Week of November 23 - November 19

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**Patricio Clark - University of Rome**

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**Location:** Gibson Hall 310

**Time:** 3:30

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

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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

**Ali Mohajer - Tulane University**

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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.

**Time:** 12:30

**Andrew Papanicolaou - Institution**

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**Location:** Gibson Hall 126

**Time: ** 3:00

**A.V. Jayanthan - Indian Institute of Technology, Madras**

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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

**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.

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**Time:** 4:30

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Week of November 9 - November 5

Nan Chen - University of Wisconsin, Madison

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**Location:** Gibson Hall 310

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.

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**Time:**3:30

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Jamie Haddock - UCLA

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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.

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**Time:**3:00

**Jaime Lopez - Tulane University
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**Location: Stanley Thomas 316
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**Time: 4:30
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• 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 -
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**Abstract:
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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

**Christopher Beattie - Virginia Polytechnic Institute and State University
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**Location: ** Gibson Hall 310

**Time:** 3:30

**Sushovan Majhi - Tulane University
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**Location:** Gibson Hall 400-D

**Time:** 12:30

**Phil Kopel - University of Colorado Boulder
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**Location:** Gibson Hall 126

**Time: ** 3:00

**Minh Lam - Institute of Mathematics, VAST
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**Location:** Gibson Hall 31

**Time:** 3:00

**Thai Nguyen - Tulane University
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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

**Anna Pun - Drexel University
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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

**Reginald McGee | College of the Holy Cross
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**Abstract:
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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

**Kayo Idee - University of Maryland (Host Glatt-Holtz, Mondaini)
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**Location: ** Gibson Hall 325

**Time: ** 3:30

**Michael Mislove - Tulane University**

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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

**Robyn Brookr - Tulane University
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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

**Ha Minh Lam - Institute of Mathematics, VAST
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**Abstract:
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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
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**Time: 3:00**

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**Aram Bingham - Tulane University
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**Location:** Gibson Hall 325

**Time:** 3:00

Week of October 19 - October 15

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

**Selvi Kara - Institution
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**Location:** 400-D

**Time:** 1:30

**Rafał Komendarczyk - Tulane University
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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
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**Time:12:30**

**Franz Baumdicker - University of Freiburg
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**Abstract:
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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

**Cooper Boniece - Tulane University
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**Location: Stanley Thomas 316
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**Time: 4:30**

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Week of October 12 - October 8

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**Diego Villamizar - Tulane University
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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

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Week of October 5 - October 1

**Denys Bondar - Institution
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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

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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
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**Time: 3:00**

**Wen Yan - Simons Foundation
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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

**Nathan Bedell - Institution
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**Abstract:
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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**

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Week of September 28 - September 24

**Shilpa Khatri - Tulane University
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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

**Igor Rivin - Temple University (Host: Victor Moll)
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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

**Al Vitter - Tulane University
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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

**Matthew Junge - Duke University
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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
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**Time: 3:00**

**Dana Ferranti - Tulane University
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**Location: Stanley Thomas 316
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**Time: 4:30**

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Week of September 21 - September 17

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**Shilpa Khatri - UC Merced
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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

**Karl Hofmann - Tulane University
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**Location: Gibson Hall 325
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**Time: 3:00**

**Robyn Brooks - Tulane University
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**Abstract:** TBA

**Location: ** Stanley Thomas 316

**Time:** 4:30

**Sheila Sundaram - Pierrepont School
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**Location: Gibson Hall 325
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**Time: 3:00**

Week of September 14 - September 10

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**Tai Ha - Tulane University
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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
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**Time:** 1:30

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Week of September 7 - September 3, 2018

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