Week of October 6 - October 2
Tuesday, October 3
Graduate Colloquium
Topic: A Brief Introduction to the Theory of Water Waves
Daniela Florez Pineda - Tulane University
Abstract: The theory of water waves plays a significant role in applied mathematics, and it is the main subject in coastal hydrodynamics. Euler equations are the governing equations of water waves, but due to the great difficulties studying the theoretical and numerical aspects of these equations, approximate models have been derived instead. More precisely, these models have been simplified depending upon specific features of a wave: amplitude and wavelength with respect to the water depth. We will present the basic concepts behind this theory, describe different types of waves and discuss open problems.
Location: 126
Time: 3:30pm
Week of September 29 - September 25
Friday, September 29
Applied and Computational Math Seminar
Topic: Solitons and inverse scattering transform: from the first soliton to ultra-short pulses
Katerina Gkogkou - Tulane University
Abstract: An exciting and extremely active area of research investigation is the study of solitons and the nonlinear partial differential equations that describe them. In this talk, we will discuss what solitons are, and what makes them so special. We will see when the first solitons were observed, and when the first math that describe them were derived. We will introduce ourselves to integrability and the inverse scattering transform by presenting the complex coupled short-pulse equation (ccSPE), a complex vector generalization of the short pulse equation, a nonlinear partial differential equation that describes the propagation of ultra-short pulses in optics. If time permits, we will discuss soliton solutions and their interactions in the ccSPE.
Location: Gibson Hall 325
Time: 3:00pm
Wednesday, September 27
AMS/AWM
Topic: An Overview of Various Time-Integration Methods for Solving ODEs and PDEs
Tommaso Buvoli - Tulane University
Abstract: Time integration methods are numerical algorithms for solving ordinary differential equations and spatially discretized partial differential equations. For the past fifty years they have proven indispensable for modeling a range of physical phenomena such as weather, plasmas, and fluids. In this talk I will provide a broad overview of time integration and present several different flavors of Euler's method, one of the simplest and well-known time integration methods. I will also discuss some of my recent work on parallel-in-time methods and on constructing new integrators using polynomials.
Location: Gibson Hall 126A
Time: 4:00 PM
Wednesday, September 27
Algebra and Combinatorics
Topic: Matroid lifts and representability
Dan Bernstein - Tulane
Abstract:
Matroid theory is an area of combinatorics that is becoming increasingly relevant in a broad range of research areas, from optimization to algebraic geometry. A matroid is a combinatorial structure meant to abstract the notion of linear independence in a vector space. In particular, given a vector space V and a finite subset E of V, the subsets of E that are linearly independent are an example of a matroid. Such matroids are called representable. Not all matroids are representable, but certifying that a given matroid is not representable can be a difficult task. In this talk, I will give an introduction to matroids and discuss a new certificate of non-representability that arises out of a matroid construction called lifts. This is joint work with Zach Walsh..
Location: Gibson Hall 126A
Time: 3:00 pm
Tuesday, September 26
Graduate Colloquium
Topic: Euler’s identity: “The most beautiful equation”
Vinh Pham | Tulane University
Abstract: In 1990, a poll of readers conducted by The Mathematical Intelligencer named Euler’s identity as the “most beautiful theorem in mathematics”. Euler’s identity shows a deep relation between the most important constants in mathematics. It is represented simply and beautifully. In this talk, I would like to present briefly the history and one of the proofs of Euler’s identity.
Location: 126
Time: 3:30pm
Week of September 22 - September 18
Wednesday, September 20
Algebra and Combinatorics
Topic: The Left Half and the Right Half of the Brain: Mathematics and Art
Karl Hofmann - Tulane and TU Darmstadt
Abstract:
One area in which mathematics and art approach each other is the field of advertising mathematics in posters for colloquium lectures or seminars, or in providing illustrations in books or articles. As I have been active in this direction I propose a lecture on the difficulties one encounters in the attempt to advertise mathematical contents pictorially.
Accordingly, I shall guide the audience through a short tour of recent colloquium posters for the Mathematics Department of the Technical University of Darmstadt and explain some of the problems one encounters in illustrating and advertising mathematics.
Location: Gibson Hall 126A
Time: 3:00 pm
Tuesday, September 19
Graduate Colloquium
Topic: Strong Compactness in L^p Spaces
Ketan Kalgi | Tulane University
Abstract: The idea of compactness is central to Analysis and to many other areas of mathematics. Right from the times when people thought of closed and bounded subsets of *R* as compact to the generalizations of this idea to function spaces, we shall see what additional conditions apart from being closed and bounded give us compactness in L^p. This compactness has many applications in PDEs, Fourier transform methods, etc. This is supposed to be an expository talk and would only rely on knowledge from undergraduate mathematics.undergraduate mathematics.
Location: 126
Time: 3:30pm
Week of September 15 - September 11
Friday, September 15
Applied and Computational Math Seminar
Topic: Computational modeling of small-scale ballistics
Christina Hamlet | Bucknell University
Abstract: The small, stinging organelles (nematocysts) found in Cnidarians as well as dinoflagellates are the fastest-known accelerating structures in the animal world, with rates over 5 million times the acceleration due to gravity. For the nematocyst's barb-like projectile to penetrate its prey, high accelerations facilitate the transition from a viscous regime to one where inertial forces dominate. We construct and implement a fluid-structure interaction model to numerically simulate the dynamics of a barb-like structure accelerating towards stationary, passively suspended prey. These studies help shed light on predatory and defensive strategies in small-scale interactions among microorganisms. Our results indicate that transitioning to higher Reynolds numbers is necessary to overcome the significant boundary layer interactions between the structures at low to zero Reynolds numbers usually associated with typical cellular-level interactions.
Location: Gibson Hall 325
Time: 3:00pm
Thursday, September 14
Colloquium
Topic: Scalable stochastic compartmental models for infectious disease
Marc Suchard | UCLA (Host: Ji )
Abstract: Researchers struggle with likelihood-based inference from count data that arise continuously in time but we only intermittently observe them. A major shortcoming lies in our inability to integrate most underlying stochastic processes generating the data over all possible realizations between observations. Since these processes are ubiquitous across the natural, physical and social sciences as generative models, solutions should promote the use of statistical inference in many real-world problems. One seemingly trivial example is a stochastic compartmental model tracking the count of susceptible, infectious and removed people during the spread of an infectious disease. For over 90 years, many have believed the transition probabilities of this SIR model remain beyond reach. However, applying a novel re-parameterization, integral transforms and other tools from numerical analysis shows that we can compute the transition probabilities in merely quadratic complexity in terms of the observed change in population size. Other stochastic processes for modest numbers of outcomes, such as those employed to model molecular sequence evolution, yield well to advancing computing technology, such as many-core parallelization. Examples in this talk stem from the dynamics of influenza across the global and the 2014-2015 West African ebola outbreak.
Location: Gibson Hall 126A
Time: 3:30 pm
Wednesday, September 13
AMS/AWM
Topic: Exploring Shape Reconstruction from Data Samples
Rafal Komendarczyk - Tulane University
Abstract: The challenge of figuring out unknown structures from limited data is a common problem in various scientific fields. Lately, the newly emerged field of TDA (Topological Data Analysis) has been focusing on something called "manifold reconstruction." In simpler terms, we're trying to recreate shapes from point cloud data. In this introductory talk, we will discuss various results in the manifold reconstruction as well as generalizations and open problems.
Location: Gibson Hall 126A
Time: 4:00 PM
Tuesday, September 12
Graduate Colloquium
Topic: A Journey From Linear Algebra to Statistics
John Argentino - Tulane University
Abstract: Principle Component Analysis is a common technique of dimension reduction employed in a host of fields, one that is rooted in linear algebra and optimization and utilized commonly in statistics. In this exploration we’ll examine PCA’s derivation, it’s alternate interpretations, it’s more sophisticated applications, and hopefully perform some rudimentary implementations…ations…ations…ations.
Location: 126
Time: 3:30pm
Week of September 8 - September 4
Friday, September 8
Applied and Computational Math Seminar
Topic: Navigating from statistical mechanics to random matrix theory: exploring the realm of integrability
Guido Mazzuca - Tulane University
Abstract: This presentation delves into the fascinating relationship between integrable systems theory and random matrix theory. After a general introduction explaining how these two fields are connected, we delve into a more concrete example. In particular, we show a method to describe the eigenvalue density of the Ablowitz-Ladik lattice with random initial data sampled from a Generalized Gibbs ensemble. This characterization is achieved in two ways: by the transfer operator approach, and by employing a large deviation principle (LDP). Additionally, based on these characterizations, we establish a connection between the Ablowitz–Ladik lattice and the Circular beta ensemble in the high-temperature regime. As a result, we can explicitly compute the eigenvalue density of the Ablowitz-Ladik lattice using the density of the random matrix ensemble. This talk is mainly based on separate works with R. Memin and T. Grava.
Location: Gibson Hall 325
Time: 4:00pm
Wednesday, September 6
Probability and Statistics
Topic: Many-core algorithms for scaling phylogenetic inference
Karthik Gangavarapu | UCLA
Abstract: The rapid growth in genomic pathogen data spurs the need for efficient inference techniques, such as Hamiltonian Monte Carlo (HMC) in a Bayesian framework, to estimate parameters of these phylogenetic models where the dimensions of the parameters increase with the number of sequences N. HMC requires repeated calculation of the gradient of the data log-likelihood with respect to (wrt) all branch-length-specific (BLS) parameters that traditionally takes O(N^2) operations using the standard pruning algorithm. A recent study proposes an approach to calculate this gradient in O(N), enabling researchers to take advantage of gradient-based samplers such as HMC. The CPU implementation of this approach makes the calculation of the gradient computationally tractable for nucleotide-based models but falls short in performance for larger state-space size models, such as codon models. Here, we describe novel massively parallel algorithms to calculate the gradient of the log-likelihood wrt all BLS parameters that take advantage of graphics processing units (GPUs) and result in many fold higher speedups over previous CPU implementations. We benchmark these GPU algorithms on three computing systems using three evolutionary inference examples: carnivores, dengue and yeast, and observe a greater than 128-fold speedup over the CPU implementation for codon-based models and greater than 8-fold speedup for nucleotide-based models. As a practical demonstration, we also estimate the timing of the first introduction of West Nile virus into the continental United States under a codon model with a relaxed molecular clock from 104 full viral genomes, an inference task previously intractable. We provide an implementation of our GPU algorithms in BEAGLE v4.0.0, an open source library for statistical phylogenetics that enables parallel calculations on multi-core CPUs and GPUs.
Location: Gibson 414
Time: 4:00 pm
Algebra and Combinatorics
Topic: The number of F_q-points on diagonal hypersurfaces with monomial deformation.
Dermot McCarthy - Texas Tech University
Abstract: The abstract had a lot of special characters, so I'll just assume that anyone who's actually interested will read it on Kalina's website
Location: Gibson 126 A
Time: 3:00 pm
Tuesday, September 5
Graduate Colloquium
Topic: Flag Matroids as Greedoids
Nathaniel Vaduthala | Tulane University
Abstract:
Matroids were developed in the 1930s in order to provide a combinatorial abstraction of linear subspaces and have become ubiquitous in modern combinatorics. In a similar manner, flag matroids can be seen as combinatorial abstractions of flags of linear subspaces. Despite their name however, flag matroids are not matroids, but rather can be viewed as greedoids, which themselves are generalizations of matroids. In this talk, we will briefly discuss the basics of matroid and greedoid theory and look at some properties and results related to flag matroids.
Location: 126
Time: 3:30pm
Wednesday, September ?
Probability and Statistics
Topic: TBA
Speaker | University
Abstract:
TBA
Location: TBA
Time: 2:00pm
Monday, September ?
Joint AG & GT Seminar
Topic: TBA
Speaker | University
Abstract:
TBA
Location: TBA
Time: TBA
