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Geometry and Topology Seminar: Jiahua Zou, Brown University, Free boundary minimal surfaces in the Euclidean three-ball close to boundary

SAS 4201

I will talk about the new construction of genus-zero free boundary minimal surfaces embedded in the unit ball in the Euclidean three-space which are compact and lie arbitrarily close to the boundary unit sphere with an arbitrarily large number of connected boundary components. The construction is by PDE gluing methods and the surfaces are desingularizations…

Algebra and Combinatorics Seminar: Jianping Pan, NC State, A bijection between K-Kohnert diagrams and reverse set-valued tableaux

SAS 2225

Lascoux polynomials are K-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux (RSVT) rule for Lascoux polynomials and reverse semistandard Young tableaux (RSSYT) rule for key polynomials. Besides, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with RSSYT. Ross and…

Differential Equations/Nonlinear Analysis Seminar: Ryan Murray, NC State, Adversarially robust classification, non-local perimeters, and geometric flows

SAS 4201

Classification is a fundamental task in data science and machine learning, and in the past ten years there have been significant improvements on classification tasks (e.g. via deep learning). However, recently there have been a number of works demonstrating that these improved algorithms can be “fooled” using specially constructed adversarial examples. In turn, there has been increased…

Applied Math Graduate Student Seminar: Abhijit Chowdhary, NC State, Computing Eigenvalue Sensitivities for Sensitivity Analysis of the Information Gain in Bayesian Linear Inverse Problems

SAS 4201

We consider sensitivity analysis of Bayesian inverse problems with respect to modeling uncertainties. To this end, we consider sensitivity analysis of the information gain, as measured by the Kullback-Leibler divergence from the posterior to the prior. This choice provides a principled approach that leverages key structures within the Bayesian inverse problem. Also, the information gain…

Numerical Analysis Seminar: Wuchen Li, University of South Carolina, Mean-Field Games for Scalable Computation and Diverse Applications

SAS 4201

Mean field games (MFGs) study strategic decision-making in large populations where individual players  interact via specific mean-field quantities. They have recently gained enormous popularity as powerful research tools with vast applications. For example, the Nash equilibrium of MFGs forms a pair of PDEs, which connects and extends variational optimal transport problems. This talk will present…

Algebra and Combinatorics Seminar: Nicholas Russoniello, Willam & Mary,

SAS 2225

Jointly in person and virtually on Zoom. SAS 2225 for in-person participation. The Zoom link is sent out to the Algebra and Combinatorics mailing list, please contact Corey Jones at cmjones6@ncsu.edu to be added.   Speaker’s webpage: https://www.wm.edu/as/mathematics/faculty-directory/russoniello_n.php

Pure Math Graduate Student Seminar: Ashley Tharp, NC State, Arcs and shards

SAS 2235

The group of permutations is the canonical example of a finite Coxeter group, and each permutation can be represented visually by a noncrossing arc diagram. Each diagram encodes the canonical join representation of its permutation, and diagrams can be used to understand lattice congruences on the weak order of type A, equivalence relations that respect the…

Applied Math Graduate Student Seminar: Alexander Mendez, NC State, Extreme Events in Natural Phenomena

SAS 4201

Extreme events are events that have an extremely low probability of occurring, but often have immense consequences. For this presentation, we focus on extreme events in climate change and wildfires. In the context of climate change, we examine the avoidance of so-called climate tipping points, which are climate regimes where small changes significantly alter the…

Numerical Analysis: Malik Hassanaly, National Renewable Energy Laboratory (NREL), Generative models and scientific sampling

Zoom

Realistic image generation has benefited from recent groundbreaking advances in the ML community. At the core of generative models lies the capability to sample high-dimensional distributions with relatively small support and a priori unknown shape. In many scientific applications, this capability is a limiting factor that has led to modeling choices that circumvent the sampling…

Geometry and Topology Seminar: Joey Zou, Northwestern, Microlocal Methods for The Elastic Travel Time Tomography Problem for Transversely Isotropic Media

Zoom

I will discuss the travel time tomography problem for elastic media in the transversely isotropic setting. The mathematical study of this problem relates to X-ray tomography and boundary rigidity problems studied by de Hoop, Stefanov, Uhlmann, Vasy, et al., which reduce the inverse problems to the microlocal analysis of certain operators obtained from a pseudolinearization…

Algebra and Combinatorics Seminar: Seth Sullivant, NC State, Maximum Agreement Subtrees

SAS 2225

BSTRctProbability distributions on the set of trees are fundamental in evolutionary biology, as models for speciation processes. These probability models for random trees have interesting mathematical features and lead to difficult questions at the boundary of combinatorics and probability. This talk will be concerned with the question of how much two random trees have in…

Differential Equations and Nonlinear Analysis Seminar: Alexei Novikov, PSU, USA, Long-time behavior of a randomly perturbed oscillator

Zoom

We consider a long-time behavior of a stochastically forced nonlinear oscillator. In a long-time limit the force converges to fractional Brownian motion, a process that has memory. In contrast, we show that the  limit of the nonlinear oscillator driven by this force converges to diffusion driven by standard (not fractional) Brownian motion, and thus retains…

Teaching and Learning Seminar: Bevin Maultsby, NC State, MATLAB Grader Workshop

SAS 4201

We will look at the brand new MATLAB Grader functionality in Moodle, featuring examples, tips and tricks, and a few drawbacks. Participants are encouraged to activate their MathWorks account first (https://www.mathworks.com/, use your Unity credentials) and bring a laptop to experiment with. If you would like to be a student in a Moodle Project space…

Colloquium: Thomas J.R. Hughes, University of Texas at Austin, The Finite Element Method and Computational Mechanics: Past, Present, and a Vision of the Future

Zoom

I will begin by probing into the past to discover the origins of the Finite Element Method (FEM), and then trace the evolution of those early developments to the present day in which the FEM is ubiquitous in science, engineering, mathematics, and medicine, and the most important discretization technology in Computational Mechanics. However, despite its…

Differential Equations and Nonlinear Analysis Seminar: Theodore D. Drivas, Stony Brook University, Remarks on the long-time dynamics of 2D Euler

Zoom

We will discuss some old and new results concerning the long-time behavior of solutions to the two-dimensional incompressible Euler equations. Specifically, we discuss whether steady states can be isolated, wandering for solutions starting nearby certain steady states, singularity formation at infinite time, and finally some results/conjectures on the infinite-time limit near and far from equilibrium.…

Symbolic Computation: Parker Edwards, University of Notre Dame, Feature Sizes and Bottlenecks for Algebraic Manifolds

SAS 4201

 In computational topology and geometry, theoretical guarantees for algorithms often take the following form: Start with a finite sample of points from a subspace of . If the sample is "dense enough" with respect to the subspace, then the algorithm outputs a quantity of interest for the subspace, for example its Betti numbers. The quantities associated…