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Seminar: Papri Dey, Georgia Institute of Technology, Hyperbolic Polynomials in Combinatorics and Optimization

SAS 4201

 Hyperbolic polynomials are coordinate free generalization to the notion of real rooted polynomials. A special class of hyperbolic polynomials are determinantal polynomials and they bound spectrahedra, feasible sets of semidefinite programming. I shall discuss some techniques of real algebraic geometry to deal with convex semialgebraic sets such as spectrahedra, and  demonstrate the applications of hyperbolic…

Seminar: Nadejda Drenska, Johns Hopkins University, A PDE Interpretation of Prediction with Expert Advice

SAS 4201

We study the problem of prediction of binary sequences with expert advice in the online setting, which is a classic example of online machine learning. We interpret the binary sequence as the price history of a stock, and view the predictor as an investor, which converts the problem into a stock prediction problem. In this framework, an investor, who predicts the daily…

Seminar: Anna Weigandt, MIT, Combinatorial Aspects of Determinantal Varieties

SAS 4201

Schubert calculus has its origins in enumerative questions asked by the geometers of the 19th century, such as “how many lines meet four fixed lines in three-space?”  These problems can be recast as questions about the structure of cohomology rings of geometric spaces such as flag varieties.  Borel’s isomorphism identifies the cohomology of the complete…

Seminar: Jacob Matherne, University of Bonn and Max Planck Institute for Mathematics, Germany, Polynomials in combinatorics and representation theory

SAS 4201

Many polynomials in combinatorics (and in other areas of mathematics) have nice properties such as having all of their roots being real numbers, or having all of their coefficients being nonnegative.  By surveying recent advances in the Hodge theory of matroids (namely, the nonnegativity of Kazhdan-Lusztig polynomials of matroids and Dowling and Wilson's top-heavy conjecture…

Financial Mathematics Seminar: Jean-Perre Fouque, University of California, Santa Barbara, Reinforcement Learning Algorithm for Mixed Mean Field Control Games

Park Shops 200

We present a new combined Mean Field Control Game (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between the groups. Within each group the players coordinate their strategies. An example of such a situation is a modification of the classical trader's problem. Groups…

Pure Math Graduate Student Seminar: Jack Reever, A 2-parameter family of helicoidal surfaces

SAS 2102

Of course, anybody can deform a surface in whatever way they want. However, is there a way to deform a surface of revolution into a helicoid while preserving an isometry? How many ways are there? All these questions and more will be answered on Monday, February 13. Zoom Meeting link:  https://ncsu.zoom.us/j/92762214990?pwd=MnA1TnNVQUpzUlo3cTM5RmlNWVF4Zz09      Password: noodle

Pure Math Graduate Student Math Seminar: Andrew Shedlock, A smooth two Parameter Family of Geodesically Equivalent Metrics

SAS 2102

In Riemannian geometry, given a Riemannian manifold (M,g) one can use geodesics associated with (M,g) to determine information about the shortest distance between points, curvature, triangles on a manifold and Euler characteristic of the space of M in special cases. Thankfully, given a metric on a manifold, we can always determine geodesics on said manifold.…

Applied Mathematics Graduate Student Association Seminar: William Anderson, Fast and Scalable Computation of Reduced-Order Nonlinear Solutions for PDEs, Abhijit Chowdhary, Sensitivity Analysis of the Information Gain in Infinite-Dimensional Bayesian Linear Inverse Problems

SAS 4201

- Presenter: William Anderson - Title: Fast and Scalable Computation of Reduced-Order Nonlinear Solutions for PDEs - Abstract: We develop a method for fast and scalable computation of reduced-order nonlinear solutions (RONS). RONS is a framework to build reduced-order models for time-dependent partial differential equations (PDEs), where the reduced-order solution depends nonlinearly on time-varying parameters. With…

Pure Math Graduate Student Seminar: Daniel Profili, NC State, Eigenvalue configurations for real symmetric matrices

SAS 2102

Real symmetric matrices appear in a wide range of disciplines. One geometric problem that can be asked of two real symmetric matrices is: how are their eigenvalues arranged on the real line? Can we characterize all matrices whose eigenvalues realize a certain arrangement? In this talk, we will use principles from basic algebraic geometry and…

Pure Math Graduate Student Seminar: Kylan Schatz, NC State, Fusion Rules for G-crossed Extensions of Modular Categories

SAS 2102

Determining the fusion coefficients for an abstract fusion category is very difficult, and generalizes the problem of plethysm for group representations. As is the case in finite groups, restricting the class of objects we consider can help us to obtain better general results. When one has a group acting on a modular category, it is possible to…

Numerical Analysis Seminar: Deep Ray, The University of Maryland, VarMiON: A variationally mimetic operator network

SAS 4201

Operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions and boundary data to the solution of a PDE, i.e., they learn the solution operator of the PDE. In this talk, we consider a new type…

Numerical Analysis Seminar: Deep Ray, University of Maryland, College Park, VarMiON: A variationally mimetic operator network

SAS 4201

Operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions and boundary data to the solution of a PDE, i.e., they learn the solution operator of the PDE. In this talk, we consider a new type…

Triangle Topology Seminar: Nur Saglam, Georgia Tech , Fillability of Contact Structures on the 3-manifolds obtained by surgeries on the trefoil knot

SAS 4201

Let M be the 3-manifold obtained by r-surgery on the right handed trefoil knot. Classification of contact structures on such manifolds have been mostly understood for r\geq 1 and r=0. Etnyre-Min-Tosun has an upcoming work on the classification of the tight contact structures for all r. The fillability of contact structures on M is mostly understood if r is not…

Differential Equations and Nonlinear Analysis Seminar: Ayman Rimah Said, Duke University, Logarithmic spirals in 2d perfect fluids

SAS 4201

In this talk I will present recent results with In-Jeong from Seoul national university where we study logarithmic spiraling solutions to the 2d incompressible Euler equations which solve a nonlinear transport system on $\mathbb{S}$. We show that this system is locally well-posed in $L^p, p\geq 1$ as well as for atomic measures, that is logarithmic…