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Events of week
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Spring 2026 Math For All; April 10-11, 2026
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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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