# Events This Week

Week of November 23 - November 19

Friday, November 23

## Thanksgiving Holiday

Thursday, November 22

## Thanksgiving Holiday

Wednesday, November 21

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Tuesday, November 20

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Monday, November 19

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Week of November 16 - November 12

Friday, November 16

## Taming turbulence via nudging

Patricio Clark - University of Rome

Abstract:

The technique of nudging is commonly used to incorporate empirical data into a simulation in order to control its chaotic evolution and reproduce a given dynamical benchmark. We show how to do this in fully developed three dimensional turbulence using data both in configuration and Fourier space. Our results show that given enough data, nudging is successful in reconstructing the whole turbulent field. We give physical arguments for the choice of optimal parameters and the amount and quality of data needed to do this. Nudging thus serves as a way to probe for key degrees of freedom in a flow. We also turn the algorithm on its head and show how it can be used to infer the values of parameters and the presence of unknown physical mechanisms in the data.

Location: Gibson Hall 310

Time: 3:30

Thursday, November 15

## Stochastic Partial Differential Equations and Bayesian Inversion with Applications in Nanoscale Sensors and Tomography

Clemens Heitzinger - TU Vienna (Host:Glatt-Holtz)

Abstract:

Applications such as electrical-impedance tomography, nanoelectrode sensors, and nanowire sensors lead to deterministic and stochastic partial differential equations that model electrostatics and charge transport.  The main model equations are the nonlinear Poisson-Boltzmann equation and the stochastic drift-diffusion-Poisson-Boltzmann system.  After a discussion of the model equations, theoretic results as well as a numerical method, namely optimal multi-level Monte Carlo, are presented.

Knowing these model equations, the question how as much information as possible can be extracted from measurements arises next.  We use computational Bayesian PDE inversion to reconstruct physical and geometric parameters of the body interior in electrical-impedance tomography and of target molecules in the two nanoscale sensors considered here.  Computational Bayesian estimation provides us with the ability not only to estimate unknown parameter values but also their probability distributions and hence the uncertainties in reconstructions, which is important in the case of ill-posed inverse problems.  In addition to showing the well-posedness of the Bayesian inversion problem for the nonlinear Poisson-Boltzmann equation, numerical results for the three applications such as multifrequency reconstruction for nanoelectrode sensors are shown.

Location:  Location: Gibson Hall 325

Time: 3:30

Thursday, November 15

## Density bounds on binary packings of disks in the plane

Ali Mohajer - Tulane University

Abstract:

In this talk we develop methods for establishing upper density bounds for saturated two-radius packings of disks in the plane.

Define the homogeneity of a packing of disks in the plane to be the infimum of the ratio of radii of disks in the packing. It has been known since 1953 (L. Fejes-Toth) that if the homogeneity of a packing is close enough to 1, the density of that packing cannot exceed $\frac{$\pi}{\sqrt{12}},$the upper bound on the density of a single-radius packing. "Close enough” was refined in 1963 by August Florian to mean a homogeneity in the interval (0.902…, 1], and in 1969, Gerd Blind extended the left bound of this interval to approximately 0.742. In 2003, sharp upper density bounds were established by Aladar Heppes for a handful of two-radius packings at homogeneities which admit arrangements wherein each disk is tangent to a ring of disks, each of which is tangent to its two cyclic neighbors. We will discuss recent progress in establishing a bound sharper than the best one known for binary packings at a homogeneity that does not admit such regularity. Location: Gibson Hall 400-D Time: 12:30 Wednesday, November 14 ## Probability and Statistics ## Consistent Inter-Model Specification for Time-Homogeneous SPX Stochastic Volatility and VIX Market Models Andrew Papanicolaou - Institution Abstract: This talk is about the recovering of stochastic volatility models (SVMs) from market models for the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs, and therefore they are better-suited for pricing VIX futures and derivatives. But the VIX itself is a derivative of the S\&P500 (SPX) and it is common practice to price SPX derivatives using an SVM. Hence, a consistent model for both SPX and VIX derivatives would be one where the SVM is obtained by inverting the market model. A function for stochastic volatility function is the solution of an inverse problem, with the inputs given by a VIX futures market model. Several models are analyzed mathematically and explored numerically. Location: Gibson Hall 126 Time: 3:00 Wednesday, November 14 ## Algebra and Combinatorics ## Upper bound for the regularity of powers of edge ideals of graphs. Part 1 A.V. Jayanthan - Indian Institute of Technology, Madras Abstract: Let G be a finite simple graph and I(G) denote the corresponding edge ideal. In this paper, we obtain an upper bound for reg(I(G)^q) in terms of certain invariants associated with G. We also prove certain weaker versions of a conjecture by Alilooee, Banerjee, Bayerslan and Hà on an upper bound for the regularity of I(G)^q and we prove the conjectured upper bound for the class of vertex decomposable graphs. Location: Gibson Hall 325 Time: 3:00 Tuesday, November 13 ## Chudnovsky's Conjecture and Waldschmidt Constant Sankhaneel Bisui - Tulane University Abstract: A well-studied question in algebraic geometry is : Given a finite set of points in a projective space, what is the minimal degree of a hypersurface that will pass through the points with a given multiplicity? To answer this question Chudnovsky gave a Conjecture using the multiplicity. We are going to see the basic facts of the Conjecture. In this aspect, Waldschmidt constant plays an important role. We will see the general version of the conjecture. Waldschmidt constant has some important connection with LPP. So, if time allows we are going to see some. Location: Stanley Thomas 316 Time: 4:30 Monday, November 12 ## Topic Speaker - Institution Abstract: Location: Time: Week of November 9 - November 5 Saturday, November 10 ## Commutative Algebra and Representation Theory Conference Friday, November 9 ## Commutative Algebra and Representation Theory Conference Friday, November 9 ## Applied and Computational Mathematics ## A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Nonlinear Turbulent Dynamical Systems Nan Chen - University of Wisconsin, Madison Abstract: A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of complex nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. This talk will include three applications of such conditional Gaussian framework. The first part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the second part, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high-dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions. In the last part of this talk, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The other related topics such as parameter estimation and causality analysis will also be briefly discussed. Location: Gibson Hall 310 Time: 3:30 Thursday, November 8 ## Commutative Algebra and Representation Theory Conference Thursday, November 8 ## Colloquium ## Microorganism locomotion in viscoelastic fluids Becca Thomases - UC Davis (Host:Fauci, Lisa) Abstract: Many microorganisms and cells function in complex (non-Newtonian) fluids, which are mixtures of different materials and exhibit both viscous and elastic stresses. For example, mammalian sperm swim through cervical mucus on their journey through the female reproductive tract, and they must penetrate the viscoelastic gel outside the ovum to fertilize. A swimming stroke emerges from the coupled interactions between the complex rheology of the surrounding media and the passive and active body dynamics of the swimmer. We use computational models of swimmers in viscoelastic fluids to understand these interactions. I will show results from several recent investigations, and give mechanistic explanations for some different experimental observations. In particular I will discuss how flexible filaments (such as flagella) can store energy from the fluid to obtain speed enhancements from fluid elasticity. Location: Gibson Hall 325 Time:3:30 Thursday, November 8 ## Topic Speaker - Institution Abstract: Location: Time: Thursday, November 8 ## Topic Speaker - Institution Abstract: Location: Time: Wednesday, November 7 ## Probability and Statistics ## Iterative projection methods for noisy and corrupted systems of linear equations Jamie Haddock - UCLA Abstract: Iterative linear solvers have gained recent popularity due to their computational efficiency and low memory footprint for large-scale linear systems. We will discuss two classical methods, Motzkin's method (MM) and the Randomized Kaczmarz method (RK). MM is an iterative method that projects the current estimation onto the solution hyperplane corresponding to the most violated constraint. Although this leads to an optimal selection strategy for consistent systems, for noisy least squares problems, the strategy presents a tradeoff between convergence rate and solution accuracy. We analyze this method in the presence of noise. RK is a randomized iterative method that projects the current estimation onto the solution hyperplane corresponding to a randomly chosen constraint. We present RK methods which detect and discard corruptions in systems of linear equations, and present probabilistic guarantees that these methods discard all corruptions. Location: Gibson Hall 126 Time:3:00 Tuesday, November 6 ## Graduate Student Colloquium ## GRAPHS AS REDUCED MODELS FOR DISCRETE FRACTURE NETWORKS Jaime Lopez - Tulane University Abstract: Discrete fracture networks (DFNs) can be modeled with computationally expensive numerical schemes. We present the formulation of using a graph as a reduced model for a DFN and pose the inversion problem central to this research. We solve the corresponding equations on the graph representation to obtain breakthrough curves, which closely match those created by the high fidelity model. Our solution finds lumped parameters representing the fracture properties, and is used to reduce the computational time required for particle transport calculations. We present examples of creating these reduced models for DFNs with 500 fractures to illustrate the methodology and optimization scheme used to obtain an improved result over a previous formulation. Location: Stanley Thomas 316 Time: 4:30 Monday, November 5 ## Topic Speaker - Institution Abstract: Location: Time: Week of November 2 - October 29 Friday, November 2 ## Special Seminar Applied and Computational Topic: Mathematics and the Law ## Summary • Criminal law and statistics with real world examples: a serial killer case • Civil law and statistics with real world examples: a$40,000,000 import case •    Battle of the statisticians from the civil import case •    Q&A with attendees

Dr. Bruce Krell -

Abstract:

The speaker is a former Tulane undergrad with over 43 years experience as an Applied Mathematician.  He will show examples of the use of applied statistics in the real world.

Criminal law: The Grim Sleeper was accused of 10 murders based on matching marks from bullets found in the bodies of victims. An examination of the evidence leads to doubts about the underlying science. An example of the use of 3-D laser scans, materials science, hypotheses, and statistics is presented.

Civil law: An importer states the weight of his product. This weight is used to determine import duties. An examination of the sample size and statistical approach by the Customs labs leads to doubts about their methods. An example of the use of sample size calculation, regression, hypothesis testing, and manufacturing quality control is presented.

Location:  Gibson Hall 325

Time: 12:00

Friday, November 2

## An Overview of Model Reduction

Christopher Beattie - Virginia Polytechnic Institute and State University

Abstract:

Dynamical systems form the basic modeling framework for a large variety of complex systems.  Direct numerical simulation of these dynamical systems is one of few means available for accurate prediction of the associated physical phenomena.  However, ever increasing needs for improved accuracy require the inclusion of ever more detail in the modeling stage, leading inevitably to ever larger-scale, ever more complex dynamical systems that must be simulated.   Simulations in such large-scale settings can be overwhelming and may create unmanageably large demands on computational resources; this is the main motivation for model reduction, which has as its goal the extraction simpler dynamical systems that retain essential features of the original systems, especially high fidelity emulation of input/output response and conserved quantities.   I will give a brief overview of the objectives and methodology of system theoretic approaches to model reduction, focussing eventually on projection methods that are both simple and capable of providing nearly optimal reduced models in some circumstances.  These methods provide a framework for model reduction that allows retention of special model structure such as parametric dependence, passivity/dissipativity, and port-Hamiltonian structure.

Location:  Gibson Hall 310

Time: 3:30

Thursday, November 1

## Discrete Morse theory and its applications to metric graph reconstruction

Sushovan Majhi - Tulane University

Abstract:

Discrete Morse theory has recently been used as a powerful tool for topological reconstruction and simplification in the field of Applied and Computational Topology.  We discuss some its very recent and successful applications in data analysis. In particular, we talk about a recent development in threshold-based topological and geometric reconstruction of metric graphs from a density concentrated around it.

Location: Gibson Hall 400-D

Time:  12:30

Wednesday, October 31

## Universality for Products of Random Matrices

Phil Kopel - University of Colorado Boulder

Abstract:

Random matrices have played an increasingly significant role in diverse areas of pure and applied mathematics over the last fifty years. In the first half of this talk, I will provide a brief overview of the subject: some of the things we study, some of the methods we use, some major results obtained, and several tantalizing unsolved problems. This will hopefully be accessible and informative for a general mathematical audience -- no prior experience required! In the second half of the talk, I will discuss some recent results obtained (in collaboration with Sean O'Rourke and Van Vu) establishing universality of fluctuations in the spectral bulk for products of independent entry ensembles, and outline the proofs.

Location:  Gibson Hall 126

Time:  3:00

Wednesday, October 31

## Associated primes of powers of edge ideals and ear decompositions of graphs (Part II)

Minh Lam - Institute of Mathematics, VAST

Abstract:

We give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establishes a relationship between two seemingly unrelated notions of Commutative Algebra and Combinatorics. It covers all previous major results in this topic and has several interesting consequences.

Location: Gibson Hall 31

Time: 3:00

Tuesday, October 30

## Normality of Monomial Ideals

Thai Nguyen - Tulane University

Abstract:

In this talk, I will give an introduction to the concepts of integral closure and normality of rings and ideals and explain why I care about them. Focusing on monomial ideals, I will talk about some approaches to tackle the problem of determining the normality of a monomial ideal provided that some of its ordinary powers are integrally closed. It turns out that there is a surprisingly interesting connection between them and some important objects and problems in convex geometry, graph theory and integer programming.

Location: Stanley Thomas 316

Time:4:30

Monday, October 29

## Catalan Functions and k-Schur functions

Anna Pun - Drexel University

Abstract:

Li-Chung Chen and Mark Haiman studied a family of symmetric functions called Catalan (symmetric) functions which are indexed by pairs consisting of a partition contained in the staircase (n-1, ..., 1,0) (of which there are Catalan many) and a composition weight of length n. They include the Schur functions ,the Hall-Littlewood polynomials and their parabolic generalizations. They can be defined by a Demazure-operator formula, and are equal to GL-equivariant Euler characteristics of vector bundles on the flag variety by the Borel-Weil-Bott theorem. We have discovered various properties of Catalan functions, providing a new insight on the existing theorems and conjectures inspired by Macdonald positivity conjecture.

A key discovery in our work is an elegant set of ideals of roots that the associated Catalan functions are k-Schur functions and proved that graded k-Schur functions are G-equivariant Euler characteristics of vector bundles on the flag variety, settling a conjecture of Chen-Haiman. We exposed a new shift invariance property of the graded k-Schur functions and resolved the Schur positivity and k-branching conjectures by providing direct combinatorial formulas using strong marked tableaux. We conjectured that Catalan functions with a partition weight are k-Schur positive which strengthens the Schur positivity of Catalan function conjecture by Chen-Haiman and resolved the conjecture with positive combinatorial formulas in cases which capture and refine a variety of problems.

This is joint work with Jonah Blasiak, Jennifer Morse and Daniel Summers.

Location:  Gibson Hall 325

Time:  3:00

Week of October 26 - October  22
Friday, October  26

## A bundled approach for high-dimensional informatics problems

Reginald McGee | College of the Holy Cross

Abstract:

As biotechnologies for data collection become more efficient and mathematical modeling becomes more ubiquitous in the life sciences, analyzing both high-dimensional experimental measurements and high-dimensional spaces for model parameters is of the utmost importance. We present a perspective inspired by differential geometry that allows for the exploration of complex datasets such as these. In the case of single-cell leukemia data we present a novel statistic for testing differential biomarker correlations across patients and within specific cell phenotypes. A key innovation here is that the statistic is agnostic to the clustering of single cells and can be used in a wide variety of situations. Finally, we consider a case in which the data of interest are parameter sets for a nonlinear model of signal transduction and present an approach for clustering the model dynamics. We motivate how the aforementioned perspective can be used to avoid global bifurcation analysis and consider how parameter sets with distinct dynamic clusters contrast.

Location:  Gibson Hall 310

Time: 3:30

Thursday, October  25

## Assessing Observation Impact: Application to US Global Numerical Weather Prediction

Kayo Idee - University of Maryland (Host Glatt-Holtz, Mondaini)

Abstract:

In data assimilation that attempts to predict nonlinear evolution of the system by combining complex computational model, observations, and uncertainties associated with them, it is useful to be able to quantify the amount of information provided by an observation or by an observing system. Measures of the observational influence are useful for the understanding of performance of the data assimilation system.  The Forecast sensitivity to observation provides practical and useful metric for the assessment of observations. Quite often complex data assimilation systems use a simplified version of the forecast sensitivity formulation based on ensembles.  In this talk, we first present the comparison of forecast sensitivity for 4DVar, Hybrid-4DEnVar, and 4DEnKF with or without such simplifications using a highly nonlinear model. We then present the results of ensemble forecast sensitivity to satellite radiance observations for Hybrid-4DEnVart using a global data assimilation system.

Location:  Gibson Hall 325

Time:  3:30

Thursday, October 25

## From Lindenbaum-Tarski to Stone Duality and beyond

Michael Mislove - Tulane University

Abstract:

The Lindenbaum-Tarski Theorem states that every complete atomic Boolean algebra is isomorphic to the power set of its set of atoms. It’s easy to turn this into a duality, and the next question is how to generalize to include arbitrary Boolean algebras. This leads to Stone Duality, which has a remarkable number of applications in mathematics and other areas, including in computer science. I’ll outline how some of these results arose, focusing on contributions of two colleagues whose work has influenced my own: Hilary Priestley and Mae Gehrke.

Location: Gibson 400-D

Time: 1:30

Thursday, October  25

## Finite-type knot invariants and a proof of the Goussarov Theorem

Robyn Brookr - Tulane University

Abstract:

Finite-type knot invariants represent an active research area in knot theory.  The Goussarov Theorem shows that all such invariants can be read from the Gauss diagram of a knot.  In this talk, I will give a proof of this theorem, which provides a method by which one can generate a formula to determine the value of an invariant from its Gauss diagram.

Location:  Gibson Hall 400-D

Time:  12:30

Wednesday, October  24

## Associated primes of powers of edge ideals and ear decompositions of graphs (Part II)

Ha Minh Lam - Institute of Mathematics, VAST

Abstract:

We give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establishes a relationship between two seemingly unrelated notions of Commutative Algebra and Combinatorics. It covers all previous major results in this topic and has several interesting consequences.

Location:  Gibson Hall 325

Time: 3:00

Wednesday, October  24

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Tuesday, October  23

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Monday, October  22

## The Variety of Polarizations

Aram Bingham - Tulane University

Abstract:

Location: Gibson Hall 325

Time: 3:00

Week of October 19 - October  15

Friday, October  19

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Thursday, October 18

## Symmetries and choreographies in the N-body problem

Renato Calleja - National Autonomous University of Mexico (Host Glatt-Holtz)

Abstract:

N-body choreographies are periodic solutions to the N-body equations in which N equal masses chase each other around a fixed closed curve. In my talk I will describe numerical and rigorous continuation and bifurcation techniques in a boundary value setting used to follow Lyapunov families of periodic orbits. These arise from the polygonal system of n bodies in a rotating frame of reference. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship, the orbit is also periodic in the inertial frame. We prove that a dense set of Lyapunov orbits, with frequencies satisfying a Diophantine equation, correspond to choreographies. I will present a sample of the many choreographies that we have determined numerically along the Lyapunov families and bifurcating families. I will also talk about the computer assisted proofs that validate some of theses choreographies. This is joint work with Eusebius Doedel, Carlos García Azpeitia, Jason Mireles-James and Jean-Philippe Lessard.

Location: Gibson Hall 325

Time: 3:30

Thursday, October  18

## AMS/AWM Faculty Student

Selvi Kara - Institution

Abstract:

Location: 400-D

Time: 1:30

Thursday, October  18

## Topic: On the reconstruction problem for geodesic subspaces in the Euclidean Space

Rafał Komendarczyk - Tulane University

Abstract:

We develop a persistence based algorithm for the homology/homotopy groups reconstruction of the unknown underlying geodesic subspace of R^n from a point cloud. In the case of a metric graph, we can output a subspace which is an arbitrarily good approximation of the underlying graph. This is a collaborative work in progress.

Location: Gibson Hall 400-D

Time:12:30

Wednesday, October 17

## Estimating evolutionary rates from pattern in the CRISPR defense memory of prokaryotes

Franz Baumdicker - University of Freiburg

Abstract:

Bacteria and archaea are under constant attack by a myriad of viruses. Consequently, many prokaryotes harbor immune systems against such viral attacks. A prominent example is the CRISPR system, that led to the CRISPR-Cas genome editing technology.

The prokaryotic CRISPR defense system includes an array of spacer sequences that encode an inheritable memory of previous infections. These spacer sequences correspond to short sequence samples from past viral attacks and provide a specific immunity against this particular virus.

Notably, new spacer sequences are always inserted at the beginning of the array, while deletion of spacers can occur at any position in the array. In a sample of CRISPR arrays, spacers can thus be present in all or a subset of the sample, but the order of spacer sequences in the array will be conserved across the sample. This order represents the chronological infection history of the host.
In an evolutionary model for spacer acquisition and deletion we derived the distribution of the number of different spacers between spacers that are present in all arrays. In particular, the order of spacers in the arrays can be used to estimate the rate of spacer deletions independently of the spacer acquisition rate. A property that is usually hard to obtain in population genetics. These estimates provide a basis to study the co-evolution of CRISPR possessing prokaryotes and their viruses.

Location:  Gibson Hall 126

Time: 3:00

Tuesday, October  16

## Fractional Brownian Motion: Extensions & Estimation in 1-d, n-d and Beyond

Cooper Boniece - Tulane University

Abstract:

Fractional Brownian motion (fBm), whose origins date back to Kolmogorov, is one of the most celebrated models of scale invariance, and has been used in a wide variety of modeling contexts ranging from hydrology to economics.  In this talk, I will discuss some background related to scale invariance and fBm, introduce two extensions of fBm: tempered fractional Brownian motion (tfBm), and operator fractional Brownian motion (ofBm), and discuss some recent work related to wavelet-based estimation of tfBm (joint work with G. Didier, F. Sabzikar), as well as some preliminary results regarding estimation ofBm in a high-dimensional setting.

Location:  Stanley Thomas 316

Time:  4:30

Monday, October 15

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Week of October 12 - October  8
Friday, October 12

## Fall Break

Thursday, October 11

## Fall Break

Wednesday, October 10

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Tuesday, October  9

## Extensions of set partitions

Diego Villamizar - Tulane University

Abstract:

In this talk we will show arithmetical and combinatorial properties of set partitions that have restrictions in the size of their blocks. This was a joint work with Jhon Caicedo, Victor Moll and Jose Ramirez.

Location:  Stanley Thomas 316

Time: 4:30

Monday, October 8

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Week of October 5 - October  1
Friday, October 5

## How to deduce a physical dynamical model from expectation values

Denys Bondar - Institution

Abstract:

In this talk, we will provide an answer to the question: "What kind of observations (i.e., expectation values) and assumptions are minimally needed to formulate a physical model?" Our answer to this question leads to the new systematic approach of Operational Dynamical Modeling (ODM), which allows deducing equations of motions from time evolution of observables. Using ODM, we are not only able to re-derive well-known physical theories, but also solve open problems in quantum non-equilibrium statistical dynamics. Furthermore, ODM has revealed unexplored flexibility of nonlinear optics: A shaped laser pulse can drive a quantum system to emit light as if it were a different system (e.g., making lead look like gold).

Location: Gibson Hall 310

Time: 4:10

Thursday, October 4

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Thursday, October 4

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Wednesday, October 3

## Constructing a $S_n$ module for $(-1)^{n-1} \nabla p_n$

Speaker - Institution

Abstract:

We will outline a construction of an $S_n$ module with Frobenius characteristic $(-1)^{n-1} \nabla p_n$. The construction is realized  in two steps. First one defines an appropriate  sheaf on the Hilbert scheme of points on the plane. Subsequently, one uses Bridgeland-King-Reid correspondence to pass to $S_n$ modules.

Location:  Gibson Hall 325

Time: 3:00

Tuesday, October  2

## Algorithms for long- and short-range interactions in soft active matter

Wen Yan - Simons Foundation

Abstract:

Research Scientist, Biophysical Modeling Group, Center for Computational Biology, Flatiron Institute, Simons Foundation
Algorithms for long- and short-range interactions in soft active matter Soft matter systems often show intriguing phenomena in large spatial scales and long-time scales, due to various long and short-range interactions between the building blocks. The long-range interactions are usually through Stokes flows and Laplace fields, while steric interactions are usually the dominant effect at short-range. The Kernel Independent Fast Multipole Method is extended to various boundary conditions to allow adaptive and flexible treatment of long-range interactions. This algorithm is then extended to a new formulation for half-space Stokes flows induced by point forces or particles. To handle the short-range steric interactions, we propose a new method based on constrained minimization to circumvent the stiffness of pairwise repulsive potential. In this method collision forces are computed based on the geometric constraint that objects do not overlap. All the discussed algorithms are parallel and scalable, and we demonstrate the applications with a few active matter systems, including microtubule network and growing and dividing cells.

Location:  Stanley Thomas Hall 316

Time:  3:00

Tuesday, October 2

## The Mathematics of Music

Nathan Bedell - Institution

Abstract:

In this talk, I'll explain some of mathematical aspects of music theory. In particular, we will focus on the questions: "Why do we use the 12 notes per octave that we see today on a modern piano keyboard, and not some other collection?" and "Why does most of that music limit itself to certain 5 note (pentatonic) and 7 note (diatonic) subsets of that collection?" respectively.
Our story starts with the history of tuning in the west -- from Pythagorean and meantone temperaments -- including the extended meantone tunings of the Renaissance era, to our modern system of 12 tone equal temperament, some of the various non-western systems of tuning, and finally, to the experimental temperaments that musicians in the "xenharmonic" community have used in recent years to expand the possibilities of our sonic pallet -- all of which will be illustrated with musical examples.

Location: Stanley Thomas 316

Time: 4:30

Monday, October 1

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Week of September 28 - September 24
Friday, September 28

## Fluid-structure interactions within marine phenomena

Shilpa Khatri - Tulane University

Abstract:

To understand the fluid dynamics of marine phenomena 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 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) accurate evaluation of layer potentials near boundaries and interfaces. The first problem of modeling marine aggregates will be motivated by field and experimental work. I will discuss the related data and provide comparisons with the modeling. For the second problem of accurate evaluation of layer potentials, I will show how classical numerical methods are problematic for evaluations close to boundaries and how newly developed asymptotic methods can be used to remove the error. To demonstrate this method, I will consider the interior Laplace problem.

Location:  Gibson Hall 310

Time:  3:30

Thursday, September 27

## Geometry and topology of random curves

Igor Rivin - Temple University  (Host: Victor Moll)

Abstract:

We study (experimentally and theoretically) random curves (in many senses) in space and in the plane, including such of their properties as the knot type.

Location:  Gibson Hall 325

Time: 3:30

Thursday, September 27

## Hodge Structures and the Hodge Conjecture

Al Vitter - Tulane University

Abstract:

The most beautiful and useful invariants used to distinguish between smooth projective varieties with the same topology are the Hodge structures defined on their cohomology groups. I will define Hodge structures and discuss some theorems involving their use. I will also examine the relationship between Hodge structures and sub-varieties, which leads to the Hodge conjecture.

Location:  Gibson Hall 400-D

Time:  1:30

Wednesday, September 26

## Chase-Escape

Matthew Junge - Duke University

Abstract:

Imagine barnacles and mussels spreading across the surface of a rock. Barnacles move to adjacent unfilled spots. Mussels too, but they can only attach to barnacles. Barnacles with a mussel on top no longer spread. What conditions on the rock geometry (i.e. graph) and spreading rates (i.e. exponential clocks) ensure that barnacles can survive? Chase-escape can be formalized in terms of competing Richardson growth models; one on top of the other. New, tantalizing open problems will be presented. Joint work with Rick Durrett and Si Tang.

Location:  Gibson Hall 126

Time:  3:00

Tuesday, September 25

## The Fisher-KPP equation and traveling

Dana Ferranti - Tulane University

Abstract:

Location: Stanley Thomas 316

Time: 4:30

Monday, September 24

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Week of September 21 - September 17
Friday, September 21

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Thursday, September 20

## Simulations of Pulsating Soft Corals

Shilpa Khatri - UC Merced

Abstract:

Soft corals of the family Xeniidae have a pulsating motion, a behavior not observed in many other sessile organisms. We are studying how this behavior may give these coral a competitive advantage. We will present direct numerical simulations of the pulsations of the coral and the resulting fluid flow by solving the Navier-Stokes equations coupled with the immersed boundary method. Furthermore, parameter sweeps studying the resulting fluid flow will be discussed.

Woman mathematician of interest:  Anna-Karin Tornberg.

Location: Gibson Hall 400-D

Time: 1:30

Wednesday, September 19

## Weakly complete real vector spaces

Karl Hofmann - Tulane University

Abstract:

Location: Gibson Hall 325

Time: 3:00

Tuesday, September 18

## Unknotting the knotty notion of knots (and their finite type invariants)

Robyn Brooks - Tulane University

Abstract: TBA

Location:  Stanley Thomas 316

Time: 4:30

Monday, September 17

## Variations on the $S_n$-module $Lie_n$

Sheila Sundaram - Pierrepont School

Abstract:

Location:  Gibson Hall 325

Time: 3:00

Week of September 14 - September 10
Friday, September 14

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Thursday, September 13

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Thursday, September 13

## Combinatorial structures and invariants through algebraic lenses

Tai Ha - Tulane University

Abstract:

We shall discuss how to use algebraic formulations to approach and understand a number of problems in linear programming and graph theory. Particularly, we shall examine the (integral) optimal solutions to system of linear constraints, and important invariants in graph theory, such as the chromatic, matching and covering numbers.

Location: 400-D

Time: 1:30

Wednesday, September 12

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Tuesday, September 11

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Monday, September 10

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Week of September 7   -   September 3, 2018
Friday, September 7

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Thursday, September 6

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Wednesday, September 5

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Tuesday, September 4

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Monday, September 3

## Labor Day

Week of August 31 - August 31
Friday, August31

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Thursday, August 30

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Wednesday, August 29

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Tuesday, August  28

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Monday, August 27

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