Speaker: Vinh Pham - Tulane University
Abstract: The numerical invariant $F$-volume was first introduced by Wágner Badilla-Céspedes et al. in 2022 as a generalization of the $F$-threshold for a pair of ideals $I$ and $J$. We extend this invariant to the case of a sequence of filtrations of ideals $\mathcal{I}(1),\ldots, \mathcal{I}(t)$ and a $p$-family $J_{\bullet}$ of ideals in a Noetherian ring. Under the assumption that the filtrations are $J_{\bullet}$-admissible, we show that the $F$-volume
\[
\mathrm{Vol}_F^{J_{\bullet}}(\underline{\mathcal{I}})=\lim\limits_{e\to \infty}\dfrac{\left|V^{J_{\bullet}}_{\underline{\mathcal{I}}}(p^e)\right|}{p^{et}}
\]
exists, where $V^{J_{\bullet}}_{\underline{\mathcal{I}}}(p^e):=\{(a_1,\ldots,a_t)\in \mathbb{N}^t \mid I(1)_{a_1}\cdots I(t)_{a_t}\nsubseteq J_{p^e} \}$. This is joint work with Thai Thanh Nguyen and Souvik Dey.
Location: Dinwidie 102
Time: 2:45 PM
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March 09, 2026
Integrability and Beyond
Topic: Wigner semicircle law via some combinatorics
Speaker: Ken McLaughlin - Tulane University
Abstract: We’ll start with a brief recap of the definition of the random matrix ensembles of interest - the Gaussian Unitary Ensemble and the Gaussian Orthogonal Ensemble, as defined this semester by Guido Mazzuca. Then we will explain an interesting connection between the combinatorics of ribbon graphs, and fundamental quantities in random matrix theory (traces of powers of the random matrices). Through this connection, the Wigner semicircle describing the limiting density of eigenvalues will emerge hazily, like a Sandcrawler coming into view through a sandstorm on Tatooine.
Location: Gibson Hall, 400A
Time: 3:00 PM
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Week of March 06 - March 02
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March 05, 2026
Geometry & Topology
Topic: Persistent Homology Learning Seminar (LSC)
Speaker: Rafal Komendarczyk - Tulane University
Abstract: We will further discuss barcodes, the rank function, and the uniqueness in the Normal Form Theorem.
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This learning seminar introduces the foundations of persistent homology, a key tool in topological data analysis for capturing multiscale topological features of general metric spaces. We will study persistence modules, barcodes, and distances such as the bottleneck and interleaving metrics, with a focus on their geometric meaning.
A central goal of the seminar is to understand and prove stability theorems for persistent homology, including bounds relating bottleneck distance to the Gromov–Hausdorff distance. Core examples will come from Morse theory and Vietoris–Rips filtrations of metric spaces.
The seminar is structured as a guided, collaborative reading course and is aimed at graduate students and faculty generally interested in this aspect of topology and geometry.
Location: Hebert 210
Time: 12:30 PM
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March 03, 2026
Graduate Student Colloquium
Topic: Congruences for k-regular partition numbers
Speaker: Peter Marcus - Tulane University
Abstract: Ramanujan discovered surprising congruence relations between integer partition numbers, which arise because of properties of modular forms, in particular, the Dedekind eta-function. Finding more congruences among similar sequences has become a major application of the continually-developing theory of modular forms. I will discuss my thesis research, in which I study congruence relations between k-regular partition numbers, a variant of partition numbers which counts the number of partitions where no part is divisible by k.
Location: Dinwidie 102
Time: 2:45 PM
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Week of February 27 - February 23
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February 26, 2026
Colloquium
Topic: Matroids You Have Known
Speaker: Nancy Neudauer - Pacific University (Host): Mahir
Abstract: Matroids show up several times in the undergraduate curriculum, but most of us don’t know them by name. In 1933, three Harvard junior-fellows tied together some recurring themes in mathematics, into what Gian Carlo Rota called one of the most important ideas of our day. They were finding properties of dependence in multiple mathematical structures. What resulted is the matroid, which abstracts notions of algebraic dependence, linear independence, and geometric dependence, thus unifying several areas of mathematics. The usefulness of matroids to pure mathematical research is similar to that of groups – by studying an abstract version of phenomena that occur in different realms of mathematics, we learn something about all those realms simultaneously. We find that matroids are everywhere: Vector spaces are matroids; We can define matroids on a graph. Matroids are useful in situations that are modelled by both graphs and matrices. Yet many matroids cannot be represented by a graph nor a collection of vectors over any field. We consider the essential role of matroids in combinatorial optimization. No prior knowledge of matroids or graphs is needed.
Location: MA-200B
Time: 3:30 PM
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February 26, 2026
Geometry & Topology
Topic: Persistent Homology Learning Seminar (LSC)
Speaker: Rafal Komendarczyk - Tulane University
Abstract: We will move in the direction of Barcodes and the Normal Form Theorem.
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This learning seminar introduces the foundations of persistent homology, a key tool in topological data analysis for capturing multiscale topological features of general metric spaces. We will study persistence modules, barcodes, and distances such as the bottleneck and interleaving metrics, with a focus on their geometric meaning.
A central goal of the seminar is to understand and prove stability theorems for persistent homology, including bounds relating bottleneck distance to the Gromov–Hausdorff distance. Core examples will come from Morse theory and Vietoris–Rips filtrations of metric spaces.
The seminar is structured as a guided, collaborative reading course and is aimed at graduate students and faculty generally interested in this aspect of topology and geometry.
Location: Hebert 210
Time: 12:30 PM
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February 24, 2026
Graduate Student Colloquium
Topic: Persistent Homology Learning Seminar (LSC)
Speaker: Naveed Ahmed - Tulane University
Abstract: Principal Component Analysis (PCA) is a foundational technique in scientific computing for extracting structure from high-dimensional data. In this talk, I will introduce the mathematical ideas underlying PCA, beginning with its formulation through covariance matrices and eigendecomposition. I will then show how the singular value decomposition (SVD) provides an equivalent and numerically robust perspective. Emphasis will be placed on the geometric interpretation of PCA as a change of coordinates that identifies directions of maximal variance.
To illustrate these ideas in practice, I will present an implementation of PCA on the Fisher Iris dataset and demonstrate how a small number of principal components can capture most of the variation in the data. I will conclude with brief remarks on low-rank approximation and data reconstruction, highlighting the broader role of PCA in scientific computing.
Location: Dinwidie 102
Time: 2:45 PM
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Week of February 20 - February 16
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February 19, 2026
Geometry & Topology
Topic: Persistent Homology Learning Seminar (LSC)
Speaker: Rafal Komendarczyk - Tulane University
Abstract: We are in a position to establish stability for Morse functions in terms of the interleaving distance.
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This learning seminar introduces the foundations of persistent homology, a key tool in topological data analysis for capturing multiscale topological features of general metric spaces. We will study persistence modules, barcodes, and distances such as the bottleneck and interleaving metrics, with a focus on their geometric meaning.
A central goal of the seminar is to understand and prove stability theorems for persistent homology, including bounds relating bottleneck distance to the Gromov–Hausdorff distance. Core examples will come from Morse theory and Vietoris–Rips filtrations of metric spaces.
The seminar is structured as a guided, collaborative reading course and is aimed at graduate students and faculty generally interested in this aspect of topology and geometry.
Location: Hebert 210
Time: 12:30 PM
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Week of February 13 - February 09
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February 12, 2026
Geometry & Topology
Topic: Persistent Homology Learning Seminar (LSC)
Speaker: Rafal Komendarczyk - Tulane University
Abstract: We will go over examples of the interleaving of persistence modules and the interleaving distance.
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This learning seminar introduces the foundations of persistent homology, a key tool in topological data analysis for capturing multiscale topological features of general metric spaces. We will study persistence modules, barcodes, and distances such as the bottleneck and interleaving metrics, with a focus on their geometric meaning.
A central goal of the seminar is to understand and prove stability theorems for persistent homology, including bounds relating bottleneck distance to the Gromov–Hausdorff distance. Core examples will come from Morse theory and Vietoris–Rips filtrations of metric spaces.
The seminar is structured as a guided, collaborative reading course and is aimed at graduate students and faculty generally interested in this aspect of topology and geometry.
Location: Hebert 210
Time: 12:30 PM
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February 11, 2026
Algebra and Combinatorics
Topic: Asymptotic Resurgence of Matroid Ideals
Speaker: Louiza Fouli - New Mexico State University Host: Alessandra Costantini
Abstract: We study two monomial ideals naturally associated to the independence complex of a matroid: the Stanley–Reisner ideal and the facet ideal. Focusing on their asymptotic resurgence, we establish general bounds and, for specific families of matroids, derive exact formulas. This is joint work with Michael DiPasquale and Arvind Kumar.
Location: Gibson Hall 126
Time: 3:00 PM
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February 10, 2026
Graduate Student Colloquium
Topic: Introduction to dynamical systems
Speaker: Lahiri Sinchita - Tulane University
Abstract: Dynamical systems provide a unifying framework for understanding the time evolution of mathematical models arising across science and engineering. In this talk, I will begin with a gentle introduction to dynamical systems generated by ordinary differential equations, focusing on fundamental concepts. These finite-dimensional systems serve as a conceptual foundation for more complex models. I will then outline how this framework extends to partial differential equations, where the dynamics evolve in infinite-dimensional phase spaces. Emphasis will be placed on the basic ideas rather than technical details, including the interpretation of PDEs as dynamical systems on function spaces. In the final part of the talk, I will briefly indicate how these ideas connect to my recent research, where tools from infinite-dimensional dynamical systems are used to analyze the qualitative behavior of solutions to linear evolution equations.
Location: Dinwiddie Hall 102
Time: 2:45 PM
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Week of February 06 - February 02
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February 05, 2026
Colloquium
Topic: The prime number theorem in short intervals
Speaker: Ayla Gafni - Ole Miss (Host: Olivia)
Abstract: One form of the prime number theorem asserts that
$$\sum_{n\le x} \Lambda(n) = x(1 + o(1)),$$
where $\Lambda(n)$ is the von Mangoldt function. By the triangle inequality, this also gives
$$\sum_{x < n\le x+y} \Lambda(n) = y(1 + o(1)),$$
in the ``long interval'' setting $y\sim x$. It is expected that the prime number theorem holds for much shorter intervals, namely for $y\sim x^{\theta}$ for any fixed $\theta\in (0,1]$. From the recent zero density estimates of Guth and Maynard, this result is known for all $x$ when $\theta > \frac{17}{30} $ and for almost all $x$ when $\theta > \frac{2}{15}$. In this talk, we will discuss the connections between zero density estimates, the prime number theorem in short intervals, and the distribution of prime numbers. Further, we will present some quantitative upper bounds on the size of the exceptional set where the prime number theorem in short intervals fails. We give an explicit relation between zero density estimates and exceptional set bounds, allowing for the most recent zero density estimates to be directly applied to give upper bounds on the exceptional set via a small amount of computer assistance. This talk is based on joint work with Terence Tao.
Location: MA-200B
Time: 3:30 PM
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February 05, 2026
Geometry & Topology
Topic: Persistent Homology Learning Seminar (LSC)
Speaker: Rafal Komendarczyk - Tulane University
Abstract: We will continue our journey into the realm of persistence modules.
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This learning seminar introduces the foundations of persistent homology, a key tool in topological data analysis for capturing multiscale topological features of general metric spaces. We will study persistence modules, barcodes, and distances such as the bottleneck and interleaving metrics, with a focus on their geometric meaning.
A central goal of the seminar is to understand and prove stability theorems for persistent homology, including bounds relating bottleneck distance to the Gromov–Hausdorff distance. Core examples will come from Morse theory and Vietoris–Rips filtrations of metric spaces.
The seminar is structured as a guided, collaborative reading course and is aimed at graduate students and faculty generally interested in this aspect of topology or geometry.
Location: Hebert 210
Time: 12:30 PM
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February 04, 2026
Algebra and Combinatorics
Topic: An algebraic theory of Lojasiewicz exponents.
Speaker: Tai Ha - Tulane University
Abstract: We develop a unified algebraic and valuative theory of Lojasiewicz exponents for pairs of graded families of ideals. Within this framework, analytic local Lojasiewicz exponents, gradient exponents, and exponents at infinity are all realized as asymptotic containment thresholds between appropriate filtrations.
The main theme is a finite-max principle: under verifiable algebraic hypothesis, the a priori infinite valuative supremum describing the Lojasiewicz exponent reduces to a finite maximum and attained by divisorial valuations. We identify two complementary mechanisms leading to this phenomenon: finite testing arising from normalized blowups and Rees algebra constructions, and attainment via compactness of normalized valuation spaces under linear boundedness assumptions. This finite-max principle yields strong structural consequences, including rigidity, stratification, and stability results. We also explain classical results/problems in toric and Newton polyhedral settings.
Location: Gibson Hall 126
Time: 3:00 PM
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February 03, 2026
Graduate Student Colloquium
Topic: Riesz-Type Sums Involving Real Quadratic $L$-Values
Speaker: Tushar Karmakar - Tulane University
Abstract: In analytic number theory, summation formulas are often useful for understanding the properties of sequences which grow erratically. We explore Riesz type sums involving class number of real quadratic field. In particular, we extend recent work of Beckwith, Diamantis, Gupta, Rolen, and Thalagoda from harmonic Maass forms to sesquiharmonic Maass forms of weight $1/2$. Our approach adapts a method of Chandrasekharan and Narasimhan, which we apply to a sesquiharmonic Maass form first introduced by Duke, Imamo{\u g}lu, and T\'{o}th. (This is ongoing joint work with Professor Olivia Beckwith)
Location: Dinwiddie Hall 102
Time: 2:45 PM
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February 02, 2026
Integrability and Beyond
Topic: The (random) matrix
Speaker: Tushar Karmakar - Tulane University
Abstract:
"Red or blue pill?" Ioana asked the graduate student.
"What happens if I take the blue one?"
"Nothing," Alan replied. "The story ends. We will know that you are not curious enough, or that you think that finding the energy levels for charged atoms is not an important quest for physics."
"Or that you do not believe in the power of probability theory, only in the crude Riemann-Hilbert method," Ioana pressed.
The student was a bit perplexed: he hated RHP, but at the same time, their quest looked impossible without it. "So if I take the red one? What is going to happen?"
"Well," said Ioana, smiling, "you will start an amazing journey. You will uncover a world of beauty and possibility. We start with the simplest possible situation: we consider a symmetric random matrix with Gaussian entries and we will compute the joint probability density function of the eigenvalues explicitly. During this journey, we will learn how to tridiagonalize a matrix, how to use recurrence relations to express the Vandermonde determinant, and much more."
Alan stood up. "And the best of all? It is going to be a symphony where all the players play their part flawlessly."
The grad took the red pill and ate it. "Well, let's get started!"
Reference: "Matrix Models for Beta Ensembles" Ioana Dumitriu, Alan Edelman https://arxiv.org/abs/math-ph/0206043
Location: TBA
Time: 3:00 PM
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Week of January 30 - January 26
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January 29, 2026
*** Special Colloquium ***
Topic: Tractability of chaotic dynamics in noisy systems
Speaker: Alex Blumenthal - Georgia Tech
Abstract: Many real-world systems exhibit dynamical chaos, characterized by sensitive dependence on initial conditions and intricate, seemingly disordered behavior. While existing abstract tools from smooth ergodic theory provide a rich framework for understanding chaotic dynamics, verifying this framework in concrete systems remains a notoriously difficult problem. Even in low-dimensional toy models, rigorous proofs often lag significantly behind compelling numerical evidence. Remarkably, this problem becomes far more tractable when systems are subjected to external, time-dependent stochastic forcing. In such settings, the scope of systems for which chaotic hallmarks can be rigorously established expands dramatically, offering substantive progress toward the original promise of chaos theory: to explain and quantify dynamical disorder in nature. I will present several applications of these ideas, including towards disordered dynamical behavior exhibited in systems from fluid mechanics. This talk will include joint work with many collaborators, including Lai-Sang Young, Jinxin Xue, Jacob Bedrossian, and Sam Punshon-Smith.
Location: Dinwiddie 108
Time: 3:30 PM
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January 29, 2026
Geometry & Topology
Topic: Persistent Homology Learning Seminar (LSC)
Speaker: Rafal Komendarczyk - Tulane University
Abstract: This learning seminar introduces the foundations of persistent homology, a key tool in topological data analysis for capturing multiscale topological features of general metric spaces. We will study persistence modules, barcodes, and distances such as the bottleneck and interleaving metrics, with a focus on their geometric meaning.
A central goal of the seminar is to understand and prove stability theorems for persistent homology, including bounds relating bottleneck distance to the Gromov–Hausdorff distance. Core examples will come from Morse theory and Vietoris–Rips filtrations of metric spaces.
The seminar is structured as a guided, collaborative reading course and is aimed at graduate students and faculty generally interested in this aspect of topology or geometry.
Location: Hebert 210
Time: 12:30 PM
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January 28, 2026
Algebra and Combinatorics
Topic: Chow rings of moduli spaces of genus 0 curves with collisions
Speaker: William Newman - Ohio State University
Abstract: Simplicially stable spaces are alternative compactifications of M_{g,n} generalizing Hassett’s moduli spaces of weighted stable curves. We give presentations of the Chow rings of these spaces in genus 0. When considering the special case of \bar M_{0,n}, this gives a new proof of Keel’s presentation of CH(\bar M_{0,n}).
Location: Gibson Hall 126
Time: 3:00 PM
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January 27, 2026
Graduate Student Colloquium
Topic: Microscale flows around a sphere under random forcing or minimal microorganism models
Speaker: Erene Erazo - Tulane University
Abstract: In this talk, I will discuss microscale flows around a sphere under random forcing or minimal microorganism models. First, I will introduce a model that describes the dynamical behavior of small spherical particles immersed in a viscous fluid under the influence of thermal fluctuations. We perform theoretical and numerical analyses of particle diffusion to characterize their motion across varying particle sizes. Second, using the same framework, I will present a minimal model for swimmers and discuss some preliminary results.
Location: Dinwiddie Hall 102
Time: 2:15 PM
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Week of January 23 - January 19
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January 22, 2026
*** Special Colloquium ***
Topic: Large Effects in Perturbed Hamiltonian Systems
Speaker: Marian Gidea - Yeshiva University
Abstract: One of the fundamental laws of physics is the conservation of energy, which states that the total energy of an isolated system remains constant.
Hamiltonian dynamics provides a natural framework for modeling this law. However, real-life systems are rarely isolated and are subject to external perturbations of various types, such as periodic / quasi-periodic forcing, random perturbations, or dissipation. In this lecture, we will consider several models from celestial mechanics, engineering, and biology, and study the effects of perturbations on these systems. The upshot is that even small perturbations can accumulate over time, giving rise to large effects, such as significant energy growth, and trajectories that wander far from their initial point. In particular, we will address conjectures proposed by Arnold (1964) and Chirikov (1979).
Location: Dinwiddie 108
Time: 3:30 PM
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January 21, 2026
Algebra and Combinatorics
Topic: When Schubert Varieties Miss Being Toric by One
Speaker: Mahir Bilen Can - Tulane University
Abstract: Schubert and Richardson varieties in flag varieties provide a rich testing ground for various group actions. In this talk I will discuss two “borderline toric” phenomena. First, I will introduce nearly toric Schubert varieties. They are spherical Schubert varieties for which the smallest codimension of a torus orbit is one. Then I will explain a simple Coxeter-type classification of these examples, and why this “one step from toric” condition forces strong spherical behavior (in particular, it produces a large family of doubly-spherical Schubert varieties). Time permitting, I will also discuss toric Richardson varieties and a type-free combinatorial criterion: a Richardson variety is toric exactly when its Bruhat interval is a lattice (equivalently, it contains no subinterval of type S3, under a mild dimension hypothesis).
Location: Gibson Hall 126
Time: 3:00 PM
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January 20, 2026
*** Special Colloquium ***
Topic: Evolution equations in physical and biological systems
Speaker: Selim Sukhtaiev - Auburn University
Abstract: Disorder and pattern formation are central themes in modern science, and both play a fundamental role in the behavior of complex physical and biological systems. In this talk, we will discuss two mathematical models that illustrate these phenomena: the Anderson model of electronic transport in random media and the Keller–Segel model of chemotaxis.
We will first turn to a mathematical treatment of the Anderson model. We will discuss several natural Hamiltonians on metric trees with random branching numbers and show that their transport properties are suppressed by disorder. This phenomenon, known as Anderson localization, is a hallmark of the spectral theory of Schrodinger operators.
We will then consider the Keller–Segel system, a coupled pair of reaction–advection–diffusion equations describing the collective motion of cells in response to chemical signals. We will focus on well-posedness of this system on arbitrary compact networks, as well as the asymptotic stability, instability, and bifurcation of steady states in both the parabolic–parabolic and parabolic–elliptic realizations of the Keller–Segel model.
Location: Dinwiddie 108
Time: 3:30 PM
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Week of January 16 - January 12
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January 16, 2026
Applied and Computational Math
Topic: Soliton Gas: recent results in one and two dimensions
Speaker: Giacomo Roberti - Northumbria University Newcastle, UK (Host): Kenneth McLaughlin
Abstract: The concept of integrable turbulence, introduced by Zakharov in 2009, provides a framework for describing random nonlinear dispersive waves governed by integrable equations, such as the Korteweg–de Vries (KdV) and the focusing nonlinear Schrödinger (fNLS) equations.
Within this framework, we focus on a specialized class of integrable turbulence dominated by solitons, known as a soliton gas, first introduced by Zakharov in 1971.
In recent years, there has been rapidly growing interest in soliton gas theory and its applications, as soliton gas dynamics have been shown to underpin a wide range of fundamental nonlinear wave phenomena, including modulational instability and the formation of rogue waves.
In this talk, we present recent results on one-dimensional soliton gases, with particular emphasis on the collision of monochromatic soliton gases, as well as recent extensions of the theory to two-dimensional soliton gases.
Location: Gibson Hall, room 126
Time: 3:00 PM
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January 14, 2026
Algebra and Combinatorics
Topic: Frobenius singularities of permanental varieties
Speaker: Trung Chau - Chennai Mathematical Institute (Host): Tai Ha
Abstract: A permanent of a square matrix is exactly its determinant with all minus signs becoming plus. Despite the similarities, the computation of a determinant can be done in polynomial time, while that of a permanent is an NP-hard problem. In 2002, Laubenbacher and Swanson defined P_t(X) to be the ideal generated by all t-by-t subpermanents of X, and called it a permanental ideal. This is a counterpart of determinantal ideals, the center of many areas in Algebra and Geometry. We will discuss properties of P_2(X), including their Frobenius singularities over a field of prime characteristic, and related open questions.
Location: Gibson Hall, room 126
Time: 3:00 PM
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January 12, 2026
Soliton gas description of modulational instability
Topic: Soliton gas description of modulational instability
Speaker: Thibault Congy - Northumbria University, Newcastle, U.K.
Abstract: Soliton gases are infinite random ensembles of interacting solitons whose large-scale dynamics are governed by the elementary two-soliton collisions. By applying the spectral theory of soliton gases to the focusing nonlinear Schrödinger equation (fNLSE), we can describe the statistically stationary and spatially homogeneous integrable turbulence that emerges at large times from the spontaneous (noise-induced) modulational instability of the plane-wave and the elliptic “dn” solutions.
I will show that a special, critically dense soliton gas—the bound-state soliton condensate—provides an accurate model for the asymptotic state of both plane-wave and elliptic integrable turbulence. Moreover, certain statistical moments of the resulting turbulence can be computed analytically, allowing us to assess deviations from Gaussianity. These analytical predictions demonstrate excellent agreement with direct numerical simulations of the fNLSE.
The talk is based on the recent works:
“Statistics of Extreme Events in Integrable Turbulence”, T. Congy, G. A. El, G. Roberti, A. Tovbis, S. Randoux, and P. Suret, Phys. Rev. Lett. 132, 207201 (2024).
“Spontaneous modulational instability of elliptic periodic waves: The soliton condensate model”, D. S. Agafontsev, T. Congy, G. A. El, S. Randoux, G. Roberti, and P. Suret, Physica D 134956 (2025).
Location: Gibson Hall 126A
Time: 3:00 PM
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