Week of March 28 - March 24
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Thursday, March 27
Colloquium
Topic: INTEGRABLE COMBINATORICS
Philippe Di Francesco - University of Illinois Urbana-Champaign Host: (Ken McLaughlin)
Abstract: Combinatorics has constantly evolved from the mere counting of classes of objects to the study of their underlying algebraic or analytic properties, such as symmetries or deformations. This was fostered by interactions with in particular statistical physics, where the objects in the class form a statistical ensemble, where each element comes with some probability. Integrable systems form a special subclass: that of systems with sufficiently many symmetries to be amenable to exact solutions.
In this talk, we explore various basic combinatorial problems involving discrete surfaces, dimer models of cluster algebra, or two-dimensional vertex models, whose (discrete or continuum) integrability manifests itself in different manners: commuting operators, conservation laws, flat connections, quantum Yang-Baxter equation, etc. All lead to often simple and beautiful exact solutions.
Location: Gibson Hall 126
Time: 3:30 pm
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Thursday, March 27
Defense
Topic: Asymptotics and zeros of a special family of Jacobi polynomials.
John Lopez - Tulane University
Abstract:
Location: Howard-Tilton Memorial Library, room B11 (basement)
Time: 10:00 am
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Wednesday, March 26
AMS/AWM
Topic: Faculty Talk
Daniel Bernstein - Tulane University
Abstract: TBA
Location: Gibson Hall 310
Time: 4:15 pm
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Wednesday, March 26
Algebra and Combinatorics
Topic: Asymptotic counts of number fields generated by plane curves
Michael Allen - LSU Host: (Olivia Beckwith)
Abstract: Every irreducible polynomial f(x) with integer coefficients corresponds uniquely to a field extension of the rational numbers which consists of Q, a root x of f, and all combinations thereof under the standard arithmetic operations. For example, f(x) = x^2-2 produces the field Q(sqrt{2}) = {a + bsqrt{2} : a, b \in Q}. If f is a polynomial in two or more variables, we can produce infinitely many such fields corresponding to solutions to f=0. For f(x,y) = y^2-x^3-x-1, we have solutions (1, \sqrt{3}), (2, \sqrt{11}), (3, \sqrt{31}) and so on, and so the curve defined by f(x,y)=0 ``generates" the fields Q(\sqrt{3}), Q(\sqrt{11}), and Q(\sqrt{31}).
Recently, Mazur and Rubin suggested using this algebraic information as a means to study the geometric properties of a curve. One can easily ask the reverse question: ``If we know something about a curve C, what can we say about the fields that it generates?" We approach this question through the lens of arithmetic statistics by counting the number of such fields with bounded size---under some appropriate notion of size---for an arbitrary fixed plane curve C. This is joint work in progress with Renee Bell, Robert Lemke Oliver, Allechar Serrano L\'{o}pez, and Tian An Wong.
Location: Gibson Hall 310
Time: 3:00 pm
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Tuesday, March 25
Graduate Student Colloquium
Topic: An Introduction to Riemann-Roch and Serre Duality
Speaker: Naufil Sakran - Tulane University
Abstract: This talk aims to introduce two fundamental theorems in algebraic geometry: the Riemann-Roch theorem and Serre duality. I will develop the necessary background and present these theorems in the setting of Riemann surfaces, following the approach in Algebraic Curves and Riemann Surfaces by Rick Miranda. I will conclude my talk by given few applications of these theorems.
Location: MA 101
Time: 3:30 PM
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Monday, March 24
Probability & Statistics
Topic: Random-Walk Debiased Inference for Contextual Ranking Model with Application in Large Language Model Evaluation
Yichi Zhang - Indiana University Bloomington
Abstract: We propose a debiased inference framework to infer the ranking structure in the contextual Bradley-Terry-Luce (BTL) model. We first adopt a nonparametric maximum likelihood estimation method using ReLU neural networks to estimate unknown preference functions in the model. For the inference of pairwise ranking, we introduce a novel random-walk debiased estimator that efficiently aggregates all accessible estimating scores. In particular, under mild conditions, our debiased estimator yields a tractable distribution, and achieves the semiparametric efficiency bound asymptotically. We further extend our method by incorporating multiplier bootstrap techniques for the uniform inference of ranking structures, and adapting it to accommodate the distributional shift of contextual variables. We provide thorough numerical studies to validate the statistical properties of our method, and showcase its applicability in evaluating large language models based on human preferences under different contexts.
Location: Norman Mayer Building 101
Time: 4:00 pm
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Monday, March 24
Probability & Statistics
Topic: From Myth to Truth: An Introduction to Statisticians’ Role In Drug Development
Cindy Lu and Xinyu Cong - AstraZeneca
Abstract: Our presentation explores the evolving role of statisticians in the pharmaceutical industry, particularly within drug development. It introduces the various stages of the drug development process, from pre-clinical trials through Phase IV post-market, highlighting statisticians critical roles during those processes. The presentation aims to dispel common myths about the statistical profession in pharma, encouraging more talented graduates devote their career to the mission of bringing innovative treatments to patients.
Location: Norman Mayer Building 101
Time: 4:00 pm
Week of March 21 - March 17
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Friday, March 21
Applied and Computational Math
Topic: Inverse Problems and In-Context Operator Learning for Mean-Field Games
Siting Liu - UC Riverside Host: (Hongfei Chen)
Abstract: Mean-field game (MFG) systems provide a powerful framework for modeling the collective behavior of multi-agent systems with diverse applications. However, unknown model parameters pose challenges. In the first part of the talk, we address an inverse problem in MFGs, recovering running cost and interaction energy from noisy boundary observations. We formulate it as a constrained optimization problem and solve it efficiently using an operator-splitting algorithm. In the second part, we introduce In-Context Operator Networks (ICON), a neural framework that learns solution operators from prompts to solve MFG problems. ICON demonstrates strong few-shot learning across forward and inverse differential equation tasks, including mean-field control.
Location: Gibson Hall 325
Time: 3:00 pm
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Wednesday, March 19
AMS/AWM
Topic: Faculty Talk
Tai Ha - Tulane University
Abstract: TBA
Location: Gibson Hall 310
Time: 4:15 pm
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Wednesday, March 19
Algebra and Combinatorics
Topic: Geometric vertex decomposition
Thai Nguyen - University of Dayton
Abstract: Geometric vertex decomposition is a useful technique in various algebro-geometric contexts such as liaison theory and Groebner bases theory. It is a degeneration technique that was first used in the work of Knutson-Miller-Yong to study Schubert determinantal ideals. It can also be thought of as an ideal-theoretic generalization of vertex decomposition of simplicial complexes. It was shown in the work of Klein-Rajchgot that geometrically vertex decomposable (gvd) ideals possess various nice algebraic properties as those of the Stanley-Reisner ideal of vertex decomposable simplicial complexes. In this talk, I shall survey some results using this technique. I shall also discuss some homological invariants of gvd ideals, with emphasis on toric ideals of graphs. The talk will include results from my project with Jenna Rajchgot and Adam Van Tuyl.
Location: Gibson Hall, room 310
Time: 3:00 pm
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Tuesday, March 18
Graduate Student Colloquium
Topic: Laurent Series Expansions of $L$ -functions
Tushar Karmakar - Tulane University
Abstract: In this talk, we will be revisiting the well-known Laurent series expansion of Riemann zeta function, Hurwitz zeta function and as a generalization, Dirichlet $L$- function. Additionally, we will briefly discuss modular forms and its $L$- series and then we will see the Laurent series expansion for $L$ - function attached to cusp forms over the full modular group.
Location: Norman Mayer Building - MA-101 (G)
Time: 3:30pm
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Monday, March 17
Integrability and Beyond !!!
Topic: How to compute interesting statistical quantities in random matrices: Fredholm determinant representations for (a) spectral gaps, (b) largest eigenvalues, and (c) number statistics, Part 6.
Ken McLaughlin - Tulane University
Abstract: The plan: investigate the behavior of eigenvalues of random matrices when the size of the matrix grows to infinity, starting with more numerical experiments, and then the asymptotic behavior of the kernel, and the Fredholm determinant. The aim is to understand known asymptotic behavior and identify some interesting but tractable challenging problems.
Location: Gibson Hall 310
Time: 3:00pm
Week of March 14 - March 10
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Scientific Computing Around Louisiana (SCALA): March 14 - 15
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Friday, March 14
Algebra and Combinatorics
Topic: Developments in Interpolation Problem for Projective Spaces
Dipendranath Mahato - Affiliation
Abstract: Classical Interpolation problem of estimating new data from a set of known data is well understood under one variable situation. Here we are more interested in higher dimensional Projective Spaces, where we are trying to find the lowest possible degree of the hyper-surface passing through a given set of points with prescribed multiplicity. There are famous conjectures to tackle such problems: Chudnovsky’s Conjecture, Demailly’s Conjecture. I will be discussing those conjectures and some recent developments in this area.
Location: Gibson Hall 310
Time: 3:00pm
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Thursday, March 13
Colloquium
Topic: The Feynman-Lagerstrom criterion for boundary layers
Theodore Drivas - SUNY Stony Brook Host: (Sam)
Abstract: We study the boundary layer theory for slightly viscous stationary flows forced by an imposed slip velocity at the boundary. According to the theory of Prandtl (1904) and Batchelor (1956), any Euler solution arising in this limit and consisting of a single ``eddy" must have constant vorticity. Feynman and Lagerstrom (1956) gave a procedure to select the value of this vorticity by demanding a necessary condition for the existence of a periodic Prandtl boundary layer description. We will show that this condition is also sufficient for the existence of a periodic boundary layer described by the Prandtl equations. This is joint work with S. Iyer and T. Nguyen.
Location: Gibson Hall 126
Time: 3:30 pm
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Wednesday, March 12
Algebra and Combinatorics
Topic: Algebraic Properties of Invariant ideals.
Souvik Dey - Charles University, Prague Host: (Dipendranath Mahato, Tai Ha)
Abstract: Let R be a polynomial ring with mn many indeterminate over complex numbers. We can think of the indeterminates as a matrix, X of size m x n.
Consider the group G = Gl(m) x Gl(n). Then G acts on R via the group action (A,B)X =AXB^{-1}. In 1980, DeConcini, Eisenbud, and Procesi introduced the ideals that are invariant under this group action.
In the same paper, they described various properties of those ideals, e.g., associated primes, primary decomposition, and integral closures. In recent work with Sudipta Das, Tài Huy Hà, and Jonathan Montaño, we described their rational powers and proved that they satisfy the binomial summation formula. In an ongoing work, Alexandra Seceleanu and I are formulating symbolic properties of these ideals. In this talk, I will describe these ideals and the properties we are interested in. I will also showcase some results from my collaborations.
Location: Gibson Hall, room 310
Time: 3:00 pm
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Monday, March 10
Integrability and Beyond !!!
Topic: How to compute interesting statistical quantities in random matrices: Fredholm determinant representations for (a) spectral gaps, (b) largest eigenvalues, and (c) number statistics, Part V.
Ken McLaughlin - Tulane University
Abstract: The plan: (1) Executive summary of the connection between eigenvalues of random matrices and Fredholm determinants. (2) T random matrix theory laboratory – testing the theory. (3) Behavior of eigenvalues when the size of the matrices grows to $\infty$.
Location: Gibson Hall 310
Time: 3:00pm
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Week of February 28 - February 24
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Wednesday, February 26
Algebra and Combinatorics
Topic: A combinatorial method for the reduction number of an ideal
Alessandra Costantini - Tulane University
Abstract: In the study of commutative rings, several algebraic properties are captured by numerical invariants which are defined in terms of ideals and their powers. Among these, of particular relevance are the reduction number and analytic spread of an ideal, which control the growth of the powers of the given ideal for large exponents. Unfortunately, these invariants are usually difficult to calculate for arbitrary ideals, and different methods might be required depending on the specific features of the class of ideals under examination.
In this talk, I will discuss a combinatorial method to calculate the reduction number of an ideal, based on a homological characterization in terms of the regularity of a graded algebra. This is part of ongoing joint work with Louiza Fouli, Kriti Goel, Haydee Lindo, Kuei-Nuan Lin, Whitney Liske, Maral Mostafazadehfard and Gabriel Sosa.
Location: Gibson Hall, room 310
Time: 3:00 pm
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Tuesday, February 25
Graduate Student Colloquium
Topic: Estimation of degradation rate in biological cells
Lan Trinh - Tulane University
Abstract: In our interested biological cells, the particles were born and diffused as in Brownian motions, which could then exit, degrade or stay alive at a specific time. From the figures recording locations of alive particles, we investigate the estimation of the degradation rate and its statistical properties. In this talk, I will discuss the toy model of this problem, based on which will be developed into more sophisticated setup of real cells.
Location: Norman Mayer Building - MA-101 (G)
Time: 3:30pm
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Tuesday, February 25
Colloquium
Topic: Dynamical Systems Insights into Map Enumeration
Joceline Lega - University of Arizona - Host: (Ken McLaughlin)
Abstract: This talk will highlight techniques from discrete dynamical systems theory that have led to significant advances in map enumeration. We will start with a brief overview of generating functions for map counts and their relation to solutions of the discrete Painlevé I equation. We will then present computational and analytical results that lead to specific generating functions and, in the case of 4-valent maps, derive explicit expressions for map counts as functions of the number of vertices and the genus of the surface on which the map is embedded. We will conclude with open as well as recently solved questions associated with this research program. This is joint work with Nick Ercolani and Brandon Tippings..
Location: TBA
Time: 4:30 pm
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Monday, February 24
Integrability and Beyond !!!
Topic: A Vision of Integrability: McKean’s Unimodularity Conjecture.
Nick Ercolani - University of Arizona (Host: Ken McLaughlin)
Abstract: In a striking series of papers, titled Geometry of KdV(1) - Geometry of KdV(5), Henry Mckean formulated a precise notion of what should be the function space foliation by invariant sets for the Korteweg-deVries evolution. This is meant to pertain to initial data that is smooth but otherwise only required to be bounded below. This foliation should generalize the picture of (typically infinite dimensional) Arnold-Liouville torii familiar from the particular case of periodic initial data. The proposed answer is phrased in terms Kodaira’s elegant extension of the classical Weyl-Titchmarsh theory for spectral weights of Schrodinger operators.
The goal of the talk will be to first present an overview of McKean’s conjecture and then to describe some recent work, joint with Dylan Murphy, on analogous investigations for the Toda lattice and Jacobi operators.
Location: Gibson Hall 310
Time: 3:30pm
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Week of February 21 - February 17
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Friday, February 7
Applied and Computational Math
Topic: The unreasonable utility of symmetric three-term recurrences
Tom Trogdon - University of Washington Host: (Aikaterini Gkogkou)
Abstract: Symmetric three-term recurrences (STRs) naturally arise in the study of orthogonal polynomials, iterative methods for symmetric matrices and numerical complex analysis. While deceptively simple, STRs allow for many extremely effective numerical methods. This talk will review some classical methods and uses and connect to more recent developments related to the computation of Cauchy integrals, computing matrix functions and spectral density estimation for random matrices.
Location: Gibson Hall 325
Time: 3:00pm
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Friday, February 21
Algebra and Combinatorics
Topic: Ear decompositions of graphs: an unexpected tool in Combinatorial Commutative Algebra
Ngo Viet Trung - Institute of Mathematics, Vietnam Academy of Science and Technology Host: (Tai Ha)
Abstract: Ear decomposition is a classical notion in Graph Theory. It has been shown in [1, 2] that this notion can be used to solve difficult problems on homological properties of edge ideals in Combinatorial Commutative Algebra. This talk presents the main combinatorial ideas behind these results.
[1] H.M. Lam and N.V. Trung, Associated primes of powers of edge ideals and ear decompositions of graphs, Trans. AMS 372 (2019)
[2] H.M. Lam, N.V. Trung, and T.N. Trung, A general formula for the index of depth stability of edge ideals, Trans. AMS, to appear.
Location: Gibson Hall 310
Time: 3:00 pm
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Tuesday, February 18
Graduate Student Colloquium
Topic: Stochastic Differential Equations, Epidemic Models, and a brief overview on Chagas' Disease.
Joshua Agbomola - Tulane University
Abstract: The presentation provides an introduction to Chagas disease, a parasitic infection caused by Trypanosoma cruzi, primarily transmitted by Triatomine bugs. It outlines key transmission pathways, including vector-borne, congenital, and less common mechanisms. The discussion then shifts to the application of a stochastic SIS (Susceptible-Infected-Susceptible) model, illustrating how randomness can enhance epidemic modeling by accounting for variability and uncertainty in disease dynamics.
Location: BO 242
Time: 3:00pm
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Monday, February 17
Integrability and Beyond !!!
Topic: Random Matrices: Fredholm determinant representations for (a) spectral gaps, (b) largest eigenvalues, and (c) number statistics.
TBD - Tulane University
Abstract: We will return to the numerical experiments, to carefully develop intuition. And explore some more precise open problems. Then we will return to complete the proof of the fundamental relation between eigenvalues and Fredholm determinants.
Location: Gibson Hall 310
Time: 3:30pm
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Week of February 14 - February 10
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Clifford Lectures: February 11 - 14
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Wednesday, February 12
Prob & Stats seminar
Topic: Multidimensional Empirical Wavelet Transform
Charles-Gérard Lucas- San Diego State University
Abstract: The empirical wavelet transform, inspired by empirical mode decomposition, is an adaptive time-frequency representation that extracts the different modes of a signal or image by designing a bank of adaptive wavelet filters. The data robustness of this transform has made it the subject of intense development and a growing number of applications over the past decade. However, to date, it has mainly been studied theoretically for signals, and its extension to images is limited to a specific wavelet kernel. This presentation will focus on a multidimensional extension of this transform formulated from a wavelet kernel. Theoretical and numerical properties of this formulation will be particularly detailed. Its interest for texture segmentation will also be highlighted.
Location: 104 Norman Mayer
Time: 1:00pm
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Tuesday, February 11
Graduate Student Colloquium
Topic: Partial Betti splittings for binomial edge ideals
Aniketh Sivakumar - Tulane University
Abstract: The Free resolution of a module is an object which contains important information about the structure of the module. These resolutions are used to define several invariants associated to a module, including their Betti numbers. In this talk, we will introduce the notion of a partial Betti splitting of a homogeneous ideal, generalizing the notion of a Betti splitting first given by Francisco, Hà, and Van Tuyl. We will also define an ideal associated to a graph known as its binomial edge ideal and describe an explicit partial Betti splitting for this class of ideals.
Location: BO 242
Time: 3:30pm
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Monday, February 10
Algebra and Combinatorics
Topic: Versions of the circle method
Edna Jones - Tulane University
Abstract: The circle method is a useful tool in analytic number theory and combinatorics. The term "circle method" can refer to one of a variety of techniques for using the analytic properties of the generating function of a sequence to obtain an asymptotic formula for the sequence. We will discuss different versions of the circle method and some results that can be obtained by using the circle method.
Location: Gibson Hall, room 310
Time: 3:00 pm
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Monday, February 10
Integrability and Beyond !!!
Topic: Random Matrices: Fredholm determinant representations for (a) spectral gaps, (b) largest eigenvalues, and (c) number statistics.
Ken McLaughlin - Tulane University
Abstract: We will continue exploring the connection between random matrices and Hermite polynomials, and start the proof of the relation between eigenvalue probabilities and Fredholm determinants. Time permitting, we will return to the numerical experiments, to carefully develop intuition.
Location: Gibson Hall 310
Time: 3:30pm
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Monday, February 10
Algebra and Combinatorics
Topic: From Interpolation problems to matroids
Paolo Mantero - University of Arkansas - Host: (Alessandra Costantini)
Abstract: Interpolation problems are long-standing problems at the intersection of Algebraic Geometry, Commutative Algebra, Linear Algebra and Numerical Analysis, aiming at understanding the set of all polynomial equations passing through a given finite set X of points with given multiplicities.
In this talk we discuss the problem for matroidal configurations, i.e. sets of points arising from the strong combinatorial structure of a matroid. Starting from the special case of uniform matroids, we will discover how an interplay of commutative algebra and combinatorics allows us to solve the interpolation problem for any matroidal configuration. It is the widest class of points for which the interpolation problem is solved. Along the way, we will touch on several open problems and conjectures.
The talk is based on joint projects with Vinh Nguyen (U. Arkansas).
Location: Dinwiddie Hall, room 103 (note unusual location and day)
Time: 3:00 pm
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Week of February 7 - February 3
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Friday, February 7
Applied and Computational Math
Topic: Admissible behavior of Krylov subspace iterative methods for non-symmetric systems
Kirk Soodhalter - Trinity College Dublin (Lisa Fauci)
Abstract: In this talk, we introduce the audience Krylov subspace iterative methods, the work-horse matrix-free methods for solving linear systems and eigenvalue problems in the case that matrix is large and sparse or otherwise not available to be solved by accessing all entries of the matrix. These methods are built on the core assumption that we only have access to a procedure that multiplies the matrix times vectors at relatively low computational cost. After discussing some basic convergence theory related to polynomial interpolation, we demonstrate the complicated nature of estimating rate of convergence for such methods based on quantities such as eigenvalues when the matrix is non-normal. In particular, we discuss and contextualize a constructively proven theorem that in pathological cases, the eigenvalues need not be at all descriptive with regard to convergence behavior [Greenbaum, Pták, Strakoš 1996]. We build the language needed to describe the mechanics of how to construct such cases. We then discuss our currently running project on developing more robust theory of convergence for these methods applied to non-symmetric Toeplitz systems, the type of which arise in a variety of problems from the computational sciences. Toeplitz matrices are constant along each diagonal; thus the linear system is governed by a matrix with fewer degrees of freedom than in general. We demonstrate that tools developed in the aformentioned constructive proof can be repurposed to develop refine previous convergence theory for Toeplitz systems. This is ongoing work; thus we finish by discussing what remains to be proven and how we intend to extend this theory to generalizations of Toeplitz matrices encompassing a larger class of matrix structures often arising in the computational sciences.
Location: Gibson Hall 325
Time: 3:00pm
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Tuesday, February 4
Graduate Student Colloquium
Topic: Symbolic powers via extension
Haoxi Hu - Tulane University Host: (Moslem Uddin)
Abstract: Symbolic Powers of ideals are well-studied objects, in this talk, We investigates under which conditions the symbolic powers of the extension of an ideal is the same as the extension of the symbolic powers. Our result generalizes the known scenarios. As an application, we prove formulas for the resurgence of sum of two homogeneous ideals in finitely generated k-algebra domains, where k is algebraically closed. Initially, these were known for ideals in polynomial rings.
Location: Norman Mayer Building - MA-101 (G)
Time: 3:30pm
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Monday, February 3
Integrability and Beyond !!!
Topic: Random Matrices: Fredholm determinant representations for (a) spectral gaps, (b) largest eigenvalues, and (c) number statistics.
Ken McLaughlin - Tulane University
Abstract: We will start calculating some basic number statistics for finite sized random matrices using Hermite polynomials, and compare to numerical experiments. In the second half, I will explain the connection between random matrices and Hermite polynomials.
Location: Gibson Hall 310
Time: 3:30pm
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Week of January 31 - January 27
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Friday, January 31
Colloquium
Topic: Partitions Detect Primes
Ken Ono - University of Virginia Host: ( )
Abstract: This talk presents “partition theoretic” analogs of the classical work of Matiyasevich that resolved Hilbert’s Tenth Problem in the negative. The Diophantine equations we consider involve equations of MacMahon’s partition functions and their natural generalizations. Here we explicitly construct infinitely many Diophantine equations in partition functions whose solutions are precisely the prime numbers. To this end, we produce explicit additive bases of all graded weights of quasimodular forms, which is of independent interest with many further applications. This is joint work with Will Craig and Jan-Willem van Ittersum.
Location: Gibson Hall 126 Subject to change
Time: 4:00 pm
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Friday, January 31
Applied and Computational Math
Topic: Towards efficient deep operator learning for forward and inverse PDEs: theory and algorithms
Ke Chen - University of Delaware Host: (Hongfei Chen)
Abstract: Deep neural networks (DNNs) have been a successful model across diverse machine learning tasks, increasingly capturing the interest for their potential in scientific computing. This talk delves into efficient training for PDE operator learning in both the forward and inverse PDE settings. Firstly, we address the curse of dimensionality in PDE operator learning, demonstrating that certain PDE structures require fewer training samples through an analysis of learning error estimates. Secondly, we introduce an innovative DNN, the pseudo-differential auto-encoder integral network (pd-IAE net), and compare its numerical performance with baseline models on several inverse problems, including optical tomography and inverse scattering.
Location: Gibson Hall 325 (Room Change)
Time: 3:00pm
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Tuesday, January 28
Graduate Student Colloquium
Topic: Unearthing Latent Time Series in Repeated Survey Data
John V Argentino - Tulane University Host: (Moslem Uddin)
Abstract: In today’s world of readily available data, repeated survey data is commonplace in a variety of settings. These data are collected to model the impacts of particular variables of interest, which are often estimated using methods that assume temporal independence in the observed noise. This premise is shaky given how easily conceivable it is that variables not accounted for have some degree of continuity over time. This talk will present a method that seeks to reconcile mixed effect models and time series analysis while employing classic results from linear algebra to identify it’s potential pitfalls.
Location: DW 102
Time: 3:30pm
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Monday, January 27
Integrability and Beyond !!!
Topic: Random Matrices: Fredholm determinant representations for (a) spectral gaps, (b) largest eigenvalues, and (c) number statistics.
Ken McLaughlin - Tulane University
Abstract: How to compute interesting statistical quantities in random matrices: Fredholm determinant representations for (a) spectral gaps, (b) largest eigenvalues, and (c) number statistics.
With the assistance of the whole group, this should be very introductory.
Speakers: to be determined, starting with Ken McLaughlin on January 27.
Location: Gibson Hall 310
Time: 3:30pm
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Week of January 24 - January 20
Friday, January 24
Applied and Computational Math
Topic: Manuela Girotti - Emory University Host: (Aikaterini Gkogkou)
Di Fang - Duke University
Abstract: N. Zabusky coined the word "soliton" in 1965 to describe a curious feature he and M. Kruskal observed in their numerical simulations of the initial-value problem for a simple nonlinear PDE. The first part of the talk will be a broad introduction to the theory of solitons/solitary waves and integrable PDEs (the KdV and modified KdV equation in particular), describing classical results in the field. The second (and main) part of the talk will focus on some new developments and growing interest into a special case of solutions defined as "soliton gas".
I will describe a collection of works done in collaborations with K. McLaughlin (Tulane U.), T. Grava (SISSA/Bristol), R. Jenkins (UCF) and A. Minakov (U. Karlova).
We analyze the case of a regular, dense KdV soliton gas and its large time behaviour with the presence of a single trial soliton travelling through it.
We are able to derive a series of physical quantities that precisely describe the dynamics, such as the local phase shift of the gas after the passage of the soliton, and the velocity of the soliton peak, which is highly oscillatory and it satisfies the kinetic velocity equation analogous to the one posited by V. Zakharov and G. El (at leading order).
I will finally present some ongoing work where we establish that the soliton gas is the universal limit for a large class of N-solutions with random initial data.
Location: Gibson Hall 325
Time: 3:00pm
Week of January 17 - January 13
Friday, January 17
Applied and Computational Math Seminar
Topic: _______
Di Fang - Duke University
Abstract: Unbounded Hamiltonian Simulation: Quantum Algorithm and Superconvergence
Location: Simulation of quantum dynamics, emerging as the original motivation for quantum computers, is widely viewed as one of the most important applications of a quantum computer. Quantum algorithms for Hamiltonian simulation with unbounded operators Recent years have witnessed tremendous progress in developing and analyzing quantum algorithms for Hamiltonian simulation of bounded operators. However, many scientific and engineering problems require the efficient treatment of unbounded operators, which may frequently arise due to the discretization of differential operators. Such applications include molecular dynamics, electronic structure, quantum differential equations solver and quantum optimization. We will introduce some recent progresses in quantum algorithms for efficient unbounded Hamiltonian simulation, including Trotter type splitting and Magnus expansion based algorithms in the interaction picture. (The talk does not assume a priori knowledge on quantum computing.)
Location: Gibson Hall 126
Time: 3:00pm
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Thursday, January 16
Colloquium
Topic: On the flow of zeros of derivatives of polynomials
Andrei Martinez-Finkelshtein - Baylor University (Host: Ken)
Abstract: Assume we have a sequence of polynomials whose asymptotic zero distribution is known. What can be said about the zeros of their derivatives? Especially if we differentiate each polynomial several times, proportional to its degree? This simple-to-formulate problem has recently attracted the attention of researchers. Both the problem and the methods of its solution have exciting connections with free probability, random matrices, and approximation theory on the complex plane. In this talk, I will explain some known results in this direction and our approach to the problem, which uses only some elementary complex analysis. This is a joint work with E. Rakhmanov from the University of South Florida.
Location: Gibson Hall 126
Time: 3:30 pm
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Wednesday, January 15
Algebra and Combinatorics
Topic: Rings with extremal cohomology annihilator
Souvik Dey - Charles University, Prague Host: (Dipendranath Mahato, Tai Ha)
Abstract: The cohomology annihilator of Noetherian algebras was defined by Iyengar and Takahashi in their work on strong generation in the module category. For a commutative Noetherian local ring, it can be observed that the cohomology annihilator ideal is the entire ring if and only if the ring is regular. Motivated by this, I will consider the question: When is the cohomology annihilator ideal of a local ring equal to the maximal ideal? I will discuss various ring-theoretic and category-theoretic conditions towards understanding this question and describe applications for understanding when the test ideal of the module closure operation on cyclic surface quotient singularities is the maximal ideal.
Location: Gibson Hall, room 310
Time: 3:00 pm
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