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Events This Week




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

Applied and Computationa

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Swati Patel - Tulane University

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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

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Thursday, October 26

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Thursday, October 26

Colloquium

On Nonlinear Feedback Control and State Estimation

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

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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

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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

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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

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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

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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

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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

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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

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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

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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)

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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

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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

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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

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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

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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

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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

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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)

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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

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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)

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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

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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

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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