Week of December 4 - November 30
Applied and Computational Mathematics
Topic: Conditional Sampling with Monotone GANs: Modifying Generative Models to Solve Inverse Problems
Bamdad Hosseini | California Institute of Technology
Abstract:
Generative models such as Generative Adversarial Nets (GANs), Variational Autoencoders and Normalizing Flows have been very successful in the unsupervised learning task of generating samples from a high-dimensional probability distribution from its empirical approximation. However, the task of conditioning a high-dimensional distribution from limited empirical samples has attracted less attention in the literature. In this talk we will discuss some ideas in this direction by viewing generative modelling as a measure transport problem. In particular, we present a simple recipe using block-triangular maps and monotonicity constraints that enables standard models such as the original GAN to perform conditional sampling. We demonstrate the effectiveness of our method on various examples ranging from synthetic test sets to image in-painting and function space inference in porous medium flow.
Zoom access:
Meeting ID:
Zoom meeting starts at 3:30pm
Week of November 27 - November 23
Defense
Topic: Topological Methods in Shape Reconstruction and Comparison
Sushovan Majhi’s - Tulane University
Abstract:
Most of the modern technologies at our service rely on "shapes" in some way or the other. Be it the Google Maps showing you the fastest route to your destination 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 two decades. In this defense talk, we will catch a glimpse of the provable topological methods we propose to advance the study of Euclidean shape reconstruction and comparison. We investigate how topological concepts and results---like the Vietoris-Rips and Cech complexes, Nerve Lemma, discrete Morse theory, etc---lend themselves well to the reconstruction of geodesic spaces from a noisy sample. Our study also delves into the approximation of Gromov-Hausdorff distance, which is deemed as a robust shape comparison framework. We address some of the pivotal questions and challenges pertaining to its efficient computation---particularly for Euclidean subsets. Finally, we present an approximation algorithm, with a tight approximation factor of (1+1/4), for the Gromov-Hausdorff distance on the real line.
Zoom access: Contact cwenk@tulane.edu
Time: 10:00 am
Week of November 20 - November 16
Applied and Computational Mathematics
Topic: Bayes in the time of Big Data
Andrew Holbrook | UCLA
Abstract:
Big Bayes is the computationally intensive co-application of big data and large, expressive Bayesian models for the analysis of complex phenomena in scientific inference and statistical learning. Standing as an example, Bayesian multidimensional scaling (MDS) can help scientists learn viral trajectories through space and time, but its computational burden prevents its wider use. Crucial MDS model calculations scale quadratically in the number of observations. We mitigate this limitation through massive parallelization using multi-core central processing units, instruction-level vectorization and graphics processing units (GPUs). Fitting the MDS model using Hamiltonian Monte Carlo, GPUs can deliver more than 100-fold speedups over serial calculations and thus extend Bayesian MDS to a big data setting. To illustrate, we employ Bayesian MDS to infer the rate at which different seasonal influenza virus subtypes use worldwide air traffic to spread around the globe. We examine 5392 viral sequences and their associated 14 million pairwise distances arising from the number of commercial airline seats per year between viral sampling locations. To adjust for shared evolutionary history of the viruses, we implement a phylogenetic extension to the MDS model and learn that subtype H3N2 spreads most effectively, consistent with its epidemic success relative to other seasonal influenza subtypes.
Zoom access:
Meeting ID:
Zoom meeting starts at 3:30pm
Colloquium
Topic: Julia meets Mendel: An overview of the Open-source statistical genetic analysis project, OpenMendel
Janet Sinsheimer - UCLA (Host: Xiang Ji)
Abstract:
The size and scope of modern genetic and genomic data present challenges to statistical analyses. Although gains in computing power, e.g., through cloud computing, alleviate some of the burden, better algorithmic designs are also required. The OpenMendel Project is a multidisciplinary, collaborative project of computational statisticians and genetic epidemiologists. The goal of the project is to provide reproducible analyses that scale to big data and to foster better communication between computer scientists, statisticians, human geneticists and clinicians. Using the modern computing language Julia and Jupyter notebooks, the OpenMendel Project is designed to allow researchers and students interested in genetic analysis, the ability to contribute to state-of-the-art, open-source statistical genetic software development, without being experts in computing. I will present an overview of the OpenMendel Project and then feature as examples several recently developed statistical methods development such as Iterative Hard Thresholding for genome-wide association studies (GWAS) and ordinal multinomial regression for GWAS.
Join us:
Zoom access: Contact mbrown2@math.tulane.edu
Time: 3:30
Algebra & Combinatorics
Topic: From Posets to Equivariant Group Embeddings
Mahir Can - Tulane University
Abstract:
In this talk we will introduce and discuss a class of affine equivariant embeddings of algebraic groups. More precisely, we will consider the algebraic monoid structure of an incidence algebra. Specializing to the solvable case, we will give a complete classification of the toric incidence monoids. In addition, we will discuss the automorphism groups of incidence monoids.
Time: 3:00
Week of November 13 - November 9
Applied and Computational Mathematics
Topic: symplectic geometry & classical mechanics
Tewodros Amdeberhan - Tulane University
Abstract:
In this semi-expository talk, we give a brief on classical mechanics in the Hamiltonian setting, describe it in the symplectic framework and draw out some interesting combinatorics. The discussion will be accessible to all.
Zoom access:
Meeting ID:
Zoom meeting starts at 3:30pm
AWM
Topic: Coffee Chat with Dr. Robyn Brookes and Dr. Jonathan O'Rourke
Dr. Robyn Brookes and Dr. Jonathan O'Rourke - Tulane University
Abstract:
Tomorrow, Wednesday, November 11th, AWM is hosting a very special coffee discussion with our recent graduates Dr. Robyn Brookes and Dr. Jonathan O'Rourke!
Come join us for a late evening coffee chat as they talk about their experience and answer your questions about being in the job market during the pandemic, or just come to say hi!
Join us:
Zoom access: Contact cwolfe@tulane.edu
Time: 5:30 PM Central Time (US and Canada)
Algebra and Combinatorics
Topic: Applications of tropical algebra methods - part 2
Kalina Mincheva - Tulane University
Abstract:
We present results on the properties of the algebraic objects introduced in the previous talk. We discuss the resulting analogues to classical theorems and aspects of dimension theory both for (tropical) ideals and congruences. We also describe connections to algebraic geometry via the theory of tropical schemes and ideals, focusing on recent results on tropical counterparts of vector bundles
Time: 3:00
Graduate Student Colloquium
Topic: Improved quasi-Monte Carlo methods for Integrating High Dimension Functions
Lin Li - Tulane University
Abstract:
Approximating the integral of a function in a high dimension more accurate and efficient is a challenge. We proposed several improved quasi-Monte Carlo methods for integrating high dimension functions from two different ways. First, we use the control variate method to reduce variation error. Second, we use Voronoi weight and surrogate points interpolation methods to reduce the discrepancy error. In each method, we give the error simulation with different function integration. Various methods to generate pseudo-random and quasi-random sequences are implemented to compare the different methods.
Zoom ID: 921 8978 2555
Time: 5:00pm
Week of November 6 - November 2
Applied and Computational Mathematics
Topic: Statistical Inference for a Partially Observed Interacting System of Hawkes Processes
Chenguang Liu - University of Paris
Abstract:
In this talk, we will first see a brief introduction of Hawkes processes and their applications. Then we will discuss the main model of this talk, Hawkes process with random connection graph. More precisely, we will deal with the estimation of the common probability of connection between edges within a directed graph describing the non-zero components of the fertility matrix of a multivariate Hawkes process. Finally, we will see the asymptotic behavior of this estimator when the number of nodes in the graph, the number of observed nodes and the observation time length tend to infinity.
Zoom access:
Meeting ID:
Zoom meeting starts at 3:30pm
AWM
Topic: Coffee Chat with Dr. Mincheva
Kalina Mincheva - Tulane University
Abstract:
This week, Wednesday October 28th, Dr. Mincheva will be kicking off the Algebra & Combinatorics seminar. After her talk, AWM will be hosting a virtual coffee chat to get to know our newest faculty member. Please stop by to give her a warm welcome!
Join us:
Zoom access: Contact cwolfe@tulane.edu
Time: 4:10 PM Central Time (US and Canada)
Algebra and Combinatorics
Topic: Overview of tropical algebra and geometry - part 1
Kalina Mincheva - Tulane University
Abstract:
In this talk we will give an overview of the field of tropical mathematics. Tropical geometry provides a new set of purely combinatorial tools to approach classical problems in algebraic geometry. The fundamental objects in tropical geometry are tropical varieties -- combinatorial ``shadows" associated to more traditional geometric objects, algebraic varieties. Until recently, the theory has focused on the geometric aspects of tropical varieties as opposed to the underlying algebra, largely due the lack of tropical analogues to commutative algebra tools. In the talk we will discuss various limitations of the approach which we try to overcome using tropical algebra methods. We will also point out some of the inherent difficulties in working with an idempotent (tropical) algebra and will introduce algebraic objects that carry geometric information.
Recording: https://tulane.zoom.us/rec/share/nNY1kcs2F5l3oUIGFITKSUiOWPEEME_V8vPHbmW...
Time: 3:00
Week of October 30 - October 26
AWM
Topic: Coffee Chat with Dr. Mincheva
Kalina Mincheva - Tulane University
Abstract:
This week, Wednesday October 28th, Dr. Mincheva will be kicking off the Algebra & Combinatorics seminar. After her talk, AWM will be hosting a virtual coffee chat to get to know our newest faculty member. Please stop by to give her a warm welcome!
Join us:
Zoom access: Contact cwolfe@tulane.edu
Time: 4:10 PM Central Time (US and Canada)
Algebra and Combinatorics
Topic: Overview of tropical algebra and geometry - part 1
Kalina Mincheva - Tulane University
Abstract:
In this talk we will give an overview of the field of tropical mathematics. Tropical geometry provides a new set of purely combinatorial tools to approach classical problems in algebraic geometry. The fundamental objects in tropical geometry are tropical varieties -- combinatorial ``shadows" associated to more traditional geometric objects, algebraic varieties. Until recently, the theory has focused on the geometric aspects of tropical varieties as opposed to the underlying algebra, largely due the lack of tropical analogues to commutative algebra tools. In the talk we will discuss various limitations of the approach which we try to overcome using tropical algebra methods. We will also point out some of the inherent difficulties in working with an idempotent (tropical) algebra and will introduce algebraic objects that carry geometric information.
Join us:
Zoom access: TBA
Time: 3:00
Graduate Student Colloquium
Topic: Mathematical Models for Biochemical Oscillation
Sang-Eun Lee - Tulane University
Abstract:
In this talk, we discuss what is mathematical modelling and how to derive the models for biochemical oscillation. If the time permits, we may discuss circadian rhythms.
Zoom ID: 921 8978 2555
Time: 5:00pm
Week of October 23 - October 19
Colloquium
Topic: Tackling epidemics and pandemics using mathematical, statistical, and computational modeling tools
Gerardo Chowell - Georgia State University (Host: James Hyman)
Abstract:
Mathematical, statistical, and computational modeling tools can clarify infectious disease transmission. These models have helped unravel the epidemiology's complexity, forecast the disease spread, and predict the impact of control interventions. I will describe our models for the recent Ebola virus disease epidemic in the Democratic Republic of Congo and the current COVID-19 pandemic. We used individual-level transmission models for the Congo Ebola epidemic to gain insight into the role that ring and community vaccination strategies had on epidemic control. I will then describe how we are applying our new models for short-term forecasts of the COVID-19 pandemic. The regional and global 20-day ahead incidence forecasts of COVID-19 from these models are updated each week to inform public health efforts worldwide (https://publichealth.gsu.edu/research/coronavirus/).
Join us:
Zoom access: Contact mbrown2@math.tulane.edu
Time: 3:30
Week of October 16 - October 12
Applied and Computational Mathematics
Topic: Scalable Bayesian Phylogenetics with Hamiltonian Monte Carlo
Alex Fisher - UCLA
Abstract:
Relaxed random walk (RRW) models of trait evolution introduce branch-specific rate multipliers to modulate the variance of a standard Brownian diffusion process along a phylogeny and more accurately model overdispersed biological data. Increased taxonomic sampling challenges inference under RRWs as the number of unknown parameters grows with the number of taxa. To solve this problem, we present a scalable method to efficiently fit RRWs and infer this branch-specific variation in a Bayesian framework. We develop a Hamiltonian Monte Carlo (HMC) sampler to approximate the high-dimensional, correlated posterior that exploits a closed-form evaluation of the gradient of the trait data log-likelihood with respect to all branch-rate multipliers simultaneously. Our gradient calculation achieves computational complexity that scales only linearly with the number of taxa under study. We compare the efficiency of our HMC sampler to the previously standard univariable Metropolis-Hastings approach while studying the spatial emergence of the West Nile virus in North America in the early 2000s. Our method achieves at least a 6-fold speed-increase over the univariable approach. Additionally, we demonstrate the scalability of our method by applying the RRW to study the correlation between five mammalian life history traits in a phylogenetic tree with 3650 tips.
Zoom access:
https://tulane.zoom.us/j/97005659934?pwd=bHltdW5wSkc1dnNVRkN1WGVJVkZVdz09
Meeting ID: 970 0565 9934
Passcode: 797272
Zoom meeting starts at 2:30pm for informal chatting with the speaker, then the talk starts at 3:00pm. Dr. Xiang Ji will be hosting the seminar.
Graduate Student Colloquium
Topic: Expected Sum Negativity Over Random Quantum States
Victor Bankston - Tulane University
Abstract:
The Sum Negativity is a property of a quantum state, which can be considered as a computational resource. We calculate the expected value of the Sum Negativity over random quantum states, drawn from the unique distribution on pure states which is invariant under unitary transformations.
Zoom ID: 921 8978 2555
Time: 5:00pm
Week of October 9 - October 5
Colloquium
Topic: "A new approach to Wallis’ integral"
Victor Moll - Tulane University
Abstract:
The theory of differentiation is based on a small number of well-defined rules. Given a class of special functions, it is possible to use these rules to obtain all derivatives of the functions in
the class. On the other hand, there is no universal algorithm for integration. It is a priori unclear why the integral of Exp(-x^2) is difficult to obtain.
The talk will present a new algorithm developed in the context of integrals coming from Feynman diagrams. It consists of a small number of rules that, up to now, has produced a large number of evaluations. Most of these rules are heuristics. The analysis and proofs related to them are open questions. The method will be illustrated with Wallis’ integral, one of the first examples of a closed-evaluation.
The talk will also include interesting mathematical questions that have appeared in our study of definite integrals.
Join us for:
1. 2:30-3:10pm: “Tea with the speaker.” Informal conversation and get to know the speaker, https://tulane.zoom.us/j/99206971883
2. 3:30-4:30pm: Colloquium. Title and abstract are given below, https://tulane.zoom.us/j/99206971883
Graduate Student Colloquium
Topic: What's Your Communication Style? Communicating Mathematics
Will Tran - Tulane University
Abstract:
In this interactive math-adjacent leadership training activity, we will assess and evaluate your personal communication style. We will see applications of communication style when communicating mathematics. Finally, we will learn about how to flex our communication style to get what we want when working with students, other T.A.s, and professors.
Zoom ID: 921 8978 2555
Time: 5:00pm
Week of October 2 - September 28
Graduate Student Colloquium
Topic: An Introduction to Lie Groups from a Geometric Perspective
Fernando Morera - Tulane University
Abstract:
Throughout this talk I am going to build a naive path from differential geometry to the definition of a Lie group. I will provide several examples as well as an intuition behind foundational definitions and propositions.
Zoom ID: 921 8978 2555
Time: 5:00pm
Week of September 21 - September 25
Graduate Student Colloquium
Topic: So... everything is a signal?
Sergio Villamarin - Tulane University
Abstract:
In this very introductory talk I'll go over classical signal processing from a math perspective, I'll try to present some of the technical terms that show up and explain their importance from a mathematical perspective. Finally, I'll illustrate an application of some signal processing tools in seismology and some cute graphs from a current project I have been working at.
Zoom ID: 921 8978 2555
Time: 5:00pm
Research Seminar Name
Topic: Title
Speaker - Institution
Abstract:
TBA
Location: TBA
Time: TBA