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Events This Week




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

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


Friday, December 8

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Thursday, December 7

Algebra and Combinatorics

Cayley Grassmannian

Ustun Yildirir - Michigan State University

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A 3-fold cross product operation exists only in dimensions 4 and 8. A 4-dimensional subspace of an 8 dimensional vector space is called a Cayley plane if it is closed under the 3-fold cross product operation. Cayley grassmannian is the space of all Cayley planes. It is naturally a homogeneous space with an algebraic torus action, and it resides in Gr(4,8). Over complex numbers, this space is not compact. In this talk, after I talk about the necessary background, I will explain some of the results I obtained on the minimal compactification of Cayley grassmannian.

Location: Norman Mayer 200-A

Time: 12:30 PM


Thursday, December 7

Geometry and Topology Seminar

Simplicial approximations and homology with local coefficients

Fang Sun - Tulane University

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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


Wednesday, December 6

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Tuesday, December 5

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Monday, December 4

Special Statistics Seminar

Bayesian Experimental Design and Hierarchical Model for Quantitative and Qualitative Responses

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

Week of December 1  -  November 27, 2017

Friday, December 1

Applied and Computational Mathematics

Regularity Problems of some Boussinesq Equations

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


Thursday, November 30

Colloquium

Burgers equation with random forcing

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


Thursday, November 30

AMS/AWM Faculty Talk

Good Choices for Great Careers

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


Thursday, November 30

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Thursday, November 30

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Wednesday, November 29

Probability and Statistics

A Bayesian Approach to Estimating Background Flows from a Passive Scalar

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


Tuesday, November 28

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Monday, November 27

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

Thanksgiving Holiday



Thursday, November 23
Thanksgiving Holiday

Wednesday, November 22

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Tuesday, November 21

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Monday, November20

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Week of November 17  -  November 13, 2017

Friday, November 17

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Thursday, November 16

Colloquium

Cell Metabolism, Mathematics, and Public Health

Michael Reed - Duke University (host: Scott Mckinley)

Abstract:


Metabolic systems are not simple sequential pathways but have cycles within cycles, so that everything is both upstream and downstream of everything else. In addition, there are multitudes of regulatory (allosteric) interactions in which metabolites affect the activity of distant enzymes in the network. Creating mathematical models based on the real underlying physiology and biochemistry is labor-intensive, but such models can be used to understand the systems behavior in health and disease. I will describe how my colleagues and I create and validate such models and some of our results. I will discuss how we can take account of biological variation and I will also discuss the different roles that stochasticity plays in biological systems. I will explain how the regulatory mechanisms buffer metabolism against large functional genetic mutations and why genotype may not be a good predictor of disease risk.  Finally, I will discuss several new, interesting questions in pure mathematics have arisen from this work.

Location:  Gibson Hall 126

Time: 3:30 pm


Thursday, November 16

AMS/AWM Faculty Talk

Anomalous Diffusion and Random Encounters in Biological Fluids

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


Thursday, November 16

Algebra-Combinatorics

Symmetric functions in superspace

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


Thursday, November 16

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Thursday, November 16

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Wednesday, November 15

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Tuesday, November 14

K-Orbits in the Flag Variety and Clansc

Ozlem Ugurlu - Tulane University

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Let G be a complex semisimple classical group and B be a Borel subgroup of G. There are many situations where it is necessary to study K(=G^t)-orbits in the flag variety G/B, where t is an involutory automorphism. In fact, their geometry is of importance in the study of Harish-Chandra modules and their closures can be considered as Schubert varieties. The focus of this talk will be on the parametrization of K-orbits for classical flag varieties by combinatorial objects, called clans. We will also talk about a combinatorial description of the weak ordering on the orbit set in terms of this parametrization for the type A case.


Location:  Stanley Thomas 316

Time:  4:30 PM


Monday, November 13

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

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Thursday, November 9

Algebra & Combinatorics seminar

Depth and Stanley Depth of monomial ideal

Prof. Yan Gu - Institution

Abstract:

Capture242

Location: Norman Mayer 200-A

Time: 12:30 PM

Thursday, November 9

Colloquium

Analysis of a stratified Kraichnan Model

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

Abstract:


We study quantitative and qualitative aspects of the problem of turbulent transport of a passive scalar quantity in a random 2-d velocity field. In particular, we give precise meaning to some of the multifractal structure of the dissipation times, predicted earlier in the physics and engineering literatures. The unexplained terms of the abstract will be described more precisely in the talk.

This is based on joint work with Jingyu Huang.

Location:  Gibson Hall 126

Time:  3:30


Wednesday, November 8

Probability and Statistics

Classification on the space of persistence diagrams

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

Abstract:


In this talk, we consider the problem of signal classification by considering their associated persistence diagrams. We endow the data space of persistence diagrams with a new metric. In contrast with the Wasserstein distance, this metric accounts for changes in small persistence and cardinality. Pulling back to the space of signals, this corresponds to detecting differences in a signal’s periodicity, underlying noise, and geometry. The metric space of persistence diagrams is proved to admit statistical structure in the form of Fréchet means and variances. The new classification method using this distance is benchmarked on both synthetic data and real acoustic signals provided by the US Army Research Lab.

Location:  Gibson Hall 414

Time:  3:00 PM


Tuesday, November 7

Graduate Student Colloquium

Rational Singularity of The Toric Ring of Matroids

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


Monday, November 6

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Week of November 3  - October 30, 2017

Friday, November 3

Applied and Computational

Transition Probabilities for ASEP on the ring

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


Thursday, November 2

Geometry and Topology

Asymptotic higher order linking in volume preserving flows

Rafał Komendarczyk - Tulane University

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

Location: Gibson Hall 414

Time: 12:30



Thursday, November 2

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Thursday, November 2

Algebra and Combinatorics

The Genesis of Involution

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


Thursday, November 2

AWM Coffee and Discussion: 

From Math Professor to Dean

Dr. Maria Calzada - Loyola University

Abstract:

We welcome Dr. Maria Calzada of Loyola University who will join us to discuss her career in mathematics and her journey to become Dean of the College of Arts and Sciences

Location:  Gibson 400A

Time: 2:30 pm


Wednesday, November 1

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Tuesday, October 31

Graduate Student Colloquium

Chudnowsky's Conjecture

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


Monday, October 30

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

Applied and Computationa

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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


Thursday, October 26

Algebra and Combinatorics

Beyond Perfect Graphs: Hypercycles and Perfect Hypergraphs

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 H\`a 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

Location:  Norman Mayer 200-A

Time: 12:30 PM

Thursday, October 26

Geometry and Topology

Topological and Geometric Reconstruction of Metric Graphs

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


Thursday, October 26

AWM/AMS

Spaces of representations and representation stability

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


Thursday, October 26

Colloquium

On Nonlinear Feedback Control and State Estimation

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

Abstract:

When computable, a linear feedback control guarantees the stability of a steady-state flow. This can, for example, be used to stabilize an unstable periodic orbit in a flow control problem.  However, as we will show, the stability region might be too small to be implemented in practice. This motivates the use of nonlinear feedback strategies to expand the stability region. These can now be efficiently computed using the nonlinear systems toolbox on very low-dimensional, reduced-order models.  Using a simple nonlinear control problem, we explore the possibility of expanding the stability region and  comment on the development of low-order nonlinear state estimators.

Location:  Gibson Hall 126


Time: 3:30 pm

Wednesday, October 25

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Tuesday, October 24

Graduate Student Colloquium

r-indecomposable Factorial and Bell numbers

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


Monday, October 23

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

Applied and Computational

Self-organized dynamics: aggregation and flocking

Dr. Changhui Tan  - Rice University

Abstract:

Self-organized behaviors are commonly observed in nature and human societies, such as bird flocks, fish swarms and human crowds. In this talk, I will present some celebrated mathematical models, with simple small-scale interactions which lead to the emergence of global behaviors: aggregation and flocking. I will discuss the models in different scales: from microscopic agent-based dynamics, through kinetic mean-field descriptions, to macroscopic fluid systems. In particular, the macroscopic models can be viewed as compressible Euler equations with nonlocal interactions. I will show some recent results on the global wellposedness theory of the systems, large time behaviors, and interesting connections to some classical equations in fluid mechanics.

Location: Gibson Hall 414

Time: 3:30 PM

Thursday, October 19

Colloquium

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

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


Thursday, October 19

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Thursday, October 19
Geometry and Topology

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


Bernardo Villarreal - University Purdue University Indianapolis

Abstract:

In this talk I will define the space BcomG arising from commuting tuples in G originally defined by A. Adem and J. Gomez. This space sits inside the classifying space BG and I will focus on describing the space BcomO(2) via its mod 2 cohomology ring and the homotopy type of the homotopy fiber of the inclusion BcomO(2) into BO(2), denoted EcomO(2). It turns out that the mod 2 cohomology ring of BO(2) is a subring of the corresponding ring for BcomO(2) and that EcomO(2) is a wedge of spheres. This is joint work with O. Antolin and S. Gritschacher.


Location:  Gibson Hall 414


Time:  12:30 PM


Thursday, October 19

Algebra and Combinatorics

Lech's inequality and its improvements

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


Wednesday, October 18

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Tuesday, October 17
Graduate Student Colloquium

A Probabilist's Perspective

Cooper Boniece - Tulane University

Abstract:

Probability Theory and Analysis are closely related disciplines.  As such, there are many results that lie squarely at the intersection of these two areas.  However, there are also some results in Analysis that are inherently non-probabilistic, for which a probabilist's perspective yields new understandings.  These perspectives also offer insight into the myriad connections between these two disciplines.  In this expository talk, after introducing some facts about martingales and Brownian Motion, we'll explore some probabilistic approaches to a wide variety of topics and theorems, from Analysis and elsewhere, including: The Dirichlet Problem; Picard's Little Theorem; The Fundamental Theorem of Algebra and more!
Location: Stanley Thomas 316
Time:  4:30 PM

Monday, October 16

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Week of October 13 - October 9, 2017
Friday, October 13

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Thursday, October 12

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Wednesday, October 11

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Tuesday, October 10

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Monday, October 9

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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

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.


Location: Gibson 400A

Time: 2:30


Thursday, October 5

Algebra & Combinatorics

Locally compact p-groups and their challenges

Karl Hofmann - TU Darmstadt and Tulane University

Abstract:

Karl


Location: Norman Mayer 200-A

Time: 12:30


Wednesday, October 5

Geometry and Topology

Topology of representation spaces and invariants of finite reflection groups

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


Wednesday, October 4

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Tuesday, October 3

Graduate Student Colloquium

Accurate Integration of High Dimensional Functions using Polynomial Detrending

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


Monday, October 2

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Week of September 29 - September 25, 2017
Friday, September 29

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Thursday, September 28

Colloquium

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

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


Thursday, September 28

Algebra and Combinatorics

Involution Schubert Polynomials and Some Ordinary Schubert Polynomial Identities

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


Thursday, September 28

Geometry and Topology

Discrete Morse Theory

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


Wednesday, September 27

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Tuesday, September 26

Grad Student Colloquium

A New Notion of Constructive Cardinality

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


Monday, September 25

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Week of September 22 - September 18, 2017
Friday, September 22

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Thursday, September 21

American Mathematical Society

COFFEE AND DISCUSSION  Career Choices

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


Thursday, September 21

Algebra & Combinatorics seminar

Determinants in Wonderland

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


Thursday, September 21

Geometry and Topology


Whitehead torsion of inertial h-cobordisms Part 2

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


Wednesday, September 20

Probability and Statistics

Long-term dynamics of particles undergoing active transport

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


Tuesday, September 19

Graduate Student Colloquium

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

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


Monday, September 18

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

Applied and Computational Mathematics

Linear Stability for 2D Boussinesq Equations

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


Thursday, September 14

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Thursday, September 14

AMS

On scaling

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


Thursday, September 14

Geometry and Topology

Whitehead torsion of inertial h-cobordisms

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


Wednesday, September 13

Probability and Statistics

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

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


Tuesday, September 12

Grad Student Colloquium

Beyond Perfect Graphs -- Hypercycles and Perfect Hypergraphs

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.


Location:  Stanley Thomas 316

Time:  4:30


Monday, September 11

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

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Thursday, September 7

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Thursday, September 7

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Wednesday, September 6

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Tuesday, September 5

Graduate Student Colloquium

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

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


Tuesday, September 5

Geometry / Topology Seminar

Organizational Meeting

Slawomir  Kwasik - Tulane University

Abstract: 

Location: Hebert Hall 201

Time: 12:15


Monday, September 4

Labor Day - University Holiday


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