Events This Week
Week of December 6 - December 2
Friday, December 6
Applied and Computational
Topic: Persistence of single and multispecies systems in the face of environmental uncertainty
William Cuello - Rutgers
Abstract:
In this talk, I will present my work on single and multispecies coexistence in environmentally fluctuating environments. The first half of the presentation is devoted to bet-hedging, desert annuals of the Sonoran Desert. Here, I have built stochastic models to track the seed densities of ten species. I will show to what extent these species keep their seeds dormant, solely due to uncertainty in precipitation. Moreover, I will show how well species-specific yield responses to precipitation and survival rates of dormant seeds predict field-observed germination rates.
We will then focus on arbitrary multispecies systems in slightly fluctuating environments. Here, I have developed a mathematical framework in which I view the stochastic dynamics of these species’ densities as small perturbations of their deterministic dynamics (i.e. dynamics in a constant environment). In doing so, I determine the locations of stationary distributions of species, and apply stochastic results from previous literature to determine their coexistence.
These are joint works with Drs. Sebastian Schreiber (UC Davis), Andy Sih (UC Davis), Jennifer Gremer (UC Davis), Pete Trimmer (Bielefeld), and Larry Venable (Univ. of Arizona).
Location: Gibson Hall 310
Time: 3:30pm
Thursday, December 5
Colloquium
Topic: Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states
Yao Yao - Georgia Tech (Host: Zhao)
Abstract:
The aggregation-diffusion equation is a nonlocal PDE driven by two competing effects: local repulsion modeled by nonlinear diffusion, and long-range attraction modeled by nonlocal interaction. I will talk about how this equation arises in modeling the collective motion of cells, and discuss several qualitative properties of its steady states and dynamical solutions. Using continuous Steiner symmetrization techniques, we show that all steady states are radially symmetric up to a translation. (joint work with Carrillo, Hittmeir and Volzone). In a recent work, we further investigate whether they are unique within the radial class, and show that for a given mass, uniqueness/non-uniqueness of steady states are determined by the power of the degenerate diffusion, with the critical power being m = 2. (joint work with Delgadino and Yan.)
Location: Dinwiddie 102
Time: 3:30pm
Thursday, December 5
Colloquium
Topic: Analysis and combinatorics: through a number theoretic lens
Amita Malik - Rutgers University
Abstract:
The Riemann zeta function is one of the central objects in number theory, due to its close relationship with prime numbers. In this talk, we discuss this function and its connections with analysis and combinatorics. Assuming the Riemann Hypothesis (RH), it can be shown that the zeros of any fixed order derivative of the completed Riemann zeta function also lie on the critical line. However, not much is known about the vertical distribution of the zeros, even if we assume RH. The study of this distribution is the objective of the first part of the talk. For the rest of the talk, we discuss how this study can be used to obtain results about combinatorial objects such as number of restricted partitions of a positive integer. Asymptotics for the number of ordinary partitions were first studied by Hardy and Ramanujan.
Location: HE-201
Time: 1:00
Thursday, December 5
AWM
Topic: Coffee Discussion
Yao Yao - Georgia Tech
Abstract:
Coffee Discussion
Location: Stanley Thomas 404
Time: 11:30
Wednesday, December 4
Probability and Statistics
Topic: A probabilistic approach to conformal blocks and conformal bootstrap for Liouville theory.
Guillaume Remy - Columbia University
Abstract:
Liouville theory is a fundamental example of a conformal field theory (CFT) first introduced by A. Polyakov in the context of string theory. Very recently it has been rigorously constructed using a probabilistic framework. In this talk we will present work in progress to understand the integrable structure of Liouville theory via conformal blocks and the conformal bootstrap formalism of CFT using probability. We will also mention some connections with the AGT correspondence. Based on joint work with Promit Ghosal, Xin Sun, and Yi Sun.
Location: Gibson Hall 126
Time: 3:00pm
Wednesday, December 4
Colloquium
Topic: Scalable Modeling and Inference for Phylogenetics: from Interlocus Gene Conversion to Evolving Pathogens
Xiang Ji - University of California, Los Angeles
Abstract:
Advances in genome sequencing technology are generating genetic data at an ever-increasing pace. This burst of data provides opportunities to look at the underlying biological processes that generate evolutionary patterns. However, these opportunities are accompanied by both statistical and computational challenges that require scalability for both modeling with large state space and inference with large amount of sequences. In this talk, I will discuss our attempt for scalable modeling with an example of incorporating interlocus gene conversion into existing phylogenetic substitution models that previously only consider point mutations. I will then introduce our linear-time gradient algorithm and its associated scalable inference techniques with an example of inferring the branch-specific evolutionary rates of large-scale datasets of fast-evolving pathogens under a mixed-effects model. With previous approaches, these inferences would have been computationally intractable.
Location: Dinwiddie 102
Time: 2:00
Tuesday, December 3
Graduate Student Colloquium
Topic: End semester celebration
Sankhaneel Bisui - Tulane University
Abstract:
Today we will celebrate our end of this fall semester (to be appropriate last week of this semester). We will also decide the talks of spring 2020. Please come and join us and enjoy the food and drink.
Location: Stanley Thomas 316
Time: 5:00pm
Tuesday, December 3
Colloquium
Topic: Approximation of Hilbert-Kunz multiplicity
Ilya Smirnov - Stockholm University
Abstract:
An analytic singularity is given by (convergent) power series, while algebraists prefer to study polynomial equations. In 1956 Samuel bridged this gap and showed that an isolated hypersurface singularity is preserved by taking a long enough (Taylor) truncation of the defining power series. Numerous authors extended this result and it still remains a topic of active research. In particular, it is now known that isolated singularity is a necessary assumption, thus we must study a weaker question: what properties can be generally preserved by a long enough truncation?
I will present results from my joint paper with Thomas Polstra that studied this question for Hilbert-Kunz multiplicity, a number that measures severity of a singularity.
Location: Dinwiddie 102
Time: 1:00
Week of November 29 - November 26
Tuesday, November 26
Graduate Student Colloquium
Topic: A brief overview of Stationary ARMA processes and the Wold's decomposition.
Sergio Nicolas Villamarin Gomez | Tulane University
Abstract:
We will introduce the basics of Stationary and ARMA processes along with some examples and simulations. Additionally, we will present proofs of some classical results and explain the context of the Wold's decomposition.
Location: Stanley Thomas 316
Time: 5:00pm
Week of November 22 - November 18
Friday, November 22
Applied and Computational
Topic: PDE models of Active Matter
Leonid Berlyand - Penn State University
Abstract:
In this talk we attempt to demonstrate how mathematics could be helpful in the study of active matter, with the focus on active gels and cell motility.
We first discuss mathematical challenges and developments of novel mathematical tools due to out-of-equilibrium state of active matter such as active cytoskeleton gels, bacterial suspensions, etc.
Next we present three minimal PDE models of active gels: (i) phase-filed model (ii) mean curvature type free boundary model and (iii) Hele-Shaw type free boundary model. These models are designed to capture key biophysical phenomena in cell motility such as persistent & turning motion, symmetry breaking, and viscous fingering while having minimal set of parameters and variables.
Our goal is to provide theoretical understanding of the key biophysical phenomena via mathematical analysis of stability/instability and bifurcations from steady states to traveling waves. This is done by identification of key mathematical structures behind the models such as gradient coupling in phase-field model, Liouville type equation, Keller-Segel cross-diffusion, and nonlinearity due to the free boundary. We employ mathematical techniques of (i) sharp interface limit via asymptotic analysis, (ii) construction of steady states and traveling waves via Crandall-Rabinowitz bifurcation theory and (iii) topological methods such as Lerey-Schauder degree theory.
These are joint works with V. Rybalko (ILTPE, Kharkiv, Ukraine), J. Fuhrman (PSU & Mainz, Germany), M. Potomkin (PSU, USA).
Location: Location: Gibson Hall 310
Time: 3:30 pm
Friday, November 22
AMS/AWM
Topic: Anomalous Diffusion of Foreign Particles in Biological Fluids
Dr. Scott McKinley - Tulane University
Abstract:
The last twenty years have seen a revolution in tracking data of biological agents across unprecedented spatial and temporal scales. An important observation from these studies is that path trajectories of living organisms can appear random, but are often poorly described by classical Brownian motion. The analysis of this data can be controversial because practitioners tend to rely on summary statistics that can be produced by multiple, distinct stochastic process models. Furthermore, these summary statistics inappropriately compress the data, destroying details of non-Brownian characteristics that contain vital clues to mechanisms of transport and interaction. In this talk, I will describe the stochastic integro-differential equation framework we use to model this behavior and the associated statistical challenges that have arisen from recent work on the movement of foreign agents, particularly synthetic microparticle probes, in human mucus.
Location: Norman Mayer 106
Time: 2:30pm
Thursday, November 20
Colloquium
Topic: Vector Products and Division Algebras
Joerg Feldvoss - University of South Alabama (Host: Mahir Can)
Abstract:
Location: Dinwiddie 102
Time: 3:30pm
Wednesday, November 20
Algebra & Combinatorics
Topic: Cohomology of Leibniz Algebras
Joerg Feldvoss - University of South Alabama
Abstract:
Location: Dinwiddie Hall 108
Time: 3:00pm
Wednesday, November 20
Probability and Statistics
Topic: Systematic constructions of Markov duality functions
Jeffrey Kuan - Texas A&M
Abstract:
Markov duality in spin chains and exclusion processes has found a wide variety of applications throughout probability theory. We review the duality of the asymmetric simple exclusion process (ASEP) and its underlying algebraic symmetry. We then explain how the algebraic structure leads to a wide generalization of models with duality, such as higher spin exclusion processes, zero range processes, stochastic vertex models, dynamic models, and their multi-species analogues.
Location: Gibson Hall 126
Time: 3:00pm
Tuesday, November 19
Graduate Student Colloquium
Topic: A simple proof of Bell’s Inequalities
Oliver Orejola | Tulane University
Abstract:
Bell’s theorem is an important scientific result which discriminates between quantum mechanics and all theories which seem to be “common sense”. I will provide a very simple proof of Bell’s inequalities leveraging “common sense” assumptions and standard probability theory, as well as an example utilizing Bell’s inequalities demonstrating Bell’s theorem. I will also discuss the implications and ramifications of the violation of Bell’s inequalities.
Location: Stanley Thomas 316
Time: 5:00pm
Week of November 15 - November 11
Friday, November 15
Applied and Computational
Topic: Random perturbation of Hamiltonian systems and SPDEs on graphs
Guangyu Xi - University of Maryland - College Park
Abstract:
Freidlin and Wentzell studied the small random perturbation of Hamiltonian systems and showed that the limit are diffusions on the Reeb graph. Here we discuss the asymptotics of a family of stochastic reaction-diffusion-advection equations. We will present the convergence to solutions of an SPDE defined on the graph. This is a recent joint work with Sandra Cerrai
Location: Location: Gibson Hall 310
Time: 4:00 pm
Friday, November 15
Fun with Probabilities
Topic: This talk will present fundamental concepts of probability theory through “probabilistic" parlor games:
Nick Hengartner - Los Alamos National Laboratory
Abstract:
(1) How to unmask fake sequences of heads and tails.
(2) Guess the higher of two numbers with greater probability greater than 1/2
(3) A betting game with good odds
(4) How to use spaghetti to calculate pi without calculus. Hint, it is better when cooked.
(5) Guessing your magic number
This talk welcomes audience participation and is accessible to anyone curious about probability.
Before this ‘fun talk,’ the speaker will talk describe his career experiences in both academia (as a former Yale professor) and as a Research Scientist/Leader at a National Laboratory.
If you are interested in considering nonacademic career, then please join us. He has extensive experience in hiring and leading research scientists at Los Alamos and help you identify what courses and skills will help you in finding job in industry or at a research lab.
Location: Location: Gibson Hall 400D
Time: 2:00pm
Thursday, November 14
Colloquium
Topic: Sensing swarms for environmental threat reconstruction
Nick Hengartner - Los Alamos National Laboratory (Host: Hyman)
Abstract:
Aedes Aegypti, a mosquito that transmits Zika, Dengue and Chikungunya, form nearly stationary louds. One may be interested in mapping these hotspots. Suppose that humans go about their regular life with a GPS tracking their movement (ie, carry a cell phone). When they show up at a hospital, they are diagnosed with Zika, or not, and their GPS traces are downloaded.
This talk presents a framework to do a tomographic reconstruction of the hotspots. A challenge is that paths are complex. The theory of reproducing kernel Hilbert space can guide our approach. We will compute empirically the difficulty of the reconstruction and identify the "well-posed questions in this ill-posed problem".
Location: Dinwiddie 102
Time: 3:30pm
Wednesday, November 13
Probability and Statistics
Topic: Bayesian Factor Regression Analysis in Heterogeneous High-dimensional Biological Data
Alejandra Avalos Pacheco - Harvard Medical School
Abstract:
Two key challenges in modern statistical applications are the large amount of information recorded per individual, and that such data are often not collected all at once but in batches. These batch effects can be complex, causing distortions in both mean and variance. We propose a novel sparse latent factor regression model to integrate such heterogeneous data. The model provides a tool for data exploration via dimensionality reduction while correcting for a range of batch effects. We study the use of several sparse priors (local and non-local) to learn the dimension of the latent factors. Our model is fitted in a deterministic fashion by means of an EM algorithm for which we derive closed-form updates, contributing a novel scalable algorithm for non-local priors of interest beyond the immediate scope of this model. We present several examples, with a focus on bioinformatics applications. Our results show an increase in the accuracy of the dimensionality reduction, with non-local priors substantially improving the reconstruction of factor cardinality, as well as the need to account for batch effects to obtain reliable results. Our model provides a novel approach to latent factor regression that balances sparsity with sensitivity and is highly computationally efficient.
Location: Gibson Hall 126
Time: 3:00pm
Wednesday, November 13
Algebra & Combinatorics
Topic: Generic Links of Determinantal Varieties
Youngsu Kim - University of Arkansas
Abstract:
Linkage is a classical topic in algebraic geometry and commutative algebra. Fix an affine space A. We say two subschemes X, Y of A are (directly) linked if their union is a complete intersection in A while X and Y having no common component. Two linked subschemes share several properties in common. Linkage has been studied by various people, Artin-Nagata, Peskine-Szprio, Huneke-Ulrich, to name a few.
In 2014, Niu showed that if Y is a generic link of a variety X, then LCT (A, X) <= LCT (A, Y), where LCT stands for the log canonical threshold. In this talk, we show that if Y is a generic link of a determinantal variety X, then X and Y have the same log canonical threshold. This is joint work with Lance E. Miller and Wenbo Niu.
Location: Dinwiddie Hall 108
Time: 3:00pm
Tuesday, November 12
Graduate Student Colloquium
Topic: Matroids and connection to Algebraic Geometry
Sankhaneel Bisui | Tulane University
Abstract:
In this talk, I will give a basic introduction to matroids and talk about how it is related to points with special configurations known as Star-Configuration. We also see some known results about points in Star-Configuration.
Location: Stanley Thomas 316
Time: 5:00pm
Week of November 8 - November 4
Friday, October 4
Applied and Computational
Topic: Stochastic comparisons for stochastic heat equations
Le Chen - Emory University
Abstract:
Location: Location: Gibson Hall 310
Time: 3:30pm
Friday, November 8
AMS/AWM
Topic: Stranded in Linear Algebra?
Mahir Can - Tulane University
Abstract:
How many lines in 3-space, in general, intersect four given lines? To answer such questions, the 19th century mathematicians, especially Hermann Schubert, developed not only the main ideas of cohomology groups (which were made more precise later by Poincare) but also developed the theory of projective spaces, grassmannians, flag varieties, as well as the variety of complete quadrics. Although it was an important test example for the first ideas of the cohomology theories, the variety of complete quadrics was ignored (and feared) by all but a few algebraic geometers. In 1986, one my heroines, Elizabetta Strickland, managed to compute the Betti numbers of this variety. In this talk, I will tell you the tale of the complete quadrics. No background in algebraic geometry/topology is assumed.
Location: Gibson 400A
Time: 2:30pm
Thursday, November 7
Colloquium
Topic: Persistence, competition, evolution: The game of movement
Yuan Lou - Ohio State (Host: Zhao)
Abstract:
Organisms exploit resources to persist, compete with other organisms for survival, and sometimes evolve themselves to adapt to changing environment. In this talk several partial differential equation models from spatial ecology will be discussed, aiming to understand the role of movement in population dynamics. The mathematical findings, partly based on game theoretic approach, are closely related with the biological theory of ideal free distribution. The talk will be accessible to general audience.
Location: Dinwiddie 102
Time: 3:30pm
Wednesday, November 6
Probability and Statistics
Topic: Recent Advances in Statistical Inference for Stochastic PDEs
Igor Cialenco - Department of Applied Mathematics; Illinois Institute of Technology
Abstract:
In the first part of the talk we will discuss the parameter estimation problems for discretely sampled SPDEs driven by an additive space-time white noise. We will present some general results on derivation of consistent and asymptotically normal estimators based on computation of the p-variations of stochastic processes and their smooth perturbations, that consequently are conveniently applied to SPDEs. Both the drift and the volatility coefficients are estimated using two sampling schemes that use surprisingly little information: observing the solution at a fixed time and on a discrete spatial grid, and at a fixed space point and at discrete time instances of a finite interval. </p>
In the second part of the talk we will examine the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. We exploit the somewhat unusual structure of the observations coming from these equations that leads to an interesting interplay between classical and non-traditional statistical models. We derive several types of estimators for the drift and/or diffusion coefficients of these equations and prove their relevant properties. The theoretical results will be illustrated via numerical examples.
Location: Gibson Hall 126
Time: 3:00pm
Wednesday, November 6
Algebra & Combinatorics
Topic: Ramsey theory, Discrepancy Theory, Zero-Sums and Symmetric Functions
Arie Bialostocki - University of Idaho
Abstract:
Location: Dinwiddie Hall 108
Time: 3:00pm
Tuesday, October 15
Graduate Student Colloquium
Topic: Vertex Decomposability and the Graph G_k
Joseph Skelton - Tulane University
Abstract:
This will be an introduction to graph vertex decomposability, and the implications of this property for graphs on regularity. I will also discuss symbolic powers of monomial ideals, cover ideals, and the associated graph G_k first introduced by S. Fakhari in 2016.
Location: Stanley Thomas 316
Time: 5:00pm
Week of November 1 - October 28
Thursday, October 31
Colloquium
Topic: Symmetry in stationary and uniformly rotating solutions of active scalars
Javier Gómez-Serrano - Princeton (Host: Glatt-Holtz)
Abstract:
In this talk, I will discuss a Liouville type theorem for stationary or uniformly-rotating solutions of 2D Euler and other similar equations. The main question we want to address is whether every stationary/uniformly-rotating solution must be radially symmetric. Based on joint work with Jaemin Park, Jia Shi and Yao Yao.
Location: Dinwiddie 102
Time: 3:30pm
Wednesday, October 30
Probability and Statistics
Topic: Influence of media on opinion dynamics in social networks
Heather Zinn Brooks - UCLA
Abstract:
Many people rely on online social networks for news, and the spread of media content influences online discussions and impacts actions offline. To examine such phenomena, we generalize bounded-confidence models of opinion dynamics on a social network by incorporating media accounts as influencers. We quantify partisanship of content as a continuous parameter, and we present higher-dimensional generalizations to incorporate nuanced political positions and content quality (a key novel contribution of our work). We use simulations to quantify the entrainment of non-media content to the ideologies of media accounts. We maximize media impact over a social network by tuning the number of media accounts that promote the content and the number of followers per account. We find that entrainment of the ideology of content spread by non-media accounts to media ideology depends on structural features of the network. Finally, we incorporate multiple media sources with ideological biases and quality-level estimates drawn from real media sources to demonstrate that our model can produce communities that are polarized in both ideology and quality. Our model provides a step toward understanding content spreading dynamics, with ramifications mitigating the spread of undesired content.
Location: Gibson Hall 126
Time: 3:00pm
Wednesday, October 30
Algebra & Combinatorics
Topic: Decompositions of Toric Ideals of Finite Simple Graphs
Graham Keiper - McMaster University
Abstract:
I will discuss recent joint work which allows us to construct new finite simple graphs from two known ones in a specified way such that the corresponding toric ideals split. This construction more generally behaves well with respect to generators of the toric ideals of the graphs used in the construction. In some cases the technique allows us to recover the graded betti numbers of the resulting graph given that this information is known for the graphs used to construct it. I will also discuss more general results about the independence of generators of toric ideals. Finally, I hope to also discuss recent work which connects such splittings to the fundamental group of the graph.
Location: Dinwiddie Hall 108
Time: 3:00pm
Tuesday, October 29
Graduate Student Colloquium
Topic: Elusive f-Ideals
Jonathan L O'Rourke | Tulane University
Abstract:
In combinatorial commutative algebra, we may associate a squarefree monomial ideal to each of a pair of simplicial complexes, known as the non-face complex and the facet complex. An f-ideal is an ideal for which the f-vectors of these two complexes coincide. I will give the necessary background to discuss the problem of finding and enumerating f-ideals.
Location: Stanley Thomas 316
Time: 5:00pm
Week of October 25 - October 21
Thursday, October 24
Colloquium
Topic: Hypergeometric Supercongruences
Ling Long - Louisiana State University (Host: Victor Moll)
Abstract:
In this talk, we give a gentle introduction to supercongruences and the related hypergeometric objects. Then we will establish the supercongruences for the fourteen rigid Calabi--Yau threefolds, occurring as special fibers of explicit hypergeometric families. These supercongruences were conjectured by Rodriguez-Villegas.
This is a joint work with Fang-Ting Tu, Noriko Yui and Wadim Zudilin. Most of the talk is accessible to graduate students.
Location: Dinwiddie 102
Time: 3:30pm
Thursday, October 24
AWM
Topic: Coffee discussion
Ling Long - Louisiana State University
Abstract:
This is an informal meeting to have coffee and good conversation with our colloquim speaker.
Come say hi! There will be coffee and cookies! Don't forget your reusable mugs.
Here's the link to her website: https://www.math.lsu.edu/~llong/
Location: Gibson Hall, Common room 426
Time: 11:30
Wednesday, October 23
Probability and Statistics
Topic: Stochastic persistence and extinction
Alex Hening - Tufts University
Abstract:
A key question in population biology is understanding the conditions under which the species of an ecosystem persist or go extinct. Theoretical and empirical studies have shown that persistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics of n interacting species that live in a stochastic environment. Our models are described by n dimensional piecewise deterministic Markov processes. These are processes (X(t), r(t)) where the vector X denotes the density of the n species and r(t) is a finite state space process which keeps track of the environment. In any fixed environment the process follows the flow given by a system of ordinary differential equations. The randomness comes from the changes or switches in the environment, which happen at random times. We give sharp conditions under which the populations persist as well as conditions under which some populations go extinct exponentially fast. As an example we show how the random switching can `rescue' species from extinction. The talk is based on joint work with Dang H. Nguyen (University of Alabama).
Location: Gibson Hall 126
Time: 3:00pm
Wednesday, October 23
Algebra & Combinatorics
Topic: Smooth Schubert Varieties
Mahir Bilen Can - Tulane University
Abstract:
In this talk, we will discuss our proof of the sphericity of the smooth Schubert varieties. (This is a joint work with Reuven Hodges.)
Location: Dinwiddie Hall 108
Time: 3:00pm
Tuesday, October 22
Graduate Student Colloquium
Topic: Mathematics around the world
Padi Fuster | Tulane University
Abstract:
In this 'hands-on' talk we will explore the arithmetic of different numerical systems from around the world. I will also introduce the concept of ethnomathematics and the importance of reconnecting mathematics with society through culture.
Location: Stanley Thomas 316
Time: 5:00pm
Monday, October 21
Algebraic Geometry
Topic: The Classification of the Fixed-Point Orbits of the Generalized Symmetric Spaces for $\SL_2(\mathbb{F}_q)$.
Jennifer Schaefer - Dickinson College
Abstract:
In this talk, we will discuss the orbits of the fixed-point group on the generalized symmetric spaces of $\SL_2(k)$ where $k$ is a finite field. Specifically, we will provide a characterization and classification of the representatives for the maximal $k$-split and $k$-anisotropic tori. Together with earlier results classifying the orbits of the unipotent elements in these spaces, we have representatives for the orbits of the fixed-point group on the generalized symmetric space for all involutions of $\SL_2(k)$ over any finite field.
Location: Gibson Hall 126
Time: 3:00pm
Week of October 18 - October 14
Friday, October 18
Thursday, October 17
Wednesday, October 16
Tuesday, October 15
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
Tuesday, October 15
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
Tuesday, October 15
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
Tuesday, October 8
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
Friday, October 4
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
Thursday, October 3
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
Thursday, October 3
AWM Student Chapter
Topic: AWM Coffee discussion
Candice Price - University of San Diego
Abstract:
Coffee discussion
Location: Stanley Thomas 404
Time: 1:30
Wednesday, October 2
Algebra and Combinatorics
Topic: f-IDEALS, f-GRAPHS AND f-SIMPLICIAL COMPLEXES
Hasan Mahmood - GC University Lahore
Abstract:
Wednesday, October 2
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
Tuesday, October 1
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
Tuesday, October 1
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
Friday, September 27
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
Thursday, September 26
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
Thursday, September 26
AWM Student Chapter
Topic: AWM Coffee discussion
Yi Jiang - Georgia State
Abstract:
Coffee discussion
Location: Stanley Thomas 404
Time: 11:30am
Wednesday, September 25
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
Tuesday, September 24
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
Friday, September 20
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.
Friday, September 20
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
Wednesday, September 18
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
Tuesday, September 17
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
Tuesday, September 10
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
Thursday, September 5
AWM Student Chapter
Topic: Coffee Discussion
Dana Mendelson - University of Chicago
Abstract: Coffee discussion
Location: Stanley Thomas 316
Time: 1:30pm
Thursday, September 5
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
Tuesday, September 3
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