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Algebra and Combinatorics Seminar: Radmila Sazdanovic, NC State, Categorification: knots, graphs and more

SAS 2225

Categorification is a method that has many emanations hence eludes a precise definition. Therefore, we will discuss categorification through several examples of categorifying polynomials arising from different fields of mathematics, including knots, graphs, and orthogonal polynomials. Speaker’s webpage: https://sazdanovic.wordpress.ncsu.edu/ Location: Jointly in person and virtually on Zoom. SAS 2225 for in-person participation. The Zoom link is sent out…

Differential Equations and Nonlinear Analysis Seminar: Guillaume Carlier, CEREMADE, Université Paris-Dauphine, A refined Fenchel-Young inequality and applications to optimal transport and convex duality

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In this talk, I will first present a very simple quantitative form of the Young-Fenchel inequality.  I will then discuss some applications: a short proof of the Brøndsted-Rockafellar in Hilbert spaces and a primal-dual attainment for perturbed convex minimization problems. I will finally explain how this inequality (or some generalizations) can be used for quantitative…

Graduate Training Seminar: Laura Colmenarejo, NC State, Traveling for research

SAS 4201

During this presentation we will discuss the topics like how to find interesting conferences in your field, how to apply for funding, what you should prepare before the conference, what to do while at the conference, and how to make your trip a fun and productive experience. There will be some discussion for those looking…

Pure Math Graduate Student Seminar: Francisco Ponce Carrion, Marginal Independence Models

SAS 2235

Marginal independence models have been commonly studied in the context of graphical models, where we use a graph to convey the different marginal independence relations between random variables. However, there are marginal independence relations that cannot be expressed with a graph, which is why we provide a more general framework in which we can define…

Numerical Analysis: Weiqi Chu, UCLA, Non-Markovian opinion models inspired by random walks

SAS 4201

For social networks, nodes encode social entities, such as people, twitter accounts, etc., while edges encode relationship or events between entities. Opinion dynamics model opinion evolution as dynamical processes on social networks. Traditional models of opinion dynamics consider how opinions evolve either on time-independent networks or on temporal networks with edges that follow Poisson statistics.…

Geometry and Topology Seminar: Kai Xu, Duke, Isoperimetric inequalities on closed surfaces

SAS 4201

Let Σ be a closed surface (i.e. a 2-dimensional Riemannian manifold) satisfying the following condition: the first eigenvalue of the elliptic operator -Δ+βK is nonnegative, where K is the Gauss curvature and β is a positive constant . This condition was mainly motivated by the studies of positive scalar curvature in dimension three, and soon…

Algebra and Combinatorics Seminar: Qing Zhang, Purdue, Classification of Modular Categories by Galois Orbit Count

SAS 2225

Given a modular category C, the irreducible characters of its fusion ring are in one-to-one correspondence with the set Irr(C) of isomorphism classes of simple objects of C. Consequently, the action of the absolute Galois group on these characters induces a permutation action on Irr(C). The analysis of this action is essential to the classification…

Differential Equations and Nonlinear Analysis Seminar: Marco Antonio López Cerdá, Universidad de Alicante, A survey of the subdifferential of the supremum function. Featured applications

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his talk presents various characterizations of the subdifferential of the pointwise supremum of an arbitrary family of convex functions, as well as some featured applications. Starting by the maximum generality framework, we move after to particular contexts in which some continuity and compacity assumptions are either imposed or inforced via processes of compactification of the…

Teaching and Learning Seminar: Bradley Davis, NC State, Office of Student Conduct Workshop

SAS 4201

The learning session will focus on the general operations of the Office of Student Conduct.  The presenter will discuss the key procedures associated with academic misconduct cases, including proper adjudication techniques for faculty and how to properly report cases to OSC.  The presenter will also provide best practices for promoting academic integrity in courses and how to…

Colloquium: Naihuan Jing, NC State, Quantum Linear Algebra

SAS 1102

In linear algebra we know that the Pfaffian of an antisymmetric matrix is a square root of the determinant of matrix. In this talk I will explain how one does the quantum linear algebra, a recent popular area that can be traced back to Gauss and is well connected with many areas of mathematics such as…

Symbolic Computation Seminar: Josué Tonelli Cueto, The University of Texas at San Antonio, Computing numerically the homology of semialgebraic sets

SAS 4201

Computing the homology of semialgebraic sets is a central problem in computational real algebraic geometry. However, as of today, all symbolic algorithms for this problem require still time that is doubly exponential with respect to the number of variables. The latter is so although the size of the Betti numbers is known to be singly…

Numerical Analysis Seminar: Shiying Li, UNC-Chapel Hill, Transport transforms for machine learning applications

SAS 4201

Data or patterns (e.g., signals and images) emanating from physical sensors often exhibit complicated nonlinear structures in high dimensional spaces, which post challenges in constructing effective models and interpretable machine learning algorithms.  When data is generated through deformations of certain templates, transport transforms often linearize data clusters which are non-linear in the original domain. We…

Geometry and Topology Seminar: Vladimir Medvedev, National Research University, Higher School of Economics, Moscow, On the Morse index of the critical Moebius band

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In this talk I will show that the Morse index of the critical Moebius band in the 4-dimensional Euclidean ball equals 5. This result makes use of the quartic Hopf differential technique and a comparison theorem between the index of a free boundary minimal surface in the Euclidean ball and its spectral index. The latter also enables us to reprove…

Algebra and Combinatorics Seminar: Sinan Aksoy, Pacific Northwest National Lab

SAS 2225

Speaker’s webpage: http://sinanaksoy.com/ Location: 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.

Numerical Analysis Seminar: Boaz Nadler, Weizmann Institute, Completing Large low rank Matrices with only few observed entries: A one-line algorithm with provable guarantees

SAS 4201

Suppose we observe very few entries from a large matrix. Can we predict the missing entries, say assuming the matrix is (approximately) low rank ? We describe a very simple method to solve this matrix completion problem. We show our method is able to recover matrices from very few entries and/or with ill conditioned matrices,…

Applied Math Graduate Student Seminar: Harley Hanes, NC State, Talk 1 Low-cost Quantification of Fluid Flow Parameter Sensitivity using Reduced-order Modeling, Talk 2 Convergent Uncertainty Quantification in Fluid Dynamics using Reduced-order Models and Machine Learning

SAS 4201

Talk 1: Low-cost Quantification of Fluid Flow Parameter Sensitivity using Reduced-order Modeling - Abstract 1: Sensitivity analysis for computational fluid dynamics (CFD) simulations is a complicated procedure, which still relies, in many cases, on engineering judgment and factors of safety. This is, in part, because the computational cost of quantifying the simulation's sensitivity to all…

Numerical Analysis Seminar: Yuehaw Khoo, University of Chicago, New approaches in simulation of transition paths

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Tensor method can be used for compressing high-dimensional functions arising from partial differential equations (PDE). In this talk, we focus on using these methods for the simulation of transition processes between metastable states in chemistry applications, for example in molecular dynamics. To this end, we also propose a novel generative modeling procedure using tensor-network without…

Geometry and Topology Seminar: Alec Payne, Duke University, The Structure of Shrinking Solutions to G2-Laplacian Flow

SAS 4201

In this talk, we will survey G2-structures, which are cross product structures on 7-manifolds, and we will discuss recent developments on a natural geometric flow of G2-structures called Laplacian flow. The Laplacian flow was introduced by Robert Bryant as a tool to explore the geometry of G2-structures on 7-manifolds and to construct examples of G2-holonomy…