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Events This Week




Week of September 5 - September 9, 2016
Monday, September 5
Labor Day University Holiday

Tuesday, September 6

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Wednesday, September 7

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Thursday, September 8

COLLOQUIUM

Numerical Methods for Hyperbolic Systems of PDEs with Uncertainties

Alina ChertockNorth - Carolina State University (Host: Alexander Kurganov)

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Many system of hyperbolic conservation and balance laws contain uncertainties in model parameters, initial or boundary data due to modeling or measurement errors. Quantifying these uncertainties is important for many applications since it helps to conduct sensitivity analysis and to provide guidance for improving the models. Among the most popular numerical methods for uncertainty quantification are stochastic spectral methods. Such methods decompose random quantities on suitable approximation bases. Their attractive feature is that they provide a complete probabilistic description of the uncertain solution.  

 A classical choice for the stochastic basis is the set of generalized Polynomial Chaos (gPC) spanned by random polynomials, continuous in the stochastic domain and truncated to some degree. It is well-known, however, that when applied to general nonlinear (non-symmetric) hyperbolic systems, such approximations result in systems for the gPC coefficients, which are not necessarily globally hyperbolic since their Jacobian matrices may contain complex eigenvalues. In this talk, I will present a splitting strategy that allows one to overcome this difficulty and demonstrate the performance of the proposed approach on a number of numerical examples including systems of shallow water and compressible Euler equations.

Location: Gibson Hall 414

Time: 3:30


Friday, September 9

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Week of September 12 - September 16, 2016
Monday, September 12

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Tuesday, September 13

GEOMETRY and TOPOLOGY

Manifolds with the Fixed Point Property and Their Squares

Slawomir Kwasik - Tulane University

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Location: Gibson Hall 310

Time: 12:30


Wednesday, September 14

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Thursday, September 15

COLLOQUIUM

Ramanujan's Mock Theta Functions and Quantum Modular Forms

Holly Swisher - Oregon State University (Host: Victor Moll)

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Nearly 100 years after his untimely death, Ramanujan's legacy is still intriguing mathematicians today.  One of the last obsessions of Ramanujan were what he called mock theta functions.  In this talk, we will begin by discussing Ramanujan's work on integer partitions and how they connect to objects called modular forms and mock theta functions.  Then we will continue by exploring some recent work in this area, including the construction of a table of mock theta functions with some interesting properties, including what is called quantum modularity.   Part of this work is joint with Sharon Garthwaite, Amanda Folsom, Soon-Yi Kang, and Stephanie Treneer.  The rest is joint with Brian Diaz and Erin Ellefsen from their undergraduate REU project this summer.

Location: Gibson Hall 414

Time: 3:30


Friday, September 16

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Week of September 19 - September 23, 2016
Monday, September 19

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Tuesday, September 20
GEOMETRY and TOPOLOGY

Introduction to Smith Homology

Fang Sun - Tulane University

Abstract: N/A

Location: Gibson Hall 310

Time:  12:30


Tuesday, September 20

STUDENT COLLOQUIUM

Regularity of Powers of Unicyclic Graphs

Selvi Beyarslan - Tulane University

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Location:  Stanley Thomas 316

Time:  4:15


Wednesday, September 21

PROBABILITY and STATISTICS

Antibody-Mediated Immobilization of Virions in Mucus

Melanie Jensen - Tulane University

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In recent years, particle tracking experiments have provided new insights into interactions between our immune system and foreign bodies like viruses and bacteria. Sam Lai (UNC-Chapel Hill, Pharmacy) and collaborators have demonstrated that certain types of antibodies have the capacity to essentially immobilize Herpes virus in mucus and it is believed that a similar effect will be true for HIV. Because antibodies are too small to be directly observed in these experiments, the physical mechanism underlying this effect remains unclear. Using particle tracking data for Herpes virions, we construct a multi-scale model for virion movement and virion-antibody-mucin reaction kinetics to investigate the impact of varying antibody concentrations on virion movement.

First, we develop a classification system for path data to distinguish among diffusive, subdiffusive, and stationary motions. We use a continuous-time Markov model to describe virion-antibody-mucin kinetics and introduce a multi-scale approximation to compute important properties of the system that help us predict what fraction of a virion population should be immobilized at a given time, and how long a virion's immobilization should last.  To specify our model with the data, we use identifiability analysis to set mathematically optimal and biological feasible parameter values. Finally, we compare theoretical immobilization times with observed immobilization times to determine whether prominent qualitative features of the data are predicted by our linear stochastic model.

Location: Gibson Hall 310

Time: 3:00


Thursday, September 22

COLLOQUIUM

Combinatorial Hopf Algebras and Antipode

Nantel Bergeron - York University (Host: Mahir Can)

Abstract:

Given a family of combinatorial objects we often have operations that allow us to combine them to create larger objects and/or ways to decompose them into smaller members of the family. In the best situation we have in fact an algebraic structure, i.e. a graded Hopf algebra. I will give example of such structure using graphs, trees, set partitions, etc.

The antipode is a map from the Hopf algebra into itself that is defined recursively, with a lot of cancelation and is difficult to compute in general. I will motivate why we should care about the antipode and why we should aim to find a cancelation free formula.

An important example is the combinatorial Hopf algebra of graphs. In this case, a cancelation free formula of for its antipode is given by, Humpert and Martin. We will see that such formula gives a structural understanding of certain evaluations of the combinatorial invariants for graphs. In particular we recover very nicely a classical theorem of Stanley for the evaluation of the chromatic polynomial at -1.

I will discuss some generalization of this example.

Location: Gibson Hall 414

Time: 3:30


Friday, September 23

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Week of September 26 - September 30, 2016
Monday, September 26

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Tuesday, September 27

Fluid-Structure Interactions: Applications to Marine Phenomena

Shilpa Khatri - University of California-Merced, Applied Mathematics

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To understand the fluid dynamics of marine phenomena, for example particles settling, droplets rising, and pulsating coral, fluid-structure interaction problems must be solved. Challenges exist in developing analytical and numerical techniques to solve these complex flow problems with boundary conditions at fluid-structure (solid and porous) interfaces. I will present details of two different problems where these challenges are handled: (1) modeling of marine aggregates settling in density stratified fluids and (2) modeling of pulsating soft corals. These problems will be motivated by field and experimental work in the marine sciences. I will discuss these related data and provide comparisons with the modeling.


Location: Stanley Thomas 316

Time: 3:00


Tuesday, September 27

Probabilistic Numerics

Alexej Gossmann  - Tulane University

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Location: Stanley Thomas 316

Time: 4:15


Wednesday, September 28
PROBABILITY and STATISTICS

Anomalous Dynamics of Switching Diffusion

Lukasz Sikora - Tulane University

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An ongoing effort in the study of microparticle movement in biofluids is the proper characterization of subdiffusive processes i.e. processes whose mean-squared displacement scales as a sublinear power law.  In order to describe phenomena that lead to subdiffusive behavior, a few models have been developed: fractional Brownian motion, the generalized Langevin equation, and random walks with dependent increments. We will present perhaps a simpler model that leads to subdiffusion and is designed to characterize systems where a regularly diffusive particle intermittently becomes trapped for long periods of time.

To start with, we introduce the rigorous model of switching diffusion. We present a stochastic differential equation perspective and, using heavy tail analysis methods, we will present a proof that switching diffusion with heavy-tailed immobilization times is asymptotically subdiffusive.

Location: Gibson Hall 310

Time: 3:00


Thursday, September 29

ALGEBRA and COMBINATORICS

Infinite-Dimensional Reductive Monoids Associated to Highest Weight Representations of Kac-Moody Groups

Zhenheng Li - University of South Carolina, Aiken

Abstract:

We show in this talk how to construct a monoid from a highest weight representation of a Kac-Moody group over the complex numbers. The unit group of the monoid is the image of the Kac-Moody group under the representation, multiplied by the nonzero complex numbers. We then show that this monoid has similar properties to those of a J-irreducible reductive linear algebraic monoid. More specifically, the monoid is unit regular and has a Bruhat decomposition, and the idempotent lattice of the generalized Renner monoid of the Bruhat decomposition is isomorphic to the face lattice of the convex hull of the Weyl group orbit of the highest weight.

Location: Gibson Hall 414

Time: 2:00


Thursday, September 29

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Friday, September 30

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Week of October 3 - October 7, 2016
Monday, October 3

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Tuesday, October 4

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Wednesday, October 5
PROBABILITY and STATISTICS

Diffusion and Transient Binding with a Non-Linear Tether

John Fricks - Arizona State University

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In living cells, Brownian forces play a dominant role in the movement of small and not so small particles, such as vesicles, organelles, etc.  However, proteins and other macromolecules bind to one another, altering the underlying Brownian dynamics.  In this talk, classical approaches in the biophysical literature to time series observations which switch between bound and unbound states will be presented, and an alternative approach using stochastic expectation-maximization algorithm (EM) combined with particle filters will be proposed along with extensions for non-quadratic potentials when the particle is bound

Location: Gibson 310

Time: 3:00


Thursday, October 6
GEOMETRY & TOPOLOGY

Surgeries on four-dimensional Hamiltonian systems with S1 symmetry

Margaret Symington - Mercer University

Abstract:

Blowing up and down are fundamental surgeries in symplectic geome- try. In dimension four, equivariant blow-ups of symplectic four-manifolds equipped with a T2-action or an S1-action are well understood. It is less clear how to perform these operations while preserving the structure of a manifold with an S1 R-action. In this talk I will describe a class of com- pletely integrable Hamiltonian systems with two degrees of freedom that are \nice" enough for study via surgeries and then explain the topology, sym-plectic geometry and the Hamiltonian aspects of two types of surgeries in this setting: nodal trades and blowing up or down.

Location: Tilton Hall 305

Time:  12:30


Thursday, October 6

COLLOQUIUM

Early sub-exponential epidemic growth: Implications for disease forecasting and estimation of the reproduction number

Prof Gerardo Chowell - GEORGIA STATE UNIVERSITY (Host: James Hyman)

Abstract:

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.


Location: Gibson Hall 414

Time: 3:30


Friday, October 7

APPLIED and COMPUTATIONAL MATHEMATICS

An Interface-Fitted Adaptive Mesh Method for Free Interface Problems

Xiaoming Zheng - CENTRAL MICHIGAN UNIVERSITY (Host KUN ZHAO)

Abstract:

This talk presents a novel two-dimensional interface-fitted adaptive mesh method to solve elliptic problems of jump conditions across the interface, and its application in free interface problems with surface tension. The interface-fitted mesh is achieved by the projection of mesh nodes onto the interface and the insertion right on the interface. The interface-fitting technique is combined with an existing adaptive mesh approach which uses addition/subtraction and displacement of mesh nodes. We develop a simple piecewise linear finite element method built on this interface-fitted mesh and prove its almost optimal convergence for elliptic problems with jump conditions across the interface. Applications to two free interface problems, a sheared drop in Stokes flow and the growth of a solid tumor, are presented. In these applications, the interface surface tension serves as the jump condition or the Dirichlet boundary condition of the pressure, and the pressure is solved with the interface-fitted finite element method developed in this work. This is a joint work with John Lowengrub of University of California at Irvine.


Location: Gibson Hall 325

Time: 3:30

Week of October 10 - October 14, 2016
Monday, October 10

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Tuesday, October 11

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Wednesday, October 12

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Thursday, October 13
Fall Break

Friday, October 14
Fall Break
Week of October 17 - October 21, 2016
Monday, October 17

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Tuesday, October 18

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Wednesday, October 19

PROBABILITY and STATISTICS

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Veronica Ciocanel - Brown University (Host Scott McKinley)

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Location:  Gibson Hall 310

Time: 3:00


Thursday, October 20

ALGEBRA and COMBINATORICS

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Arindam Banerjee - Purdue University

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Location: Gibson Hall 414

Time:  2:00


Thursday, October 20

COLLOQUIUM

Deterministic and Stochastic Reduced Order Modeling of Microscopic Organism Motility Mechanisms

Prof. Sorin Mitran - UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL (Host: LISA FAUCI)

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Microscopic organisms exhibit various modes of propulsion: ciliary or flagellar beating, lamellipodium protrusion followed by attachment/detachment to a substrate, taking over control of actin production in a host cell. High-throughput computational simulation can provide detailed description of specific motility aspects, but their cost and complexity is an impediment to furthering biological understanding of organism propulsion. This talk presents work on the transformation of detailed computational simulation into tractable reduced-order models. Two specific cases are considered: (1) ciliary propulsion to illustrate model reduction of a deterministic system, and (2) propulsion of Listeria monocytogenes to illustrate aspects of stochastic model reduction. In ciliary propulsion, molecular dynamics level computation is used to furnish a detailed description of mechanical behavior of the microtubule constituents of a cilium. The data is used to construct a finite element model that is markedly different from the Euler-Bernoulli beam models typically used in cilia studies. L. monocytogenes moves by taking over the production of actin within a host cell. Stochastic modeling of the growth of the host cytoskeleton catalyzed by L. monocytogenes is used to construct a statistical model of the flight/forage behavior that can be used to infer infection virulence. Model reduction in this case involves consideration of the differential geometry of probability distributions, a field of study known as information geometry. The model reduction procedures are presented at a conceptual level, avoiding technical details, concentrating on the goal of arriving at correct models of direct utility to biology.

Location: Gibson Hall 414

Time: 3:30


Friday, October 21

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Week of October 24 - October 28, 2016
Monday, October 24

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Tuesday, October 25

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Wednesday, October 26

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Thursday, October 27
ALGEBRA and COMBINATORICS

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Laura Matusevich - Texas A&M

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Location: Gibson Hall 414

Time: 2:00


Thursday, October 27

COLLOQUIUM

Limit Theorems for Composition of Functions

Michael Anshelevich - TEXAS A&M (Host: MAHIR CAN)

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Limit theorems for sums of independent random variables (or, equivalently, for convolutions of measures) are a cornerstone of classical probability theory. Distributions arising as limits in these theorems are called infinitely divisible.

We will discuss limit theorems for repeated composition of functions on the upper half-plane. Note that unlike addition or convolution, composition is a non-commutative operation. What are the limit theorems? Which functions arise as limits? We will see both parallels and differences from the usual setting. This is joint work with John D. Williams.

Location: Gibson Hall 414

Time: 3:30


Friday, October 28

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Week of October 31 - November 4, 2016
Monday, October 31

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Tuesday, November 1

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Wednesday, November 2

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Thursday, November 3

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Friday, November 4

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Week of November 7 - November 11, 2016
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Tuesday, November 8

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Wednesday, November 9

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Thursday, November 10

ALGEBRA & COMBINATORICS

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Jonathan Montaño - University of Kansas

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Location: Gibson Hall 414

Time: 2:00


Thursday, November 10

COLLOQUIUM

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Friday, November 11

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Week of November 14 - November 18, 2016
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Tuesday, November 15

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Wednesday, November 16

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Thursday, November 17

COLLOQUIUM

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Geordie Richards - UTAH STATE UNIVERSITY (Host:  NATHAN GLATT-HOLTZ)

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Location: Gibson Hall 414

Time: 3:30


Friday, November 18

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Week of November 21 - November 25, 2016
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Tuesday, November 22

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Wednesday, November 23

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Thursday, November 24
Thanksgiving Holiday

Friday, November 25
Thanksgiving Holiday
Week of November 28 - December 2, 2016
Monday, November 28

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Tuesday, November 29

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Wednesday, November 30

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Thursday, December 1
COLLOQUIUM

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Prof. Leo Rebholz - Clemson University (Host Kun Zhao)

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Location: Gibson Hall 414

Time: 3:30


Friday, December 2

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Week of December 5 - December 9, 2016
Monday, December 5

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Tuesday, December 6

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Wednesday, December 7

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Thursday, December 8

COLLOQUIUM

Spectral and Nonlinear Stability of Viscous Detonation Waves

Gregory Lyng - UNIVERSITY OF WYOMING (HOST: VINCENT MARTINEZ)

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In this talk we give an overview of a body of results pertaining to the stability of detonation waves. These are particular, dramatic solutions to systems modeling mixtures of reacting gases. They are known to have delicate stability properties. On the mathematical side, the centerpiece of the program is the Evans function. This is a spectral determinant whose zeros agree in location and multiplicity with the eigenvalues of the linearized operator about the wave; it enters the analysis at both the nonlinear and linear/spectral levels. We discuss both theoretical aspects of the Evans function and also issues related to its practical computation.  On the physical side, much of the novelty of this body of work stems from the inclusion of oft-neglected diffusive effects (e.g., viscosity, heat conductivity, species diffusion) in the analysis. Indeed, this modeling choice sometimes leads to surprising results.

Location: Gibson Hall 414

Time:  3:30


Friday, December 9

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