**Week of October 18 - October 14**

Graduate Student Colloquium

**Topic:** *We will present context and the key ideas from the proof of the Sensitivity Theorem.*

**Victor Bankston - Tulane University**

**Abstract: **

We will present context and the key ideas from the proof of the Sensitivity Theorem.

**Location:** Stanley Thomas 316**Time:** 5:00pm

Special Colloquium

**Topic:** *Waves and solitons: the case of a Korteweg-de Vries solitonic gas*

**Manuela Girotti - Colorado State (Host: Victor Moll)**

**Abstract:**

N. Zabusky coined the word "soliton" in 1965 to describe a curious feature he and M. Kruskal observed in their numerical simulations of the initial-value problem for a simple nonlinear PDE.The first part of this talk will be a broad introduction to the theory of solitons/solitary waves and integrable PDEs (the KdV equation in particular), describing classical results in the field. The second part will focus on some new developments and growing interest into a special case of solitons defined as "solitonic gas" or "integrable turbulence". In particular, I will talk about a recent work where we want to study the asymptotic behaviour (for large time and for large space parameter) of such type of solitons. We will achieve our results by first framing the problem in the setting of a Riemann--Hilbert problem and then by rigorously analyzing it using the powerful technique of nonlinear steepest descent.

**Location: **Hebert Hall 201**Time: **3:30pm

AWM Student Chapter

**Topic:**** ***AWM Coffee discussion*

**Manuela Girotti **-** Colorado State University**

**Abstract:**

Coffee discussion

**Location:** Stanley Thomas 404 (Conference room)**Time:** 10:00-11:00

**Week of October 11 - October 7**

Graduate Student Colloquium

**Topic:** *Shape Reconstruction and Comparison*

**Sushovan Majhi - Tulane University**

**Abstract: **

Most of the modern technologies at our service rely on "shapes" in some way or other. Be it the Google Maps showing you the fastest route to your destination eluding a crash or the 3D printer on your desk creating an exact replica of a relic; shapes are being repeatedly sampled, reconstructed, and compared by intelligent machines. With the advent of modern sampling technologies, shape reconstruction and comparison techniques have matured profoundly over the last decade.

We will eat pizza and talk about the topological techniques we developed for reconstruction and comparison of Euclidean shapes. We will also demonstrate the software that implements our algorithm.

**Location:** Stanley Thomas 316**Time:** 5:00pm

**Week of October 4 - September 30**

Applied and Computational

**Topic:** *Probabilistic global flow for energy-supercritical PDE*

**Mouhamadou Sy - University of Virginia**

**Abstract:**

Global wellposedness for energy-supercritical Schrödinger (and Wave) equations is an important open problem in the dispersive PDE field. The well-known probabilistic alternatives (Gibbs measures theory or Fluctuation-dissipation) come across hight difficulties when applied to these equations. In this talk, I will present a combination of these two probabilistic methods in order to construct a global probabilistic flow for the energy-supercritical NLS. If the time permits, I will sketch the application of that approach to the 3D Euler equations.

**Location: **Location: Gibson Hall 310**Time: **3:30pm

Colloquium

**Topic:** *The Sumner-Ernst Tangle Model: An Application of Topology to BioChemistry*

**Candice Price - University of San Diego (Host: Victor Moll)**

**Abstract:**

The tangle model was developed in the 1980’s by professors DeWitt Sumner and Claus Ernst. This model uses the mathematics of tangles to model protein-DNA binding. An n-string tangle is a pair (B,t) where B is a 3-dimensional ball and t is a collection of n non-intersecting curves properly embedded in B. N-string tangles are formed by placing 2n points on the boundary of B, and attaching n non-intersecting curves inside B. Tangles, like knots and links, are studied through their diagrams. In this model for protein-DNA interaction, one is required to solve simultaneous equations for unknown tangles when the product of these interactions are DNA knots and links. This discussion will give a review of the tangle model and will include important biological and mathematical definitions.

**Location: **Dinwiddie 102**Time: **3:30pm

AWM Student Chapter

**Topic:**** ***AWM Coffee discussion*

**Candice Price **-** University of San Diego**

**Abstract:**

Coffee discussion

**Location:** Stanley Thomas 404**Time:** 1:30

Algebra and Combinatorics

**Topic:** *f-IDEALS, f-GRAPHS AND f-SIMPLICIAL COMPLEXES*

**Hasan Mahmood - GC University Lahore**

**Abstract: **

Seminars: Probability and Statistics

**Topic:** * Landscape configuration drives persistent spatial patterns of occupant distributions*

**Elizabeth Hamman - Tulane, Mathematics**

**Abstract: **

Variation in the density of organisms among habitat patches is often attributed to variation in inherent patch properties. For example, higher quality patches might have higher densities because they attract more colonists or confer better post-colonization survival.

However, variation in occupant density can also be driven by landscape configuration if neighboring patches draw potential colonists away from the focal habitat (a phenomenon we call propagule redirection).

Here, we develop and analyze a stochastic model to quantify the role of landscape configuration and propagule redirection on occupant density patterns. We model a system with a dispersive larval stage and a sedentary adult stage. The model includes sensing and decision-making in the colonization stage and density-dependent mortality (a proxy for patch quality) in the post-colonization stage.

This investigation of how landscape variation can drive spatial patterns in the populations of occupants set the stage for our forthcoming work, where we study how the spatial distribution of the occupants can in turn affect the shape of the landscape itself.

**Location:** Gibson Hall 126**Time:** 3:00pm

Graduate Student Colloquium

**Topic:** Getting a handle on the derivation of the Navier-Stokes equations

**Dana Ferranti - Tulane University**

**Abstract: **

In applied mathematics, there is always some distance between what the mathematician cares about and what a person directly involved in the field cares about. For example, an applied mathematician may care about existence/uniqueness of solutions of a differential equation but may have no interest in understanding the derivation of the differential equation itself. Because of this difference, I have found few satisfying derivations of the Navier-Stokes equations in mathematical fluid dynamics books. In this talk, I will explain in simple terms the key ideas necessary in understanding where these equations come from. In particular, I will discuss the Cauchy stress tensor and the assumptions underlying the constitutive equations for viscous fluid flow.

**Location:** Stanley Thomas 316**Time:** 5:00pm

**Dissertation Defense**

**Topic:** *Stability of the center of the symplectic group rings*

**Safak Ozden - Tulane University**

**Abstract:**

**Location:** Stanley Thomas 316**Time:** 11:00

**Week of September 27 - 23**

Applied and Computational

**Topic:** *Mapping TASEP back in time*

**Leonid Petrov - University of Virginia**

**Abstract:**

We obtain a new relation between the distributions μ_t at different times t ≥ 0 of the continuous-time TASEP (Totally Asymmetric Simple Exclusion Process) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions μ_t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a ver- sion of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving μ_t which in turn brings new identities for expectations with respect to μ_t. Based on a joint work with Axel Saenz.

**Location: **Location: Gibson Hall 310**Time: **3:30pm

Colloquium

**Topic:** *Using Mathematical Models to Understand Collective Cancer Invasion*

**Yi Jiang - Georgia State (Host: James Hyman)**

**Abstract:**

A major reason for cancer treatment failure and disease progression is the heterogeneous composition of tumor cells at the genetic, epigenetic, and phenotypic levels. While tremendous efforts have tried to characterize the makeups of single cells, much less is known about interactions between heterogeneous cancer cells and between cancer cells and the microenvironment in the context of cancer invasion. Clinical studies show that cancer invasion predominantly occurs via collective invasion packs, which invade more aggressively and result in worse outcomes. Using non-small cell lung cancer spheroids, we show that the invasion packs consist of leaders and followers. In vitro and in silico experiments show that leaders and followers engage in mutualistic social interactions during collective invasion. Many fundamental questions remain: What is the division of labor within the heterogeneous invasion pack? How does the leader phenotype emerge? Are phenotypes plastic? How do the invasion packs interact with the stroma? Can the social interaction network be exploited to devise novel treatment strategies? I will present the recent experimental and modeling efforts that try to address these questions. I will try to convince you that analyzing this social interaction network can potentially reveal the ‘weak-links’, which when perturbed can disrupt collective invasion and potentially prevent malignant progression of cancer.

**Location: **Dinwiddie 102**Time: **3:30pm

AWM Student Chapter

**Topic:**** ***AWM Coffee discussion*

**Yi Jiang - **Georgia State

**Abstract:**

Coffee discussion

**Location:** Stanley Thomas 404**Time:** 11:30am

Algebra and Combinatorics

**Topic:** The Group Algebra of a Compact Group and Tannaka Duality for Compact Groups

**Karl Hoffmann - Tulane University**

**Abstract: **

In the preparation of the 4th edition of the text- and handbook \The Structure of

Compact Groups" (de Gruyter, Berlin-Boston, 1998, 2007, and 2013), Sidney A.

Morris and I decided to include the Tannaka-Hochschild Duality Theorem which

says that the category of compact groups is dual to the category of real reductive

Hopf algebras.

In the lecture I hope to explain why this theorem was not featured in the preceding

3 editions and why we decided to present it now.

Our deliberations led us into a new theory of group algebras for compact groups

on which I reported in this seminar in March. I shall review the essential aspects

of the previous seminar and include some new ones now. One major theorem was

not available yet in March; it describes rather precisely the algebra structure of

the group algebra K[G] of the compact group G over the elds K = R and K = C.

(This result will appear in \On Weakly Complete Group Algebras of Compact

Groups," J. of Lie Theory 29 (2019), 18 pp., with Linus Kramer.)

TBA

**Location:** Dinwiddie Hall 108**Time:** 3:00pm

Graduate Student Colloquium

**Topic:** Quantum Computing: Teleportation, Zombie Cats, and Spooky Action at a Distance

**Zachary Bradshaw - Tulane University**

**Abstract: **

Quantum computing is a computation model that abuses the properties of superposition and entanglement in quantum mechanics, often making it possible to construct algorithms which solve problems faster than a classical computer can. One example of this is Shor’s algorithm, which theoretically factors integers much faster than any known classical algorithm. If a quantum computer capable of implementing Shor’s algorithm is ever built, it will break much of modern encryption. In this talk, I attempt to demystify quantum computing, starting from Schrödinger’s cat and quantum entanglement, which Einstein called “Spooky action at a distance”, and ending with an interesting example referred to as, “Quantum teleportation”.

**Location:** Stanley Thomas 316**Time:** 5:00pm

**Week of September 20 - 16**

**Applied and Computational **

**Topic:** *A minimal model of the hydrodynamical coupling of flagella on a spherical body*

**Karin Leiderman - Colorado school of Mines**

**Abstract:**

Flagella are hair-like appendages attached to microorganisms that allow the organisms to traverse their fluid environment. The algae Volvox are spherical swimmers with thousands of individual flagella on their surface that coordinate in a way that is not fully understood. In this work, we have extended a previously developed minimal model of flagella synchronization on a plane to examine synchronization on the outer surface of a sphere. Each beating flagella tip is modelled as a small rotating sphere, elastically attached to a point just above the spherical surface and a regularized image system for Stokes flow outside of a sphere is used to enforce the no-slip condition. Biologically relevant distributions of rotors results in a rapidly developing and robust symplectic metachronal wave traveling from the anterior to the posterior of the spherical Volvox body.

**AMS/AWM **

**Topic:** *What you have to know to compute integrals*

**Victor Moll - Tulane University**

**Abstract:**

This talk will discuss several questions that have appeared in our goal to obtain closed-form expressions for definite integrals. Examples will include some recurrences and an interesting dynamical system.

**Location:** Gibson 400A**Time:** 2:30pm

**Algebra & Combinatorics**

**Topic: ** *Fiber invariants of projective morphisms and regularity of powers of ideals*

**Tai Ha - Tulane University**

**Abstract:**

We introduce an invariant, associated to a coherent sheaf of graded modules over a projective morphism of schemes, which controls when sheaf cohomology can be passed through the given morphism. We then use this invariant to estimate the stability indexes of the regularity and a*-invariant of powers of homogeneous ideals. This is a joint work with Sankhaneel Bisui and Abu Thomas.

**Location:** Dinwiddie Hall 108**Time:** 3:00PM

**Graduate Student Colloquium**

**Topic: ** *How to Give a (good) Math Talk*

**Robyn Brooks - Tulane University**

**Abstract:**

Giving a research talk is an important part of any mathematics career, but preparing a good math talk can be daunting. In this colloquium, we will discuss what exactly makes a talk “good”. I will also give suggestions and tips on how to best prepare, practice, and execute a good math talk.

**Location:** Stanley Thomas 316**Time:** 5:00pm

**Week of September 13 - 9**

**Graduate Student Colloquium**

**Topic: ** *MTW Sums*

**Kristina Vandusen - Tulane University**

**Abstract:**

Mordell-Tornheim-Witten sums are an interesting extension of the Riemann zeta function which appears in the evaluation of log gamma integrals. In this talk, I will give an overview of MTW sums and their special cases, and some relations of MTW sums to other known special functions.

**Location:** Stanley Thomas 316**Time:** 5:00pm

**Week of September 6 - 3**

AWM Student Chapter

**Topic:**** ***Coffee Discussion*

**Dana Mendelson - University of Chicago**

**Abstract:** Coffee discussion

**Location:** Stanley Thomas 316**Time:** 1:30pm

Colloquium

**Topic:** *Probabilistic methods for nonlinear dispersive PDEs*

**Dana Mendelson - University of Chicago (Host: Fauci, Lisa and Glatt-Holtz)**

**Abstract:**

Nonlinear dispersive equations model wave propagation phenomena for many physical systems, from water waves to quantum gases. For the last few decades, research on these equations has centered around questions on the existence of solutions, their long time behavior, and the possibility of singularity formation. Fundamental progress has been made in many settings, yet in some regimes, the nonlinear interactions overwhelm the dispersion of the waves, and standard methods break down.

In recent years, probabilistic tools have been instrumental in analyzing the behavior of these equations in previously inaccessible regimes. This approach, which goes back to the seminal work of Bourgain in the 90s on invariant Gibbs measures for Hamiltonian PDEs, has opened the door to new and exciting questions in a variety of settings. In this talk, we will give a general overview of the progress in this area and discuss some of the topics of current research.

**Location: **Stanley Thomas 316**Time: **3:30pm

Graduate Student Colloquium

**Topic:** *Counting Lattice Points in Reflexive Polygons*

**Corey Wolfe - Tulane University**

**Abstract:**

The study of toric varieties contains elegant theorems and deep connections with polytopes, polyhedra, combinatorics, commutative algebra, symplectic geometry, and topology. In this talk, we explore one of those connections mysteriously relating the number of lattice points lying on the boundary of a reflexive polygon and the number of lattice points lying on the boundary of its dual to the number 12. Using the cohomology theory of sheaves on toric surfaces, we hope to demystify the appearance of the number 12.

**Location:** Stanley Thomas 316**Time:** 5:00pm