Week of December 11 - December 15, 2017

*Wednesday, December 13*

## Probability and Statistics

**Using Remote Sensing, Weather, and Demographic Data to Create Risk Maps for Zika, Dengue, and Chikungunya in Brazil**

Week of December 8 - December 4, 2017

*Friday, December 8*

**Topic**

*Thursday, December 7*

## Algebra and Combinatorics

**Cayley Grassmannian**

*Thursday, December 7*

## Geometry and Topology Seminar

**Simplicial approximations and homology with local coefficients**

*Wednesday, December 6*

**Topic**

*Tuesday, December 5*

**Topic**

*Monday, December 4*

## Special Statistics Seminar

**Bayesian Experimental Design and Hierarchical Model for Quantitative and Qualitative Responses**

Week of December 1 - November 27, 2017

*Friday, December 1*

## Applied and Computational Mathematics

**Regularity Problems of some Boussinesq Equations**

*Thursday, November 30*

## Colloquium

**Burgers equation with random forcing**

*Thursday, November 30*

## AMS/AWM Faculty Talk

**Good Choices for Great Careers**

*Thursday, November 30*

**Topic**

*Thursday, November 30*

**Topic**

*Wednesday, November 29*

## Probability and Statistics

**A Bayesian Approach to Estimating Background Flows from a Passive Scalar**

*Tuesday, November 28*

**Topic**

*Monday, November 27*

**Topic**

**Week of November 24 - November 20, 2017**

*Friday, November 24*

**Thanksgiving Holiday**

*Thursday, November 23*

**Thanksgiving Holiday**

*Wednesday, November 22*

**Topic**

*Tuesday, November 21*

**Topic**

*Monday, November20*

**Topic**

Week of November 17 - November 13, 2017

*Friday, November 17*

**Topic**

*Thursday, November 16*

## Colloquium

**Cell Metabolism, Mathematics, and Public Health**

*Thursday, November 16*

## AMS/AWM Faculty Talk

**Anomalous Diffusion and Random Encounters in Biological Fluids**

*Thursday, November 16*

## Algebra-Combinatorics

**Symmetric functions in superspace**

*Thursday, November 16*

**Topic**

*Thursday, November 16*

**Topic**

*Wednesday, November 15*

**Title**

*Tuesday, November 14*

**K-Orbits in the Flag Variety and Clansc**

**Location: Stanley Thomas 316**

*Monday, November 13*

**Topic**

**Week of November 10 - November 6, 2017**

*Friday, November 10*

**Topic**

*Thursday, November 9*

## Algebra & Combinatorics seminar

**Depth and Stanley Depth of monomial ideal**

*Thursday, November 9*

## Colloquium

**Analysis of a stratified Kraichnan Model**

This is based on joint work with Jingyu Huang.

*Wednesday, November 8*

## Probability and Statistics

**Classification on the space of persistence diagrams**

*Tuesday, November 7*

## Graduate Student Colloquium

**Rational Singularity of The Toric Ring of Matroids**

*Monday, November 6*

**Topic**

**Week of November 3 - October 30, 2017**

*Friday, November 3*

## Applied and Computational

**Transition Probabilities for ASEP on the ring**

*Thursday, November 2*

## Geometry and Topology

**Asymptotic higher order linking in volume preserving flows**

*Thursday, November 2*

**Topic**

*Thursday, November 2*

## Algebra and Combinatorics

**The Genesis of Involution**

*Thursday, November 2*

## AWM Coffee and Discussion:

**From Math Professor to Dean**

Location: Gibson 400A

*Wednesday, November 1*

**Topic**

*Tuesday, October 31*

## Graduate Student Colloquium

**Chudnowsky's Conjecture**

*Monday, October 30*

**Topic**

**Week of October 27 - October 23, 2017**

*Friday, October 27*

## Applied and Computationa

**Topic**

*Thursday, October 26*

## Algebra and Combinatorics

**Beyond Perfect Graphs: Hypercycles and Perfect Hypergraphs**

**Location: Norman Mayer 200-A**

Time: 12:30 PM

*Thursday, October 26*

## Geometry and Topology

**Topological and Geometric Reconstruction of Metric Graphs**

*Thursday, October 26*

## AWM/AMS

**Spaces of representations and representation stability**

*Thursday, October 26*

## Colloquium

**On Nonlinear Feedback Control and State Estimation**

Location: Gibson Hall 126

Time: 3:30 pm

*Wednesday, October 25*

**Topic**

*Tuesday, October 24*

## Graduate Student Colloquium

**r-indecomposable Factorial and Bell numbers**

*Monday, October 23*

**Topic**

**Week of October 20 - October 16, 2017**

*Friday, October 20*

## Applied and Computational

**Self-organized dynamics: aggregation and flocking**

Dr. Changhui Tan - Rice University

Location: Gibson Hall 414

Time: 3:30 PM

*Thursday, October 19*

## Colloquium

**Short-term probabilistic hazard mapping -- forecasting catastrophe without stationary assumptions**

*Thursday, October 19*

**Topic**

*Thursday, October 19*

Geometry and Topology

**The classifying space of transitionally commutative O(2)-bundles**

Bernardo Villarreal **- University Purdue University Indianapolis**

*Thursday, October 19*

## Algebra and Combinatorics

**Lech's inequality and its improvements**

*Wednesday, October 18*

**Topic**

*Tuesday, October 17*

Graduate Student Colloquium

**A Probabilist's Perspective**

Cooper Boniece - Tulane University

Location: Stanley Thomas 316

Time: 4:30 PM

*Monday, October 16*

**Topic**

*Friday, October 13*

**Topic**

*Thursday, October 12*

**Topic**

*Wednesday, October 11*

**Topic**

*Tuesday, October 10*

**Topic**

*Monday, October 9*

**Topic**

Week of October 6 - October 2, 2017

*Friday, October 6*

**Wentzell Conference**

*Thursday, October 5*

**Wentzell Conference**

*Thursday, October 5*

## AMS

**Combining Mathematical Modeling, PDE Concepts, and Computational**

Methods to Study the Interaction of Microorganisms and the Fluid Flow

**Location: Gibson 400A**

*Thursday, October 5*

## Algebra & Combinatorics

**Locally compact p-groups and their challenges**

**Location: Norman Mayer 200-A**

*Wednesday, October 5*

## Geometry and Topology

**Topology of representation spaces and invariants of finite reflection groups**

*Wednesday, October 4*

**Topic**

*Tuesday, October 3*

## Graduate Student Colloquium

**Accurate Integration of High Dimensional Functions using Polynomial Detrending**

*Monday, October 2*

**Topic**

**Carrie Manore - Los Alamos National Laboratory
**

**Abstract:
**

Mosquito-borne diseases such as Zika, dengue, and chikungunya viruses have dynamics coupled to weather, ecology, human infrastructure, socio-economic demographics, and behavior. We use both mechanistic process-based models and statistical models to understand risk for Zika and dengue. Using deterministic and stochastic models, we quantified Zika risk in the eastern United States and estimated outbreak size in Central and South American countries. Time-varying remote sensing and weather data, along with demographics and internet data were used to predict risk through time for dengue outbreaks in Brazil with distributed lag methods, quantifing the lag between outbreaks and weather. Our statistical and mechanistic models indicate that the relationships between the variables are complex, but that quantifying risk is possible with the right data at appropriate spatio-temporal scales.

**Location: Gibson Hall 414
**

**Time: 3:00 PM**

Week of December 8 - December 4, 2017

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Ustun Yildirir - Michigan State University
**

**Abstract:
**

**Location: Norman Mayer 200-A
**

**Time: 12:30 PM
**

**Fang Sun - Tulane University
**

**Abstract:
**

We will apply two types of simplicial approximations to tackle some problems in homology and cohomology with local coefficients.

**Location: Gibson Hall 414
**

**Time: 12:30 PM
**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Lulu Kang - Illinois Institute of Technology Statistical and Applied Mathematical Sciences Institute (SAMSI)
**

**Abstract:
**

In many science and engineering systems both quantitative and qualitative output observations are collected. For short, we call such a system QQ system. In this talk, I will talk about a systematical approach for the experimental design and data analysis for the QQ system.

Classic experimental design methods are not suitable here because they often focus on one type of responses. We develop both Bayesian D and A-optimal design methods for experiments with one continuous and one binary responses. Both noninformative and conjugate informative prior distributions on the unknown parameters are considered. The proposed design criterions has meaningful interpretations in terms of the optimality for the models for both types of responses. Efficient design construction algorithms are developed to construct the local D-and A-optimal designs for given parameter values

To capture a correlation between the two types of responses, we propose a Bayesian hierarchical modeling framework to jointly model a continuous and a binary response. Compared with the existing methods, the Bayesian method overcomes two restrictions. First, it solves the problem in which the model size (specifically, the number of parameters to be estimated) exceeds the number of observations for the continuous response. Second, the Bayesian model can provide statistical inference on the estimated parameters and predictions. Gibbs sampling scheme is used to generate accurate estimation and prediction for the Bayesian hierarchical model. Both simulation and real case study are shown to illustrate the proposed method. (http://math.iit.edu/~lkang2/)

**Location: Location: Gibson 414
**

**Time: 3:00 PM**

**Prof. Chongsheng Cao - Florida International University
**

**Abstract:
**

Boussinesq systems are governing equations to the fluid flow of oceans and atmosphere. The systems are the Navier-Stokes equations and a heat transport equation. The global wellposedness of the 3D Boussinesq equations is still open. In this talk we will discuss some reduced 3D Boussinesq systems and also 2D Boussinesq systems. We will present results about the global regularity to these systems.

**Location: Gibson Hall 414
**

**Time: 3:30 PM**

**Yuri Bakhtin - New York University (Host: Nathan Glatt-Holtz, Scott McKinley)
**

**Abstract:
**

The Burgers equation is a basic nonlinear evolution PDE of Hamilton--Jacobi type related to fluid dynamics and growth models. I will talk about the ergodic theory of randomly forced Burgers equation in noncompact setting. The basic objects are one-sided infinite minimizers of random action (in the inviscid case) and polymer measures on one-sided infinite trajectories (in the positive viscosity case). This is joint work with Eric Cator, Kostya Khanin, and Liying Li.

**Location: Gibson Hall 126
**

**Time: 3:30 pm**

**Mac Hyman - Tulane University
**

**Abstract:
**

The choices that scientists make early in their careers will impact them for a lifetime. I will use the experiences of scientists who have had great careers to identify universal distinguishing traits of good career choices that can guild decisions in education, choice of profession, and job opportunities to increase your chances of having a great career with long-term sustained accomplishments.

I ran a student internship program at Los Alamos National Laboratory for over 20 years. Recently, I have been tracking the careers past students and realized that the scientists with great careers weren't necessarily the top students, and that some of the most brilliant students now had some of the most oh-hum careers.

I will describe how the choices made by the scientists with great careers were based on following their passion, building their talents into a strength supporting their profession, and how they identified a supportive engaging work environment. I will describe some simple guidelines that can help guide your choices, in school and in picking the right job that can lead to a rewarding career and more meaningful life.

The topic is important because, so far as I can tell, life is not a trial run - we have one shot to get it right. The choices you are making right now to planning your career will impact your for a lifetime.

Please join us for an engaging discussion on how to make the choices that will lead to a great career.

**Location: Gibson 400A
**

**Time: 2:30 pm**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Justin Krometis - Virginia Tech, Mathematics Department
**

**Abstract:
**

We consider the statistical inverse problem of estimating a background flow field from the partial and noisy observation of a passive scalar - e.g., estimating wind patterns by measuring a pollutant in the air. Here our unknown is a vector field that is specified by large or infinite number of degrees of freedom. Our work expands on frameworks developed in recent years for infinite-dimensional Bayesian inference. The talk will begin with some of the background required to formulate and analyze this problem: the advection-diffusion equation, ill-posed inverse problems, Bayesian inference, and Markov Chain Monte Carlo (MCMC). We then approach the inference both analytically and computationally, developing Metropolis-Hastings type algorithms to generate unbiased samples from the posterior distribution.

Location: Gibson Hall 414

**Time: 3:00**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

Week of November 17 - November 13, 2017

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Michael Reed - Duke University (host: Scott Mckinley)
**

**Abstract:
**

**Location: Gibson Hall 126
**

**Time: 3:30 pm**

**Scott McKinley - Tulane University
**

**Abstract:
**

The last twenty years have seen a revolution in tracking data of biological agents across unprecedented spatial and temporal scales. An important observation from these studies is that path trajectories of living organisms can appear random, but are often poorly described by classical Brownian motion. The analysis of this data can be controversial because practitioners tend to rely on summary statistics that can be produced by multiple, distinct stochastic process models. Furthermore, these summary statistics inappropriately compress the data, destroying details of non-Brownian characteristics that contain vital clues to mechanisms of transport and interaction. In this talk, I will survey the mathematical and statistical challenges that have arisen from recent work on the movement of foreign agents, including viruses, antibodies and synthetic microparticle probes, in human mucus.

**Location: Gibson 400A
**

**Time: 2:30 pm**

**Miles Jones - University of California San Diego
**

**Abstract:
**

The theory of symmetric functions is a well-studied field that has many applications in mathematics and beyond. Recently, mathematicians found a promising extension of this field in the setting of superspace whose definition was inspired by a physical phenomenon involving bosons and fermions and how they interact. It seems as though this generalization may lead to better understanding of classical symmetric function theory. In this talk, I will introduce basic topics of symmetric function theory and their analogues in superspace. I will share some results and projects that I am working on now.

**Location: Norman Mayer 200-A
**

**Time: 12:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Name - Institution
**

**Abstract:** TBA

**Location:
**

**Time:**

**Ozlem Ugurlu - Tulane University
**

**Abstract:
**

**Time: 4:30 PM**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Prof. Yan Gu - Institution
**

**Abstract:
**

**Location: Norman Mayer 200-A
**

**Davar Khoshnevisan - University of Utah (Host: Nathan Glatt-Holtz)
**

**Abstract:
**

This is based on joint work with Jingyu Huang.

**Location: Gibson Hall 126
**

**Time: 3:30**

**Vasileios Maroulas - University of Tennessee-Knoxville (Host:Scott McKinley)
**

**Abstract:
**

**Location: Gibson Hall 414
**

**Time: 3:00 PM**

**Sankhaneel Bisui - Tulane University
**

**Abstract:
**

Matroids are very well studied objects in combinatorics and algebraic combinatorics.The study of singularities and regularities of varieties and rings in algebra, specifically in algebraic geometry has foremost importance. Rational singularities were introduced by Artin while in the study of surfaces. Later on, Smith proved that F-rational rings have rational singularities. Our objective is to study the singularities of the toric ring of matroids. I am going to introduce the preliminaries necessary to understand the problem and the explain the approach that we are taking to solve it.

Location: Stanley Thomas 316

**Time: 4:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Axel Saen - University of Virginia
**

**Abstract:
**

For ASEP on the line, the system may never reach equilibrium dynamics depending on the initial conditions. Whereas for ASEP on the ring, one expects the system to reach equilibrium dynamics given enough time. In the special case of TASEP on the ring, there are recent result that give the specific crossover from KPZ dynamics and equilibrium dynamics. In collaboration with Z. Liu and D. Wang, we obtain the transition probability formulas for the periodic ASEP model. These formulas specialize to the formulas of ASEP on the line and TASEP on the ring, which are a first step to generalize the results of ASEP on the line and TASEP on the ring.

**Location: Gibson Hall 414
**

**Time: 3:30 PM**

**Rafał Komendarczyk - Tulane University
**

**Abstract:
**

I will discuss progress towards defining asymptotic higher linking numbers for divergence-free vector fields.

**Location: Gibson Hall 414
**

**Time: 12:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Ozlem Ugurlu - Tulane University
**

**Abstract:
**

Let G be a complex semisimple algebraic group and B be a Borel subgroup of G. In many situations, it is necessary to study the Borel orbits in G=G, where is an involutory automorphism. This is equivalent to analyze K = G orbits in the agvariety G=B. In fact, their geometry is of importance in the study of Harish-Chandra modules. The focus of the talk will be enumeration problem of Borel orbits in the polarizations (SL(n;C); S(GL(p;C) GL(q;C))). Its combinatorial relation to the lattice paths will be analyzed. In particular, it will be shown that the generating function for the dimensions of Borel orbits is expressible as a sum over lattice paths (in a p + 1 by q + 1 grid) moving by horizontal, vertical and diagonal steps weighted by an appropriate statistic.

**Location: Norman Mayer 200-A
**

**Time: 12:30 PM**

**Dr. Maria Calzada - Loyola University
**

**Abstract:
**

**Time: 2:30 pm**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Abu Thomas - Tulane University
**

**Abstract:
**

We shall see a scheme theoretic point of view of approaching Chudnowsky's conjecture. This conjecture deals with the bounds on the least degree of polynomials that vanish on a variety with a fixed multiplicity. In an attempt to prove this long standing conjecture many mathematicians came up with strong containment results involving ordinary and symbolic powers of ideals.

**Location:** Stanley Thomas 316

**Time: 4:30pm**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Swati Patel - Tulane University
**

**Abstract:
**

A fundamental question in ecology and evolutionary biology is to understand the mechanisms that lead to the diversity that we observe in natural communities. In recent years, there has been empirical evidence that feedbacks between species densities and trait evolution, termed eco-evolutionary feedbacks, may play a role in maintaining diversity. In this talk, I will first discuss a mathematical framework for understanding diversity and the role of eco-evolutionary feedbacks. Then, I discuss results from applying this framework to understand the coexistence of two prey that share one predator.

**Location: Gibson Hall 414
**

**Time: 3:30 PM**

**Jonathan O'Rourke - Tulane University
**

**Abstract:
**

**Sushovan Majhi - Tulane University
**

**Abstract:
**

In the last decade, estimation of topological and geometric features of an unknown underlying space from a finite sample has received an increasing attention in the field of computational topology and geometry. For example, recently a reconstruction guarantee for the topology of an embedded smooth n-manifold from a finite cover by balls of sufficiently small radius around a dense enough finite sample is proved. Random sampling and probabilistic estimates are also considered along with the deterministic case. These estimates imply that with increasing sample size, the probability of reconstructing the underlying space tends to 1, thus we can recover the space almost surely as the sample size increases to infinity. Not all spaces are smooth manifolds. In practice, non-smooth manifolds or even non-manifolds are often of interest. We shall address the reconstruction problems for these spaces. Also, we touch upon our recent development on the reconstruction of a special type of embedded topological spaces called metric graphs.

**Location: Gibson Hall 414
**

**Time: 12:30**

**Mentor Stafar- Tulane University
**

**Abstract:
**

In this talk I will introduce the spaces of group representations and how they relate to the notions of representation and homological stability.

**Location: Gibson 400A
**

**Time: 2:30**

**Jeff Borggaard - Virginia Tech (Host: Nathan Glatt-Holtz)
**

**Abstract:
**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Diego Villamizar - Tulane University
**

**Abstract:
**

We will show some properties of this numbers, in particular their relations with difunctional relations and Tree-like tableaux.

**Location: Stanley Thomas 316
**

**Time: 4:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Abstract:
**

**Elaine Spiller - Marquette University (Host: Scott McKinley)
**

**Abstract:
**

Geophysical hazards – landslides, tsunamis, volcanic avalanches, etc. – which lead to catastrophic inundation are rare yet devastating events for surrounding communities. The rarity of these events poses two significant challenges. First, there are limited data to inform aleatoric scenario models, how frequent, how big, where. Second, such hazards often follow heavy-tailed distributions resulting in a significant probability that a larger-than-recorded catastrophe might occur. To overcome this second challenge, we must rely on physical models of these hazards to “probe” the tail for catastrophic events. Typically these physical models are computationally intensive to exercise and a probabilistic hazard map relies on an expensive Monte Carlo simulation which samples a scenario model. This approach forces one to focus resources on a single scenario model that is based on one set of assumptions. We will present a surrogate-based strategy that allows great speed-up in Monte Carlo simulations and hence the flexibility to explore the impact of non-stationary scenario modeling on short term forecasts. Additionally, this approach provides a platform to perform uncertainty quantification on hazard forecasts.

**Location: Gibson Hall 126
**

**Time: 3:30
**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Abstract:
**

**Time: 12:30 PM**

**Dr. Ilya Smirnov - University of Michigan
**

**Abstract:
**

In 1960 Lech found a simple inequality that relates the colength and the multiplicity of a primary ideal in a local ring. Unfortunately, Lech's proof also shows that his inequality is almost never sharp. After explaining the necessary background, I will present a stronger form of Lech's inequality and an even stronger conjecture that will make the inequality sharp.

**Location: Mayer 200-A
**

**Time: 12:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Abstract:
**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

Week of October 13 - October 9, 2017

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

Week of October 6 - October 2, 2017

Methods to Study the Interaction of Microorganisms and the Fluid Flow

**Ricardo Cortez - Tulane University
**

Abstract: Microscopic swimmers like bacteria and spermatozoa live in highly viscous environments. Their locomotion and the fluid flows they

generate around them have been actively investigated for the last 60 years motivated by questions about effective locomotion strategies,

the organism¹s interaction with the surrounding environment, patterns of collective motion, propulsion, and more. These issues are typically

addressed through a combination of theory, experiments, mathematical modeling and simulation. I will present an overview of work based on

the ³method of regularized Stokeslets² developed here at Tulane and used around the world. It is a computational method based on

fundamental solutions of PDEs designed for simulating these viscous flows. I will also present examples of applications.

**Time: 2:30**

**Karl Hofmann - TU Darmstadt and Tulane University
**

**Abstract:**

**Time: 12:30**

**Mentor Stafa - Tulane University
**

**Abstract:
**

In this talk we will introduce the space of representations of a finitely generated discrete group into a compact and connected Lie group. We will study the rational cohomology of these spaces and their relation to the invariant theory of finite reflection groups.

Location: Gibson Hall 414

**Time: 12:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Lin Li - Tulane University
**

**Abstract:
**

Accurate Integration of High Dimensional Functions using Polynomial Detrending Abstract: The accuracy of numerical integration of high dimensional functions is an important problem in many industrial applications. Numerical quadrature built on lattice grid can quickly suffer from the curse of dimensionality. Monte Carlo and Quasi Monte Carlo method have provided a convergence rate independent of dimensionality. Unfortunately, the errors of these Monte Carlo methods converge very slowly when there are large variations in the underlying high dimensional integrand. We proposed a new method, polynomial detrending as an efficient way of variance reduction, which can provide a desired accuracy for high dimensional integration problem even with a small number of sample points.

**Location: Stanley Thomas 316
**

**Time: 4:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

Week of September 29 - September 25, 2017

*Friday, September 29*

**Topic**

*Thursday, September 28*

## Colloquium

**Computational Topology and the Life Sciences: Finding structure in models and data**

*Thursday, September 28*

## Algebra and Combinatorics

**Involution Schubert Polynomials and Some Ordinary Schubert Polynomial Identities**

*Thursday, September 28*

## Geometry and Topology

**Discrete Morse Theory**

*Wednesday, September 27*

**Topic**

*Tuesday, September 26*

## Grad Student Colloquium

**A New Notion of Constructive Cardinality**

*Monday, September 25*

**Topic**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Sarah Day - William and Mary College, Department of Mathematics (Host: Scott McKinley)
**

**Abstract:
**

The field of topology, and in particular computational topology, has produced a powerful set of tools for studying both model systems and data measured directly from physical systems. I will focus on three classes of topological tools: computational homology, topological persistence, and, very briefly, Conley index theory. To illustrate their use, I will discuss recent projects studying coupled-patch population dynamics, flickering red blood cells, and pulse-coupled neurons.

**Location: Gibson Hall 310
**

**Time: 3:30 pm**

**Michael Joyce - Tulane University
**

**Abstract:
**

Ordinary Schubert polynomials are algebraic manifestations of a certain orbit structure on the variety of complete flags. By considering two other orbit structures, we obtain involution and fpf-involution Schubert polynomials, respectively. We will discuss some of their properties and give an application for an identity involving ordinary Schubert polynomials.

**Location: Norman Mayer 200-A
Time: 12:30**

**Fang Sun - Tulane University
**

**Abstract:
**

**Discrete Morse Theory is a combinatorial adaption of the (smooth) Morse Theory developed by Robin Forman. The theory has various applications in applied and computational mathematics, as well as group theory.
**

**Location: Gibson Hall 414
**

**Time: 12:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Nathan Bedell - Tulane University
**

Abstract:

Many mathematicians in the constructive tradition have some misgivings about Cantor's theorem and the existence of uncountable sets. In this talk, I will explain some of the basic principles of constructive mathematics, and why one might be skeptical of the ontological claim that uncountable sets exist. I then show that this view is not unreasonable in light of Cantor's theorem by seeing the constructive view of Cantor's theorem as analogous to the classical view of Russell's paradox. This argument then motivates a new conception of cardinality in terms of graded category theory, which is more in line with constructive intuitions. In particular, I will show that there are non-trivial graded categories in which all infinite sets have, in my terminology, the same absolute cardinality.

**Location: Stanley Thomas 316
**

**Time: 4:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

Week of September 22 - September 18, 2017

*Friday, September 22*

**Topic**

*Thursday, September 21*

## American Mathematical Society

**COFFEE AND DISCUSSION Career Choices**

*Thursday, September 21*

## Algebra & Combinatorics seminar

**Determinants in Wonderland**

*Thursday, September 21*

## Geometry and Topology

**Whitehead torsion of inertial h-cobordisms Part 2**

*Wednesday, September 20*

## Probability and Statistics

**Long-term dynamics of particles undergoing active transport**

*Tuesday, September 19*

## Graduate Student Colloquium

**Private Set-Union Cardinality: a cryptographic protocol for privacy-preserving distributed measurement**

*Monday, September 18*

**Topic**

**Week of September 11 - September 15, 2017**

*Friday, September 15*

## Applied and Computational Mathematics

**Linear Stability for 2D Boussinesq Equations**

*Thursday, September 14*

**Topic**

*Thursday, September 14*

## AMS

**On scaling**

*Thursday, September 14*

## Geometry and Topology

**Whitehead torsion of inertial h-cobordisms**

*Wednesday, September 13*

## Probability and Statistics

**A hop, skip, and jump-diffusion through some models of intracellular transport**

*Tuesday, September 12*

## Grad Student Colloquium

**Beyond Perfect Graphs -- Hypercycles and Perfect Hypergraphs**

*Monday, September 11*

**Topic**

**Week of September 8 - September 4, 2017**

*Friday, September 8*

**Topic**

*Thursday, September 7*

**Topic**

*Thursday, September 7*

**Topic**

*Wednesday, September 6*

**Topic**

*Tuesday, September 5*

## Graduate Student Colloquium

**A simplified human birth model - translation of a rigid cylinder through a passive elastic tube**

*Tuesday, September 5*

## Geometry / Topology Seminar

**Organizational Meeting**

*Monday, September 4*

Labor Day - University Holiday

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Amy Buchmann, Swati Patel, and Zhuolin Qu - Tulane University
**

This week we will welcome special guests Amy Buchmann, Swati Patel, and Zhuolin Qu. They will share their experience holding postdoctoral fellowships.

**Location: Gibson Hall 400A
**

**Time: 2:30**

**Tewodros Amdeberhan - Tulane University
**

**Abstract:
**

Determinants are found everywhere in mathematics and other scientific endeavors. Their particular role in Combinatorics does not need any cynical introduction or special advertisement. In this talk, we will illustrate certain techniques which proved to be useful in the evaluation of several class of determinantal evaluations. We conclude this seminar with open problem(s). The content of our discussion is accessible to anyone with "an intellectual appetite".

**Location: Norman Mayer 200-A
**

**Time: 12:30
**

**Prof. Slawomir Kwasik - Tulane University
**

**Abstract:
**

The notions of an h-cobordism and the Whitehead torsion will be discussed. Some old and new results will be presented together with various open problems and conjectures.

**Location: Gibson Hall 414
**

**Time: 12:30**

**Veronica Ciocanel - Mathematical Biosciences Institute (Host: Scott Mckinley)
**

**Abstract:
**

In many developing organisms, such as frog oocytes, mRNAs and other proteins get transported to specific cell locations to ensure that healthy asymmetric cell division can occur. The dynamics often include diffusion, bidirectional transport, and stationary states, and may be influenced by the spatial distribution of filaments inside the cell. To determine the long-term displacement of the particles, we derive their effective velocity and diffusion using dynamical systems techniques for certain PDE systems. We also outline an alternative (and potentially equivalent) stochastic approach for deriving these large-time transport quantities using renewal reward theory.

Location: Gibson Hall 414

**Time: 3:00**

**Ellis Fenske - Tulane University
**

**Abstract:
**

There are many contexts where we wish to collect data about use of a system (e.g. a computer network, medical system), but simultaneously wish to respect the privacy of these users, and it is not obvious how to do this. The Tor network is our motivating example: users connect through Tor to protect their privacy, and system operators are generally volunteers who believe in this mission and will not compromise the privacy of their users. Yet data about the network is crucial to improve it and for research and funding opportunities for network operators. While it is a solved problem to aggregate all measurements from each relay in a privacy-preserving way, the case where the same measurement can be recorded by two distinct data collectors so that we must aggregate *unique* measurements is much more complex. I will present work from a paper I have published in collaboration with researchers at Georgetown University and the US Naval Research Laboratory that solves this problem.

**Location: Stanley Thomas 316
**

**Time: 4:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Lizheng Tao - UNIVERSITY OF CALIFORNIA (Host KUN ZHAO)
**

**Abstract:
**

The 2D Boussinesq model is a partial differential equation system that models the incompressible fluid with a gravity driven components, such as temperature and density. Physically, it stands at the center of turbulence theories concerning turbulent thermal convection, like the Raleigh-Bernard convection. Mathematically, the model is also considered an insight into the 3D Navier-Stokes equations. In this talk, we will present some recent result regarding the linear stability of the solutions around the Couette flow. The perturbed solutions shows an exponential decay in the Hilbert norm stronger than the one caused by solo dissipation. This is largely due to the enhanced dissipation property of the Couette flow. The result is achieved by the hypo-coercivity theorem and a set of functionals which are equivalent to the H^s norm.

**Location: Gibson Hall 414
**

**Time: 3:30 PM**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Gustavo Didier - Tulane University
**

**Abstract:
**

Scaling relationships have been found in a wide range of phenomena that includes coastal landscapes, hydrodynamic turbulence, the metabolic rates of animals and Internet traffic. In this talk, we will look into the so-named paradigm of scale invariance, which has been applied in the analysis of dynamic signals or systems where no characteristic scale is present. Under scale invariance, a continuum of time scales contributes to the observed dynamics, and the analyst's focus is on identifying mechanisms that relate the scales, often in the form of scaling exponents. We will dedicate special attention to an important form of scale invariance, called self-similarity. No background on the subject will be assumed.

**Location: Gibson Hall 400A
**

**Time: 2:30**

**Slawomir Kwasik - Tulane University
**

**Abstract:
**

**The notions of an h-cobordism and the Whitehead torsion will be discussed. Some old and new results will be presented together with various open problems and conjectures.
**

**Location: Gibson Hall 414
**

**Time: 12:30**

**Chris Miles - UNIVERSITY OF UTAH, MATHEMATICS DEPARTMENT (HOST: SCOTT MCKINLEY)
**

**Abstract:
**

The movement of cargo within cells by small teams of molecular motors is a critical ingredient of many cellular functions. Both at the individual motor and ensemble levels, stochasticity is fundamentally unavoidable and diverse in its manifestation. Thus, fully elucidating the behavior of these systems requires disentangling a variety of noises at different temporal and spatial scales, providing a rich platform for not only biological intrigue, but also mathematical. In this talk, I'll briefly discuss some of my work modeling motor systems. The first project, inspired by motor stepping dynamics, provides some mathematical results on statistics of general jump-diffusion processes with state dependent jump rates. The second, a collaboration with experimentalists, attempts to unravel underlying sources of diffusive noise in observed transport data. Lastly, I'll mention how these projects relate to on-going work modeling transport by a curious type of motor incapable of taking many steps.

**Location: Gibson Hall 414
**

**Time: 3:00 PM**

**Jonathan O'Rourke - Tulane University
**

**Abstract:
**

In attempting to extend the notion of perfect graphs to the class of hypergraphs, my research partner and I studied a class of hypergraphs which bear some resemblance to cyclic graphs. We studied the associated primes of the cover ideals associated to this class of hypergraphs, as well as their index of stability. This study resulted in an easy-to-describe class of hypergraphs which answer a question of Francisco, Van Tuyl, and Ha regarding the relationship between the index of stability and the chromatic number of a family of hypergraphs, and in fact proving a stronger result. I will explain the preliminaries necessary to understand the problem and some of the techniques used to solve it.

**Time: 4:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Roseanna Gossmann - TULANE UNIVERSITY
**

**Abstract:
**

In order to better understand the forces on an infant during birth, this work uses a simplified model to explore the effects of fetal velocity and viscosity of the surrounding fluid on the forces associated with human birth. The model represents the fetus moving through the birth canal using a rigid cylinder (fetus) that moves at a prescribed velocity through the center of an elastic tube (birth canal). The entire system is immersed in highly viscous fluid. Low Reynolds number allows for the use of the Stokes equations to govern the fluid flow. The discrete elastic tube through which the rigid cylinder passes has macroscopic elasticity that may be matched to tubes used in physical experiments. This framework is used to explore the force necessary to move the rigid inner cylinder through the tube, as well as the buckling behavior of the elastic tube. More complex geometries as well as peristaltic activation of the elastic tube can be added to the model to provide more insight into the relationship between force, velocity, and fluid dynamics during human birth.

**Location: Stanley Thomas 316
**

**Time: 4:30 PM**

**Slawomir Kwasik - Tulane University
**

**Abstract:
**

**Location: Hebert Hall 201
**

**Time: 12:15**

Labor Day - University Holiday

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