# Events This Week

Past Year Events of the Week

Week of May 4   -   April 30, 2018
Friday, May 4

## Topic

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Thursday, May 3

## Graph complexes, formality, and configuration space integrals for braids

Robin Koytcheff - University of Louisiana, Lafayette

Abstract:

In joint work with Rafal Komendarczyk and Ismar Volic, we study the space of braids, that is, the loop space of the configuration space of points in a Euclidean space.  We relate two different integration-based approaches to its cohomology, both encoded by complexes of graphs.  On the one hand, we can restrict Bott-Taubes configuration space integrals for the space of long links to the subspace of braids.  On the other hand, there are integrals for configuration spaces themselves, used in Kontsevich’s proof of the formality of the little disks operad.  Combining the latter integrals with the bar construction and Chen’s iterated integrals yields classes in the space of braids, extending a result of Kohno.  We show that these two integration constructions are compatible by relating their respective graph complexes.  As one consequence, we get that the cohomology of the space of long links surjects onto the cohomology of the space of braids.

Location:  Gibson Hall 308

Time: 12:30

Wednesday, May 2

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Tuesday, May 1

## Mathematical Models for Predicting and Mitigating the Spread of Chlamydia Sexually Transmitted Infection

Asma Azizi Boroojeni - Tulane University

Abstract:

Location: Stanley Thomas 316

Time: 11:00

Monday, April 30

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Week of April 27   -   April 23, 2018

Friday, April 27

## Modeling Evolution and Ecology of Heterogeneous Viral Strategies in Virus-Microbe Systems

Hayriye Gulbudak - University of Louisiana at Lafayette (Host: Mac Hyman)

Abstract:

Viruses of microbes, including bacterial viruses (phage), archaeal viruses, and eukaryotic viruses, can influence the fate of individual microbes and entire populations. Here, we model distinct modes of virus-host interactions and study their impact on the abundance and diversity of both viruses and their microbial hosts. We consider two distinct viral populations infecting the same microbial population via two different strategies: lytic and chronic. A lytic strategy corresponds to viruses that exclusively infect and lyse their hosts to release new virions. A chronic strategy corresponds to viruses that infect hosts and then continually release new viruses via a budding process without cell lysis. The chronic virus can also be passed on to daughter cells during cell division. The long-term association of virus and microbe in the chronic mode drives differences in selective pressures with respect to the lytic mode. We utilize invasion analysis of the corresponding nonlinear differential equation model to study the ecology and evolution of heterogenous viral strategies. We first investigate stability of equilibria, and characterize oscillatory and bistable dynamics in some parameter regions. Then, we derive fitness quantities for both virus types and investigate conditions for competitive exclusion and coexistence.  In so doing we find unexpected results, including a regime in which the chronic virus requires the lytic virus for survival and invasion.

Location:  Gibson Hall 310

Time:  3:00

Thursday, April 26

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Wednesday, April 25

## The Global Regularity Problem for the 3D Navier-Stokes and Euler Equations

Vincent Martinez - Tulane University

Abstract:

Currently a full professor at UT-Austin, Natasha Pavlovic works in the Analysis of PDEs. Early in her career, she worked in the field of mathematical fluid dynamics and in several beautiful works with Jean Bourgain (Institute of Advanced Study-Princeton), Nets Katz (Caltech), and Susan Friedlander (University of Southern California) shed light on the issue of global regularity for the 3D Navier-Stokes and Euler equations. In these works, they offered both an insightful combinatorial perspective for attacking this issue, as well as identified a phenomena known as “norm inflation,” which precludes the property of continuity with respect to initial data from holding in certain topologies. She has since moved on to working in dispersive PDEs and the Boltzmann equation. In this talk, we will discuss a "dyadic model" introduced by Katz and Pavlovic for the incompressible Euler equations. By doing so, they are able to reduce the study of blow-up or global regularity to the study of an evolution equation on an infinite tree and consequently, to tracking how the energy transfers along the edges of this graph. Their main result is a negative one, namely, that the solution to this toy model becomes infinite in finite time, i.e. finite-time blow-up. We hope to derive the model, provide heuristics for why the blow up occurs, and time permitting, mention further results from this perspective and some outstanding open problems.

Location:  Gibson Hall 310

Time:  12:00

Tuesday, April 24

## Inconsistent Mathematics: What If Everything You Knew Were Wrong... and Right... at the Same Time?

Nathan Bedell - Tulane University

Abstract:

In this talk, I'll give a brief overview of some of the classic paradoxes that have arisen both in philosophy and mathematics, and then discuss some of the more unorthodox approaches to the resolution of these paradoxes: Namely, dialetheism, and paraconsistent logic -- that is, respectively, the philosophical belief in true contradictions, and the sort of mathematical framework that allows us to reason with inconsistencies in a non-trivial way. Time permitting, I'll also discuss some of the recent work of Zach Weber on paraconsistent naive set theory, and how this (and paraconsistent mathematics more generally) potentially relate to Lawvere's theorem and some of my work in graded category theory.

Location:  Location: Stanley Thomas 316

Time:  4:30

Monday, April 23

## Data Assimilation in the Boussinesq Approximation for Mantle Convection

Shane Mcquarrie - Brigham Young University

Abstract:

Many highly developed physical models poorly approximate actual physical systems because of natural random noise. For example, convection in the earth's mantle––a fundamental process for understanding the geochemical makeup of the earth's crust and the geologic history of the earth––exhibits chaotic behavior, so it is difficult to model accurately. In addition, it is impossible to directly measure temperature and fluid viscosity in the mantle, and any indirect measurements are not guaranteed to be highly accurate.

<p>Over the last 50 years, mathematicians have developed a rigorous framework for reconciling noisy observations with reasonable physical models via a technique called data assimilation. We apply data assimilation to the problem of mantle convection with the Boussinesq approximation as the model. We then test its applicability via direct numerical simulations powered by a flexible new Python package, dedalus. We also apply machine learning techniques to identify and classify relevant system features. These methods, including the simulation and analysis code, can be generalized to many other systems.

Location:  DW 102

Time:  3:00

Week of April 20   -  April 16, 2018
Friday, April 20

## PDEs Meet Data Assimilation: New Approaches to Capturing Fluid Motion

Abstract:

A major difficulty in accurately simulating turbulent flows is the problem of determining the initial state of the flow. For example, weather prediction models typically require the present state of the weather as input. However, the state of the weather is only measured at certain points, such as at the locations of weather stations or weather satellites. Data assimilation eliminates the need for complete knowledge of the initial state. It incorporates incoming data into the equations, driving the simulation to the correct solution. The objective of this talk is to discuss innovative computational and mathematical methods to test, improve, and extend a promising new class of algorithms for data assimilation in turbulent flows and related systems.

Location:  Gibson Hall 310

Time:  3:00

Thursday, April 19

## A Degenerate Isoperimetric Problem in the Plane

Peter Sternberg - Indiana University (host:Fauci, Lisa; Glatt-Holtz; Nathan; Martinez, Vincent)

Abstract:

I will describe joint work with Stan Alama, Lia Bronsard, Andres Contreras and Jiri Dadok giving criteria for existence and for non-existence of certain isoperimetric planar curves minimizing length with respect to a metric having conformal factor that is degenerate at two points, such that the curve encloses a specified amount of Euclidean area. These curves, appropriately parametrized, emerge as traveling waves for a bi-stable Hamiltonian system that can be viewed as a conservative model for phase transitions.

Location:  Gibson Hall 126

Time:  3:30

Thursday, April 19

## Topic  TBA

Sun, Fang - Tulane University

Abstract: TBA

Location: Gibson Hall 308

Time:  12:30

Wednesday, April 18

## Loss of Strict Hyperbolicity and Singularity Formation

Katarzyna Saxton - Loyola University

Abstract:

Location:  Gibson Hall 310

Time: 12:00

Tuesday, April 17

## All You Ever Wanted to Know About Differential Forms and Your Parents Did Not Tell You

Abstract:

In this talk I will give an introduction to differential forms and I will try to explain how to use Hodge Theory to rewrite PDE's on manifolds. Also some cute thing about spherical harmonics. It will be mostly tools and classic results on differential topology and algebraic topology and 3 seconds of PDE's.

Location:  Stanley Thomas 316

Time:  4:30

Monday, April 16

## A continuation

Soumya Banerjee - Tulane University

Abstract:

Location:  Gibson Hall 400A

Time:  3:00

Week of April 13   -  April 9, 2018

Friday, April 13

## Remarks on Onsager's Conjecture and Anomalous Dissipation on domains with and without boundaries.

Theo Drivas - Princeton University

Abstract:

We first discuss the inviscid limit of the global energy dissipation of Leray solutions of incompressible Navier-Stokes on the torus.  Assuming that the solutions have Besov norms bounded uniformly in viscosity, we establish an upper bound on energy dissipation. As a consequence, Onsager-type "quasi-singularities" are required in the Leray solutions, even if the total energy dissipation is o(ν) in the limit ν → 0.  Next, we discuss an extension of Onsager's conjecture for domains with solid boundaries. We give a localized regularity condition for energy conservation of weak solutions of the Euler equations assuming Besov regularity of the velocity with σ>1/3 for any U⋐Ω and, on an arbitrary thin layer around the boundary, boundedness of velocity, pressure and continuity of the wall-normal velocity. We also prove that the global viscous dissipation vanishes in the inviscid limit for Leray-Hopf solutions of the Navier-Stokes equations under the similar assumptions, but holding uniformly in a vanishingly thin viscous boundary layer.  Finally, if a strong Euler solution exists, we show that equicontinuity at the boundary within a O(ν) strip alone suffices to conclude the absence of anomalous dissipation.

The first part of the talk concerns joint work with G. Eyink, the second with H.Q. Nguyen.

Location: Gibson Hall 310

Time: 3:00

Thursday, April 12

## Ubiquity of Schubert varieties

Venkatraman Lakshmibai - Northeastern University (Host: Can, Mahir)

Abstract:

After introducing the flag&Grassmannian varieties, I shall introduce the Schubert varieties, and I will then show several examples of important algebraic varieties which are related to Schubert varieties.

Location: Gibson Hall 126

Time: 3:30

Wednesday, April 11

## An Introduction to Spherical Actions

Mahir Can - Tulane University

Abstract:

Location:  Gibson Hall 310

Time: 12:00

Wednesday, April 11

## Multivariate Self-similarity: Multiscale eigenstructures for the estimation of Hurst exponents - Application to Internet traffic monitoring.

Patrice Abry - ENS Lyon, France

Abstract:

Scale invariance has become an ubiquitous paradigm massively used to model temporal dynamics in real- world data. Self-similar processes, and particularly their Gaussian instance, fractional Brownian motion, consist of the most common stochastic model used to account for scale invariance. However, most applications of self-similarity remained so far univariate, while data collected in real world applications most often naturally come as multivariate. Recently, Operator Fractional Brownian Motion (OfBm) has been proposed in the literature as the reference model for multivariate self-similarity. It yet remained barely used because of the lake of available identification procedure for the joint estimation of the parameters entering its definition. The present contribution achieves a first major step in the full identification of M-variate OfBm by proposing a procedure permitting to estimate the vector of M-Hurst exponents underlying its temporal dynamics. The proposed estimation procedure relies on the theoretical study of the multiscale eigen structure of the wavelet spectrum of OfBm. The proposed estimator is shown theoretically to be consistent and practically efficient, with asymptotic normality. Monte Carlo simulations applied to numerous independent copies of synthetic OfBm enable us to assess practically the actual estimation performance of the proposed procedure in a M-variate setting and for finite size data.

Location:  Gibson Hall 126

Time:  3:00

Tuesday, April 10

## Counting Borel Orbits In Classical Symmetric Varieties

Ozlem Ugurlu - Tulane University

Abstract:

Let G be a reductive group, B be a Borel subgroup, and let K be a symmetric subgroup of G. The study of B orbits in a symmetric variety G/K or, equivalently, the study of K orbits in a flag variety G/B has importance in the study of Harish-Chandramodules; it comes with many interesting Schubert calculus problems. Although this subject is very well studied, it still has many open problems from combinatorial point of view. The most basic question that we want to be able to answer is that how many B orbits there are in G/K. In this thesis, we study the enumeration problem of Borel orbits in the case of classical symmetric varieties. We give explicit formulas for the numbers of Borel orbits on symmetric varieties for each case and determine the generating functions of these numbers. We also explore relations to lattice path enumeration for some cases. In type A, we realize that Borel orbits are parameterized by the lattice paths in a pxq grid moving by only  horizontal, vertical and diagonal steps weighted by an appropriate statistic. We provide extended results for type Cas well. We also present various t-analogues of the rank generating function for the inclusion poset of Borel orbit closures in type A.

Location:  Richardson Building

Time: 11:00

Tuesday, April 10

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Monday, April 9

## Anomalous Diffusion and the Generalized Langevin Equation

Hung Nguyen - Tulane University

Abstract:

Location:  Dinwiddie 103

Time: 3:00

Week of April 6  -  April 2, 2018

Friday, April 6

## The impact of laminar boundary layers on the search for the ultimate regime of turbulent convection

Abstract:

Using rigorous mathematical analysis, we demonstrate that the boundary layers in highly turbulent convection must remain laminar when the fluid satisfies a Navier-slip boundary condition, and the temperature field satisfies a fixed flux condition at the top and bottom plates.  Although this result is not surprising in the context of discussions of the ultimate regime of thermal convection, coupled with recent rigorous upper bounds for the same system, the presence of laminar boundary layers in this setting does raise questions on how the ultimate regime appears, and/or the efficacy of upper bound theory.

Location: Gibson Hall 310

Time: 3:00

Thursday, April 5

## Thinking non-locally: the rise of integro-differential equations

Nestor Guillen - University of Massachusetts at Amherst (Host:  Nathan Glatt-Holtz)

Abstract:

In mathematics as well as in physics we are well used to dealing with partial differential equations (PDE): the infinitesimal rates of change for one or more fields are constrained by a pointwise relationship representing a physical law or geometric constraint. However, many problems in physics and mathematics feature strong long range effects which impose constraints on the variation of fields beyond the infinitesimal scale, such constraints are encoded not via PDEs but via integro-differential equations. Such equations go as far back as Leibniz, who first studied the notion of a fractional order derivative. In this talk I will survey the field of integro-differential equations, discussing important examples from statistical mechanics, fluid mechanics, stochastic processes, conformal geometry, and more. I will highlight recent results in the area, and discuss a recent result obtained with Russell Schwab regarding a min-max representation formula for these operators and how it can be applied to free boundary problems.

Location: Gibson Hall 126

Time:  3:30

Wednesday, April 4

## Coffee and Discussion: Academic Job-Hunting

Amy Buchmann - Tulane University

Abstract:

Location: Gibson Hall 310

Time: 12:00 pm

Tuesday, April 3

## Arithmetic of Elliptic Curves

Vaishavi Sharma - Tulane University

Abstract:

The theory of elliptic curves is rich, varied, and vast.  I will talk about some important properties of these curves and their rational points. We will see a few examples that illustrate the method of infinite descent by Fermat and talk about the Mordell-Weil theorem.

Location:  Stanley Thomas 316

Time: 4:30pm

Monday, April 2

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Week of March 30  -  March 26, 2018

Friday, March 30
Campus Closed

Thursday, March 29

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Wednesday, March 28

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Tuesday, March 27

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Monday, March 26

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Week of March 23  -  March 19, 2018
Friday, March 23

## Koszul duality and characters of tilting modules

Pramod Achar - LSU

Abstract:

This talk is about the "Hecke category," a monoidal category that appears in various incarnations in geometric representation theory. I will explain some of these incarnations and their roles in solving classical problems, such as the celebrated Kazhdan-Lusztig conjectures on Lie algebra representations. These conjectures (proved in 1981) hinge on the fact that the derived category of constructible sheaves on a flag variety is equipped with an obvious monoidal action of the Hecke category on the right.

It turns out that there is also a second, "hidden" action of the Hecke category on the left. The symmetry between the "hidden" left action and the "obvious" right action leads to the phenomenon known as Koszul duality. In the last part of the talk, I will discuss new results on Koszul duality with coefficients in a field of positive characteristic, with applications to characters of tilting modules for algebraic groups. This is joint work with S. Makisumi, S. Riche, and G. Williamson.

Location: Gibson Hall 126

Time: 3:00 PM

Thursday, March 22

## Catalan numbers

Richard Stanley - Massachusetts Institute of Technology

Abstract:

The sequence 1, 1, 2, 5, 14, 42, 132, ... of Catalan numbers is perhaps the most ubiquitous integer sequence in mathematics. We will give a survey of these numbers for a general mathematical audience. Topics will include the history of Catalan numbers, some combinatorial interpretations (taken from the 214 interpretations in my monograph on Catalan numbers), some algebraic interpretations, one of the many known generalizations of Catalan numbers, and some connections with number theory and analysis.

Location: Gibson Hall 126

Time: 3:30

Thursday, March 22

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Wednesday, March 21

## Downscaling data assimilation algorithm - from finite to infinite dimensions and back

Cecilia Mondaini - Institution

Abstract:

The goal of data assimilation is to obtain an accurate prediction of the future state of a physical system by suitably combining a theoretical model with observational data. The challenge consists in how to use the finite-dimensional information given by the data in order to recover the true state of a complex physical system - possessing a large number of degrees of freedom. In this talk, I will consider the nudging method for data assimilation within an infinite-dimensional framework. Further, I will present about error estimates concerning finite-dimensional numerical approximations of this nudging algorithm.

Location: Gibson Hall 310

Time: 12:00 PM

Tuesday, March 20

## MMD-system, A Finite Combinatorial Approach to Boltzmann Entropy

Sergio Villamarin -ITulane University

Abstract:

In order to make a finite interpretation to the second law of thermodynamics using Boltzmann entropy, we propose a particular finite mathematical model, a Micro-Macro-Dynamical-System (MMD-system), in which we show a characterization of a perfect entropy MMD-system, showing that in a mathematical context the second law of thermodynamics almost never applies. We also find the average number of MM-systems that have a perfect entropy state by fixing the dynamics, the macro-states or both proving a combinatorial identity. After this we show how to bound the error set of an MM-system and characterize the worst-case scenario for the second law.

Location: Stanley Thomas 316

Time: 4:30 PM

Monday, March 19

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Week of March 16  -  March 12, 2018

Friday, March 16

## Finite Type Invariants in Geometric Knot Theory

Rafal Komendarczyk - Tulane University

Abstract:

I will survey the theory of finite type invariants of knots and links, originally developed by Vassiliev. Will also discuss applications to geometric knots theory such as ropelength, embedding thickness and estimates for energies of fluid knots.

Location: Gibson Hall 310

Time: 12:00 pm

Friday, March 16

## Topic

Sergey Grigorian - Sergey Grigorian

Abstract:

The group G2 is the automorphism group of the octonion algebra. Given a G2-structure on a 7-dimensional Riemannian manifold we define an octonion bundle with a fiberwise non-associative product. We then define a metric-compatible octonionic covariant derivative on this bundle that is also compatible with the octonion product. The torsion of the G2-structure is then shown to be an octonionic connection for this covariant derivative with curvature given by the component of the Riemann curvature that lies in the 7-dimensional representation of G2. The choice of a particular G2-structure within the same metric class is then interpreted as a choice of gauge and we show that under a change of this gauge, the torsion transforms as an octonion-valued connection 1-form. We will then discuss further properties of this non-associative structure on 7-manifolds.

Location:  Gibson Hall 126

Time:  3:00

Friday, March 16

## Large Solutions of Compressible Euler Equations

Geng Chen - University of Kansas

Abstract:

Compressible Euler equations (introduced by Euler in 1757) model the motion of compressible inviscid fluids such as gases. It is well-known that solutions of compressible Euler equations often develop discontinuities, i.e. shock waves. Successful theories have been established in the past 150 years for small solutions in one space dimension. The theory on large solutions is widely open for a long time, even in one space dimension.  In this talk, I will discuss some recent exciting progresses in this direction. The talk is based on my joint works with A. Bressan, H.K. Jenssen, R. Pan, R. Young, Q. Zhang, and S. Zhu.

Location: Gibson Hall 310

Time: 3:00

Friday, March 16

## Bridges Over Troubled Waters: How the WAVES Consortium is Using Science to Save Lives from Tsunami Hazards in Indonesia.

Ron Harris - Brigham Young University

Abstract:

Historical records we have compiled demonstrate that over the past 400 years there have been 105 tsunamis throughout Indonesia, which is an average of at least1 tsunami every 4 years.  Just in the past 22 years 8 tsunamis have struck Indonesia, 7 of which caused numerous fatalities (>200,000 total deaths). Women and children account for the majority of these deaths.  However, most of these lives could have been saved if those in harm’s way would have known they were at risk, the natural signs that a tsunami was approaching and how to respond.  These three fundamental aspects of tsunami disaster preparedness require an integrated, multidisciplinary approach to resolve as demonstrated in Japan during the 2011 tsunami that struck there.  The tsunamis in Indonesia and Japan were similar in size and impacted around the same numbers of people; yet, in Japan there were less than 1 death for every 10 in Indonesia.  The difference?  Resilience!

Building resilience to natural hazards in areas most at risk is the focus of the WAVES consortium, which is a multi-disciplinary partnership of academic and government research institutions dedicated to reversing the increasing losses to nature in developing countries vulnerable to natural hazards.  We identify those communities most at risk and help implement community-based disaster mitigation strategies that will save lives from future natural hazards.  The project has three integrated goals: 1) ‘Listen to Earth’ to determine who’s most at risk.  This task involves applying novel statistical inversion techniques to determine who’s most at risk based on historical, archeological and geological records of past hazardous events.  2) ‘Listen to the People’ through conducting questionnaire surveys to determine levels of awareness and readiness, and town hall meetings. This information is vital in designing presentations and public service videos to communicate risk and effective disaster mitigation strategies in a cultural context.  3) ‘Empower People to Listen to Earth’ by assisting local communities to implement and sustain their own risk reduction strategies connected to natural warning signs.

One of the most important technical aspects of the research is the construction of tsunami flooding maps for at risk communities.  These maps provided a way to communicate who is most at risk and the details for each site about expected tsunami escape times and run up heights.  A team that integrates the expertise of geoscientists, mathematicians and statisticians at BYU, Virgina Tech and Tulane University conducts the numerical modeling.

We used the tsunami inundation maps as a starting point to assist local communities in tsunami disaster mitigation planning and implementation of risk reduction strategies.  These maps include the areas likely to flood during a tsunami, predicted waves heights in these areas, the number of people inhabiting these areas and the time after the earthquake of the arrival of the tsunami.  Essentially, they communicate who is most at risk, safe evacuate sites and the time available to evacutate.  In most cases, those at risk can know a tsunami is approaching if they feel an earthquake that shakes for > 20 seconds.  At that point they may have only 20 minutes to escape to an elevation of 20 m.

Location:  Gibson Hall 310

Time:  2:00

Thursday, March 15

## Mathematics for integrating ecological, epidemiological and environmental data to inform vector-borne disease propagation patterns

Jianhong Wu - York University

Abstract:

Vector-borne diseases such as Lyme disease, Dengue fever and Zika virus have imposed significant challenges for public health decision support systems. Modern technologies and increasing global interdisciplinary collaborations have promised rich sources of data about vector and host ecology, pathogen epidemiology and environmental conditions, so it is imperative to have fundamental (mathematical and computational) frameworks which integrate data from all different sources in order to provide summative prediction of spatiotemporal patterns of disease spread and evaluation of intervention strategies.  Here we use Lyme disease as a case study to show how clinical, laboratory, field observation and surveillance data along with remote sensor and GIS information can be integrated through a structured (hyperbolic or delay differential equation) epidemiological model to produce infection risk maps using the classical Floquet theory. We will also show how to incorporate climate change induced (vector) biological invasion into a typical reaction-diffusion epidemic model, and present some recent results about the spatiotemporal patterns of these reaction diffusion equations in an wave-like environment.

Location: Gibson Hall 126

Time: 3:30

Wednesday, March 14

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Tuesday, March 13

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Monday, March 12

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Week of March 9  -  March 5, 2018
Friday, March 9

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Thursday, March 8

## Species coexistence in the face of uncertainty

Sebastian Schreiber - UC Davis (HOST Scott McKinley)

Abstract:

A long standing, fundamental question in biology is "what are the minimal conditions to ensure the long-term persistence of a population, or to ensure the long-term coexistence of interacting species?" The answers to this question are essential for  identifying mechanisms that maintain biodiversity and guiding conservation efforts. Mathematical models play an important role in identifying potential mechanisms and, when coupled with empirical work, can determine whether or not a given mechanism is operating in a specific population or community. For over a century, nonlinear difference and differential equations have been used to identify mechanisms for population persistence and species coexistence. These models, however, fail to account for intrinsic and extrinsic random fluctuations experienced by all populations. In this talk, I discuss recent mathematical results about persistence and coexistence for models accounting for demographic and environmental stochasticity.

Demographic stochasticity stems from populations consisting of a finite number of interacting individuals. These dynamics can be represented by Markov chains on a countable state space. For closed populations in a bounded world, extinction in these models occurs in finite time, but may be preceded by long-term transients. Quasi-stationary distributions (QSDs) of these Markov chains  characterize this meta-stable behavior. These QSDs correspond to an eigenvector of the transition operator restricted to non-extinction states, and the associated eigenvalue determines the mean time to extinction when the Markov chain is in the quasi-stationary state. I will discuss under what conditions (i) this mean time to extinction increases exponentially with "habitat size" and (ii) the QSDs concentrate on attractors of the mean field model of the Markov chain. These results will be illustrated with models of competing Californian annual plants and chaotic beetles.

On the other hand, environmental stochasticity stems from fluctuations in environmental conditions which influence survival, growth, and reproduction. These effects on population and community dynamics can be modeled by stochastic difference or differential equations. For these models,  "stochastic persistence" corresponds to the weak* limit points of the empirical measures of the process placing arbitrarily little weight on arbitrarily low population densities. I will discuss sufficient and necessary conditions for stochastic persistence. These conditions involve Lyapunov exponents corresponding to the "realized" per-capita growth rates of species with respect to stationary distributions supporting subsets of species. These results will be illustrated with models of Bay checkerspot butterflies and eco-evolutionary rock-paper-scissor dynamics.

Location:  Gibson Hall 126

Time: 3:30

Thursday, March 8

## The Separable Quotient Problem for Topological Groups

Arkady Leiderman - Department of Mathematics, Ben-Gurion University of the Negev, Israel (joint work with Sidney Morris, and Mikhail Tkachenko)

Abstract:

The famous Banach-Mazur problem,  which asks if  every infinite-dimensional Banach space has  an infinite-dimensional separable quotient Banach space, has remained  unsolved for 85 years, though it has been answered in the affirmative for reflexive Banach spaces and even Banach spaces which are duals. The analogous problem for locally convex spaces has been answered in the negative, but has been shown to be true for large classes of locally convex spaces including all non-normable Frechet spaces. We investigated the analogous problem of existing of separable quotients for topological groups.  Indeed there are four natural analogues: Does every non-totally disconnected topological group have a  separable quotient group which is (i) non-trivial; (ii) infinite; (iii) metrizable; (iv) infinite metrizable. All four questions are answered in the negative in our work.  However, positive answers are given for important classes of topological groups including (a) all compact groups; (b) all locally compact abelian groups; (c) all $\sigma$-compact locally compact groups; (d) all abelian pro-Lie groups; (e) all $\sigma$-compact pro-Lie groups; (f) all pseudocompact groups. We observe then that all simple algebraic groups over local fields are separable metrizable groups. Negative answers are proved for abelian precompact groups.

Location:  Gibson Hall 308

Time:  1:00 PM

Wednesday, March 7

## Graph and Monomial Ideals

Yan gu - Tulane University

Abstract:

Over the last decade or so, commutative algebraists have become interested in studying the properties of finite simple graphs through monomial ideals. The connection between graph theory and commutative algebra help people import results from graph theory to algebraic results, and at the same time, export algebraic results to graph theory results.

Location: Gibson Hall 310

Time: 12:00 pm

Tuesday, March 6

## Stem Cell Population Growth as an Age-Dependent Branching Process

Hayden Houser - Tulane University

Abstract:

Biologists studying cell population growth lack an effective way to estimate the probability of stem cell proliferation due to inconsistencies between the experimental and theoretical models. Here we study the asymptotic properties of the age-dependent branching process to gain insight into the long-term behavior of stem cell populations. We then develop a model that assigns a unique range of probabilities to each observed value of population growth, establishing a framework for analyzing similar processes which are dependent on unknown parameters.

Location:
Stanley Thomas 316

Time: 4:30pm

Monday, March 5

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Week of March 2  -  February 26, 2018

Friday, March 2

## Regularity Criteria and the Dissipation Wave Number for Equations of Fluid Motion

Karen Zaya - University of Michigan

Abstract:

The regularity of solutions to equations of fluid motion remains a significant open problem. A vast amount of literature has been devoted to studying regularity criteria, such as the classical Beale-Kato-Majda and Ladyzhenskaya-Prodi-Serrin regularity conditions. We will review some of this literature for the three-dimensional Euler, Navier-Stokes, Boussinesq, and magnetohydrodynamics equations. Then, in the framework of Kolmogorov’s theory of turbulence, we will discuss how work with the dissipation wavenumber and determining modes has produced new, weaker regularity criteria for these equations.

Location: Gibson Hall 310

Time: 3:00 PM

Friday, March 2

## Quotients of locally compact abelian groups

Karl Hofmann - Institution

Abstract:

Location: Gibson Hall 126

Time:  3:00 PM

Thursday, March 1

## ColloquiumVolume and lattice point formulas for flow polytopes

Alejandro Morales - UMass-Amherstn (Host: Tewodros Amdeberhan)

Abstract:

Flow polytopes of graphs is a rich family of polytopes that include the Pitman-Stanley polytope and a face of the polytope of doubly stochastic matrices called the Chan-Robbins-Yuen polytope. Lattice points of polytopes are counted by Kostant's vector partition function from Lie theory. In the early 2000s, Postnikov-Stanley and Baldoni-Vergne gave remarkable formulas for their volume and lattice points using the Elliott-MacMahon algorithm and residue computations respectively.

In this talk we will describe these polytopes, how to subdivide them to obtain these formulas, and a model for the formulas using certain well-known combinatorial objects called parking functions. We will illustrate the subdivision and the model with known and new examples of flow polytopes with surprising volumes.

This is based on joint work with Karola Meszaros and joint work with Carolina Benedetti, Rafael Gonzalez D'Leon, Chris Hanusa, Pamela Harris, Apoorva Khare and Martha Yip.

Location: Gibson Hall 126

Time: 3:30 PM

Wednesday, February 28

## Support points – a new way to compact big data

Simon Mak - Georgia Tech University

Abstract:

This talk presents a new method for compacting large datasets (or in the infinite-dimensional setting, distributions) into a smaller, representative point set called support points (SPs). In an era where data is plentiful but analysis is oftentimes expensive, the proposed data reduction technique can be used to efficiently tackle many challenging big data problems in engineering, statistics and machine-learning. Using a popular distance-based statistical energy measure introduced in Székely and Rizzo (2004), SPs can be viewed as minimum-energy points under the potential field induced by big data. As such, these point sets enjoy several nice theoretical properties on distributional convergence, integration performance and functional approximation. One key advantage of SPs is that it allows for an efficient and parallelizable reduction of big data via difference-of-convex programming. This talk concludes with several real-world applications of SPs, for (a) compacting Markov chain Monte Carlo (MCMC) sample chains in Bayesian computation, (b) propagating uncertainty in expensive simulations, and (c) efficient kernel learning with big data.

Location: Stanley Thomas 316

Time: 2:00 PM

Tuesday, February 27

## Directed Topology and Dihomotopy Theory

Robyn Brooks - Tulane University

Abstract:

Directed Topology is a relatively new field of topology that arose in the 90s as a result of the abstraction of homotopy theory. The general aim of this theory is to model non-reversible phenomena. In this talk I will introduce the basics of directed topology and dihomotopy theory, and provide several illustrative examples. Finally, I will discuss a few of the potential tools that may be used to further research in this area.

Location:  Stanley Thomas 316

Time:  4:30

Monday, February 26

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Week of February 23  -  February 19, 2018

Saturday, February 24

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Friday, February 23

## 2018 Gulf States Math Alliance Conference

Friday, February 23

## On the Geometric Regularity Criteria for Incompressible Navier--Stokes Equations

Siran Li - Rice University

Abstract:

On the Geometric Regularity Criteria for Incompressible Navier--Stokes EquationsSiran Li  - Rice UniversityAbstract: We present some recent results on the regularity criteria for weak solutions to the incompressible Navier--Stokes equations (NSE) in 3 dimensions. By the work of Constantin--Fefferman, it is known that the alignment of vorticity directions is crucial to the regularity of NSE in $\R^3$.  In this talk we show a boundary  regularity theorem for NSE on curvilinear domains with oblique derivative boundary conditions. As an application, the boundary regularity of incompressible flows on balls, cylinders and half-spaces with Navier boundary condition is established, provided that the vorticity is coherently aligned up to the boundary. The effects of vorticity alignment on the $L^q$, infty\$ norm of the vorticity will also be discussed.

Location:  Gibson Hall 310

Time: 3:00

Friday, February 23

## De-noetherizing Cohen-Macaulay rings

Laszlo Fuchs - Tulane University

Abstract:

The Cohen-Macaulay rings play a most important role in commutative algebra and in its applications in algebraic geometry. They are of special kind of noetherian rings, with a rich and fast developing theory. Generalizations to non-noetherian rings are scarce, none is satisfactory, since they preserve only a few selected properties of Cohen-Macaulay rings.  We introduce a new class of commutative non-noetherian rings that is a more natural generalization and enjoys the analogues of almost all of the relevant features of the classical Cohen-Macaulay theory.

Location:  Gibson Hall 126

Time:  3:00

Friday, February 23

## Zero Divisor Graphs of Matrices over Commutative Rings

Aihua Li - Montclair State University

Abstract:

Let R be a commutative ring with identity 1 and T be the non-commutative ring of all n by n upper triangular matrices over R. In this talk, I will introduce the zero divisor graph of T. Some basic graph theory properties of the graph are given, including determination of the girth and diameter. The structure of such a graph is discussed and bounds for the number of edges are given. In the case that T is a 2 by 2 upper triangular matrix ring over a finite integral domain, the structure of the graph is fully determined. In this case an explicit formula for the number of edges is given.

Location:  Gibson 308

Time:  12:00

Thursday, February 22

## Large-Scale Inference with Graphical Nonlinear Knockoffs

Jinchi Lv - University of Southern California

Abstract:

Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness for the model-X knockoffs procedure introduced recently in Candes, Fan, Janson and Lv (2017) in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model. We establish that under mild regularity conditions, the power of the oracle knockoffs procedure with known covariate distribution in high-dimensional linear models is asymptotically one as sample size goes to infinity.  When moving away from the ideal case, we suggest the modified model-free knockoffs method called graphical nonlinear knockoffs (RANK) to accommodate the unknown covariate distribution. We provide theoretical justifications on the robustness of our modified procedure by showing that the false discovery rate (FDR) is asymptotically controlled at the target level and the power is asymptotically one with the estimated covariate distribution. To the best of our knowledge, this is the first formal theoretical result on the power for the knockoffs procedure. Simulation results demonstrate that compared to existing approaches, our method performs competitively in both FDR control and power. A real data set is analyzed to further assess the performance of the suggested knockoffs procedure. This is a joint work with Emre Demirkaya, Yingying Fan and Gaorong Li.

Location: Gibson Hall 126

Time: 3:30

Wednesday, February 21

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Tuesday, February 20

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Hung Nguyen - Tulane University

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Location:  Gibson Hall 126

Time:  3:00 PM

Monday, February 19

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Week of February 16  -  February 12 , 2018

Friday, February 16

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Thursday, February 15

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Wednesday, February 14

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Tuesday, February 13

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Monday, February 12

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Week of February 9  -  January 5, 2018

Friday, February 9

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Thursday, February 8

## Topic:  Fixed point indices and 2-complexes

Michael Kelly - Loyola University

Abstract:

Given a self-map of a compact, connected topological space we consider the problem of determining upper and lower bounds for the fixed point indices of the map.  To obtain bounds one needs to restrict attention to the class of spaces considered and also the class of self-maps.  Motivated by an elementary result in the case of a 1-dimensional complex this talk will focus attention to the setting of 2-complexes.  Some past results and related examples will be presented, leading to some current joint work with D. L. Goncalves (U. Sao Paulo, Brasil).

Location: Gibson Hall 308

Time: 12:30 PM

Wednesday, February 7

## AMS Faculty Talk – Mathematical Research

Tewodros Amdeberhan - Tulane University

Abstract:

How to delve into your research? One might say, just do it! This is by no means to profess to you on "how to". Instead, I will illustrate (in detail) certain mathematical tools with which I approached concrete projects.

Location:  Gibson Hall 310

Time:  12:00 pm

Tuesday, February 6

## Navigating the stochastic filtering landscape

Vasileios Maroulas - University of Tennessee

Abstract:

This talk navigates us through the landscape of stochastic filtering, its computational implementations and their applications in science, engineering and national defense. We start by exploring properties of the optimal filtering distribution. Under general conditions, the filtering distribution does not enjoy a closed form solution. Employing several methods, e.g. particle filters, we approximate it and we explore properties of the underlying process and its engaging parameters. The parameter estimation leads us to a research path which involves a novel algorithm of particle filters blended with a Markov Chain Monte Carlo scheme, a sequential Empirical Bayes method and related sufficient estimators. Last, this talk adopts this research path and sheds light on the estimation of the spatiotemporal evolution of radioactive material caused by the disastrous accident at the Fukushima power plant station in 2011.

Location: Stanley Thomas 316

Time:  3:30 PM

Tuesday, February 6

## A Base Case for Proving the Equality of Symbolic and Ordinary Powers of Edge Ideals of Cycles

Joseph Skelton - Tulane University

Abstract:

This talk will present the foundation for the case k=2 as a base case for showing the equality of symbolic and ordinary powers of edge ideals of cycles. The proof itself works off of basic properties of ideals and rings. I will introduce basic definitions and theorems as needed.

Location: Stanley Thomas 316

Time:  4:30 PM

Monday, February 5

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Week of February 2  -  January 29, 2017
Friday, February 2

## Representation stability, homological stability, and commuting matrices.

Daniel Ramras - Institution: Indiana University – Purdue University Indianapolis

Abstract:

Spaces of commuting matrices have received considerable attention in the last 20 years, starting with conjectures of Witten  regarding their connected components. The rational homology of these spaces can be described quite explicitly in terms of classical Weyl group invariants. These descriptions expose a surprising stability pattern, and I'll discuss work in progress (joint with Mentor Stafa) regarding applications of representation stability (in the sense of Church and Farb) to this phenomenon.  No knowledge of representation stability will be assumed.

Location: Gibson Hall 308

Time: 9:00 am

Friday, February 2

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Thursday, February 1

## Knot concordance in homology spheres

Jenifer Hom - Georgia Tech

Abstract:

The knot concordance group C consists of knots in S^3 modulo knots that bound smooth disks in B^4, with the operation induced by connected sum. We consider various generalizations of the knot concordance group, and compare these to the classical case. This is joint work with Adam Levine and Tye Lidman.

Location:  Gibson Hall 308

Time: 12:30

Thursday, February 1

## Structural and practical identifiability in modeling disease dynamics

Marisa C. Eisenberg - University of Michigan  (Hosts: Ricardo Cortez, Lisa J Fauci and James Hyman)

Abstract:

Connecting dynamic models with data to yield predictive results often requires a variety of parameter estimation, identifiability, and uncertainty quantification techniques. These approaches can help to determine what is possible to estimate from a given model and data set, and help guide new data collection. Here, we will discuss differential algebraic and simulation-based approaches to identifiability analysis, and examine how parameter estimation and disease forecasting are affected when examining disease transmission via multiple types or pathways of transmission. Using examples taken from cholera and polio outbreaks in several settings, we illustrate some of the potential difficulties in estimating the relative contributions of different transmission pathways, and show how alternative data collection may help resolve this unidentifiability.

Location:  Gibson Hall 126

Time: 3:30

Wednesday, January 31

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Tuesday, January 30

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Monday, January 29

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Week of January 26  -  January 22, 2017

Friday, January 26

## A closed non-iterative formula for straightening fillings of Young diagrams

Reuven Hodges - Institution

Abstract:

Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straightening process, due to Alfred Young, that expresses a filling of a Young diagram as a sum of semistandard tableaux subject to certain relations. It has been a long-standing open problem to give a non-iterative, closed formula for this straightening process.

In this talk I will give such a formula, as well as a simple combinatorial description of the coefficients that arise. Moreover, an interpretation of these coefficients in terms of paths in a directed graph will be explored. I will end by discussing a surprising application of this formula towards finding multiplicities of irreducible representations in certain plethysms and how this relates to Foulkes' conjecture.

Location: Gibson Hall  126

Time: 3:00

Thursday, January 25

## Test for stationarity in functional time seriesc

Pramita Bagchi - Ruhr-Universitat Bochum

Abstract:

We propose a new measure for stationarity of a functional time series, which is based on an explicit representation of the L^2-distance between the spectral density operator of a non-stationary process and its best (L^2-)approximation by a spectral density operator corresponding to a stationary process. This distance can easily be estimated by sums of Hilbert-Schmidt inner products of periodogram operators (evaluated at diﬀerent frequencies), and asymptotic normality of an appropriately standardised version of the estimator can be established for the corresponding estimate under the null hypothesis and alternative. As a result we obtain conﬁdence intervals for the discrepancy of the underlying process from a functional stationary process and a simple asymptotic frequency domain level α test (using the quantiles of the normal distribution) for the hypothesis of stationarity of functional time series. Moreover, the new methodology allows also to test precise hypotheses of the form “the functional time series is approximately stationarity”, which means that the new measure of stationarity is smaller than a given threshold. Thus in contrast to methods proposed in the literature our approach also allows to test for “relevant” deviations from stationarity.

We demonstrate in a small simulation study that the new method has very good ﬁnite sample properties and compare it with the currently available alternative procedures. Moreover, we apply our test to annual temperature curves.

Location: Stanley Thomas 316

Time: 3:30

Thursday, January 25

## Organizational Meeting

Mentor Stafa - Tulane University

Abstract:

Organizational Meeting

Location: TBA

Time: 12:30

Wednesday, January 24

## Approaches to Metastability in Materials Science

Gideon Simpson - Drexel University (Host Nathan Glatt-Holtz)

Abstract:

One of the outstanding challenges in atomistic simulations of materials is how to reach physically meaningful time scales.  While the fundamental time scale of the atomistic models is that of the femtosecond, physically meaningful phenomenon may take microseconds or longer to occur.  This precludes a direct numerical simulation with, for instance, a Langevin model of the material from reaching physical time scales.  The time scale separation challenge has motivated the development of a variety of multiscale methods, including accelerated molecular dynamics, kinetic Monte Carlo, phase field models, and diffusive molecular dynamics.  In this talk, I will survey some of these approaches and discuss common mathematical assumptions that underlie them while also highlighting where approximations have been made. Rigorous results will be presented, where available, along with outstanding mathematical challenges.

Location: Stanley Thomas 316

Time: 3:00

Tuesday, January 23

## Topic

Aram Bingham - Tulane University

Abstract:

In the words of Scott Aaronson, Geometric Complexity Theory is `a staggeringly ambitious program for proving P is not equal to NP that throws almost the entire arsenal of modern mathematics at the problem, including geometric invariant theory, plethysms, quantum groups, and Langlands-type correspondences―and that relates the P = NP problem, at least conjecturally, to other questions that mathematicians have been trying to answer for a century.'' We will say as much as we can about this area in 40 minutes or so.

Location:  Stanley Thomas 316

Time: 4:30PM

Tuesday, January 23

## Height Distributions of Critical Points of Gaussian Random Fields and Their Applications in Statisticsc

Dan Cheng - Texas Tech

Abstract: The height distributions of critical points of random fields arise from p-value computations when performing hypotheses tests at critical points such as local maxima. In this talk, we will show the formulae for the height distributions of critical points of smooth isotropic Gaussian random fields. The results hold in general in the sense that there are no restrictions on the covariance function of the field except for smoothness and isotropy. The results are based on a characterization of the distribution of the Hessian of the Gaussian field by means of the family of Gaussian orthogonally invariant (GOI) matrices, of which the Gaussian orthogonal ensemble (GOE) is a special case. We then apply the results to a topological multiple testing scheme for detecting peaks in images under stationary ergodic Gaussian noise in Euclidean space, where tests are performed at local maxima of the smoothed observed signals. The developed STEM algorithms, combined with the Benjamini-Hochberg procedure for thresholding p-values, provide asymptotic strong control of the False Discovery Rate (FDR) and power consistency, with specific rates, as the search space and signal strength get large. Simulations show that FDR levels are maintained in non-asymptotic conditions. The methods are illustrated in the analysis of functional magnetic resonance images of the brain. The method of multiple testing of local maxima are also extend to Gaussian random fields on the sphere, providing a powerful tool to detect point sources in CMB data in astronomy. Another important application is detecting change points by performing multiple testing of critical points of the smoothed observed signal. We will also discuss some open problems and future research.

Location: Stanley Thomas  316

Time: 3:30

Monday, January 22

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Week of January 19  -  January 15, 2017

Friday, January 19

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Thursday, January 18

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Wednesday, January 17

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Tuesday, January 16

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Monday, January 15

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Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 math@math.tulane.edu