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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)

Abstract:

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)

Abstract:

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

Abstract:

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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

Abstract:

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

Abstract:

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

Abstract:

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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

Abstract:

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

STUDENT COLLOQUIUM

Anomalous Dynamics of Switching Diffusion

Lukasz Sikora - Tulane University

Abstract:

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: Stanley Thomas 316

Time: 4:15


Wednesday, October 5
PROBABILITY and STATISTICS

Diffusion and Transient Binding with a Non-Linear Tether

John Fricks - Arizona State University

Abstract:

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

Fractional Calculus and Fractional Brownian Motion

Cooper Boniece - Tulane University

Abstract:


What does it mean to take 1/2 of a derivative?
Or integrate 2/3 times?  Or, more generally, can we find
a family of operators that `interpolate' the integral and derivative operators?
And what sort of questions can we answer with such tools?

Fractional Brownian motion (fBm) is a generalization of Brownian motion that allows for correlated increments.  In general, fBm lacks a key property in stochastic integration theory -- it is not a semimartingale -- and so much of the machinery from classical theory is unavailable
when considering integration questions related to fBm.  In this talk, we examine some of the historical developments of fractional calculus and explore its connections with fBm and related integration theory.

Location:  Stanley Thomas 316

Time: 4:15


Wednesday, October 19

PROBABILITY and STATISTICS

Modeling mRNA Localization in Frog Egg Cells

Veronica Ciocanel - Brown University (Host Scott McKinley)

Abstract:

Messenger RNA (mRNA) localization is essential during the early development of many organisms, including during development of frog egg cells into embryos. This accumulation of RNA at the cell periphery is not well understood, but is thought to depend on diffusion, bidirectional movement and anchoring mechanisms. Our goal is to test these proposed mechanisms using dynamical systems and stochastic models and analysis, informed by parameter estimation. These methods allow us to extract asymptotic quantities such as effective velocity and diffusion, and to conclude that the PDEs considered have approximate traveling wave solutions. We confirm the hypothesis of bidirectional transport, and use the parameter estimates in numerical studies of localization.

Location:  Gibson Hall 310

Time: 3:00


Thursday, October 20

ALGEBRA and COMBINATORICS

Verifiability of Stillman's Question

Arindam Banerjee - Purdue University

Abstract:

Stillman's question asks whether one can find an upper bound for protective dimension of homogeneous ideals depending only on the degree sequence of its generating set, independent of the number of variables in the polynomial ring.  it is believed that this question has a positive answer and many researchers have proved it for different special cases in recent years. In this joint work with Giulio Caviglia, we study a variant of this question; i.e, we ask if one conjectures a bound for a a fixed degree sequence, whether that can be algorithmically verified. We answer this in affirmative and in the process we also prove some other related and interesting results.


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)

Abstract:

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

Graduate Student Colloquium

 

Basic Cryptographic Protocols

Ellis Fenske - Tulane University

Abstract:


In this short talk I will discuss protocols based on public key cryptography, with a brief discussion of the number theory underpinning much of modern asymmetric cryptography and a primary focus on a variety of cryptographic constructs we can design using only public-key cryptography as a building block: signatures, commitments, shuffles, and zero knowledge proofs.

Location:  Stanley Thomas 316

Time: 4:15


Wednesday, October 26

Central-Upwind Schemes for Shallow Water Models

Yuanzhen Cheng - Tulane University

Abstract:

Shallow water models are widely used to describe and study fluid dynamics phenomena where the horizontal length scale is much greater than the vertical length scale, for example, in the atmosphere and oceans. Since analytical solutions of the shallow water models are typically out of reach, development of accurate and efficient numerical methods is crucial to understand many mechanisms of atmospheric and oceanic phenomena. In this dissertation, we are interested in developing simple, accurate, efficient and robust numerical methods for two shallow water models --- the Saint-Venant system of shallow water equations and the two-mode shallow water equations.
 
We first construct a new second-order moving-water equilibria preserving central-upwind scheme for the Saint-Venant system of shallow water equations. Special reconstruction procedure and source term discretization are the key components that guarantee the resulting scheme is capable of exactly preserving smooth moving-water steady-state solutions and a draining time-step technique ensures positivity of the water depth. Several numerical experiments are performed to verify the well-balanced and positivity preserving properties as well as the ability of the proposed scheme to accurately capture small perturbations of moving-water steady states. We also demonstrate the advantage and importance of utilizing the new method over its still-water equilibria preserving counterpart.
 
We then develop and study numerical methods for the two-mode shallow water equations in a systematic way. Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms. We present several numerical approaches---two operator splitting methods (based on either Roe-type upwind or central-upwind scheme), a central-upwind scheme and a path-conservative central-upwind scheme---and test their performance in a number of numerical experiments. The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method for this system.

Location: Gibson Hall 325

Time:  3:00


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)

Abstract:

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

Graduate Student Colloquium


A Simplified Model of Human Birth: Translation of a Rigid Cylinder through a Passive Elastic Tube

Roseanna Gossmann - Tulane University

Abstract:

A simplified numerical model is used to explore the forces on an infant during human birth. Numerical results are compared with the results of a physical model which represents the fetus moving through the birth canal using a rigid cylinder (fetus) that moves at a constant velocity through the center of a passive elastic tube (birth canal). The entire system is immersed in a highly viscous fluid; low Reynolds number allows the Stokes equations to approximate fluid behavior. The pulling force necessary to move the rigid inner cylinder at a constant velocity through the tube is measured, and considered along with the time-evolving behavior of the elastic tube. The discrete tube through which the rigid cylinder passes has macroscopic elasticity matched to the tube used in the physical experiment. The buckling behavior of the elastic tube is explored by varying velocity, length, and diameter of the rigid cylinder, and length 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 and velocity during human birth.



Location: Stanley Thomas 316

Time: 4:15


Wednesday, November 2

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Thursday, November 3

Clifford Lectures



Friday, November 4

Clifford Lectures


Saturday, November 5

Clifford Lectures


Sunday, November 6

Clifford Lectures


Week of November 7 - November 11, 2016
Monday, November 7

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Tuesday, November 8

GRADUATE STUDENT COLLOQUIUM

Colors of Non-Euclidean Geometry

Sankhaneel Bisui and Sushovan Majhi - Tulane University

Abstract:


We will eat pizza with Euclidean seasoning and non-Euclidean toppings. We will start with Euclidean postulates and show the transition to the non-Euclidean geometry, especially hyperbolic geometry. Along with various classical models of hyperbolic geometry, we shall touch upon some applications of this strange geometry. We will also present how the physical world is related to geometry, or geometry is related to the physical world... who knows??


Location: Stanley Thomas 316

Time: 4:15 pm


Wednesday, November 9

PROBABILITY & STATISTICS


Diffusion in a Randomly Switching Environment

Sean Lawley - University of Utah

Abstract:

A number of diverse biological systems involve diffusion in a randomly switching environment. For example, such processes arise in brain biochemistry, insect respiration, intracellular trafficking, and biochemical reaction kinetics. These processes present interesting mathematical subtleties as they combine two levels of randomness: Brownian motion at the individual particle level and a randomly switching environment.

In this talk, we will describe the tools for analyzing these systems and highlight the interesting behavior that they can exhibit. Special attention will be given to establishing mathematical connections between these classes of stochastic processes. In particular, we will use these connections to study certain random PDEs by analyzing the local time of a Brownian particle in a random environment.

Location: Gibson 310

Time:  3:00


Thursday, November 10

ALGEBRA & COMBINATORIC


Local Cohomology of Powers of Monomial Idealsc

Jonathan Montaño - University of Kansas

Abstract:


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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
Monday, November 14

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Tuesday, November 15

Graduate Student Colloquium

Stochastic Methods in Turbulent Fluids

Nathan Glatt-Holtz - Tulane University

Abstract:  I will illustrate the many roles that probability and statistics play

in my research concerning turbulent fluid flows

Location: Stanley Thomas

Time: 4:15


Wednesday, November 16

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Friday, November 17

Algebra and Combinatorics

Towards a Deformation Theory for Complex G2 Manifold

Mahir Can - Tulane University

Abstract:

In differential geometry a G2 manifold is a seven dimensional manifold with a metric whose holonomy group is contained in the exceptional Lie group G2.

This topic is a highly active branch of mathematics and it has organic ties to mathematical physics.

In this talk we will make an introduction to some universal algebro-geometric objects associated with G2-manfiolds. We do not assume any background in algebraic geometry.

Location:  Gibson 414

Time:  2:00


Thursday, November 17

COLLOQUIUM

On Invariant Measures for Hamiltonian PDE

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

Abstract:

We will survey some recent results on the construction and proof of invariance for certain canonical measures, such as the Gibbs measure, under the flow of dispersive Hamiltonian PDEs.  Proving the invariance of these measures is often nontrivial due to the low regularity of functions belonging to their support.  Focus will be placed on the generalized Korteweg-de Vries (gKdV) equations; Bourgain proved invariance of the Gibbs measure for KdV and mKdV, which have quadratic and cubic nonlinearities, respectively.  Previously, we proved invariance of the Gibbs measure for the quartic gKdV by exploiting a nonlinear smoothing induced by initial data randomization.  More recently, in joint work with Tadahiro Oh (Edinburgh) and Laurent Thomann (Nantes), we have established this invariance for gKdV with any odd power (defocusing) nonlinearity using a probabilistic construction of solutions.

Location: Gibson Hall 414

Time: 3:30

Friday, November 18

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Week of November 21 - November 25, 2016
Monday, November 21

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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

Graduate Student Colloquium


Topic:    Library Resources for Mathematics Research

Althea Topek and Raquel Horlick - Tulane University

Abstract:

This will be a special information session introducing the elements of the library and those resources of particular interest to mathematics resarchers. Topics will include Interlibrary Loan, graduate study spaces, BibTeX and alternatives, e-books and journals, as well as other research tools such as Browzine and TOC alerts.

Location: Stanley Thomas 316

Time:  4:15


Wednesday, November 30

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Thursday, December 1

Algebra and Combinatorics

Towards a deformation theory in complex G2 manifolds, part IIc

Mahir Can - Tulane University

Abstract:

Part II.

In differential geometry a G2 manifold is a seven dimensional manifold with a metric whose holonomy group is contained in the exceptional Lie group G2.

This topic is a highly active branch of mathematics and it has organic ties to mathematical physics.

In this talk we will make an introduction to some universal algebro-geometric objects associated with G2-manfiolds. We do not assume any background in algebraic geometry.


Location: Gibson Hall  414

Time: 2:00


Thursday, December 1

COLLOQUIUM

Efficient Discretization Methods for Magnetohydrodynamic Flow Simulationc

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

Abstract:

After an introduction to magnetohydrodynamics (MHD), which describes the flow of electrically conducting fluids, we will discuss the major difficulties associated with computing MHD solutions.  We will then present two novel approaches to circumventing these difficulties.  The first is using the Elsasser change of variable approach, which allows for an unconditional energy-stable decoupling of the different physical processes at each time step in a temporal discretization.  A second approach is based on an algebraic decoupling scheme (build the matrix, then split) that also allows for an accurate decoupling but with a mild CFL condition.  High level details of the analysis and derivation of these methods will be discussed, and several open problems will be presented.

Location: Gibson Hall 414

Time: 3:30


Friday, December 2

Applied & Computational

Numerical Approximation of a Data Assimilation Algorithm by a Post-Processing Galerkin Method

Cecilia Mondaini - Texas A&M University  (Host Vincent Martinez)

Abstract:

Abstract: We consider a data assimilation algorithm for recovering the exact value of a reference solution of the two-dimensional Navier-Stokes equations, by using continuous in time and coarse spatial observations. The algorithm is given by an approximate model which incorporates the observations through a feedback control (nudging) term. We obtain an analytical uniform in time estimate of the error committed when numerically solving this approximate model by using a post-processing technique for the spectral Galerkin method, inspired by the theory of approximate inertial manifolds. This is a joint work with C. Foias and E. S. Titi.

Location: Gibson 325

Time: 3:30

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

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Tuesday, December 6

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Wednesday, December 7

Probability and Statistics


Group-wise feature selection with false discovery rate control

Alexej Gossmann - Tulane University

Abstract:

The method of Sorted L-One Penalized Estimation, or SLOPE, is a relatively new sparse regression method introduced by Bogdan et. al. (2015). It can be used to identify significant predictor variables in a linear model that may have more unknown parameters than observations. When the correlations between predictor variables are small, the SLOPE method is shown to successfully control the false discovery rate (the expected proportion of the irrelevant among all selected predictors) at a user specified level. However, the requirement for nearly uncorrelated predictors is too restrictive for genomic data. A possible solution is to divide the predictor variables into nearly uncorrelated groups, and to modify the procedure to select entire groups with an overall significant group effect, rather than individual predictors. Following this motivation, we extend SLOPE in the spirit of Group LASSO to Group SLOPE, a method that can handle group structures between the predictor variables, which are ubiquitous in real genomic data. Our theoretical results show that Group SLOPE controls the group-wise false discovery rate (gFDR), when groups are orthogonal to each other. For use in general, non-orthogonal settings we propose several heuristics, which lead to gFDR control with Group SLOPE in simulations on real SNP (single-nucleotide polymorphism) data. As an illustration of the merits of this method, an application of Group SLOPE to a dataset from the Framingham Heart Study results in the identification of some known DNA sequence regions associated with bone health, as well as some new candidate regions. Additionally, if time permits, further SLOPE-based methods and topics for future research will be briefly introduced.

Location: Gibson Hall 310

Time:  3:00


Thursday, December 8

COLLOQUIUM

Spectral and Nonlinear Stability of Viscous Detonation Waves

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

Abstract:

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

Topic

Speaker - Institution

Abstract: 

Location:

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