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…
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…
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…
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
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.…
- 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…
Advisor Kevin Flores, contact for Zoom access.
Advisor is Tye Lidman.
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…
Pierre Gremaud, contact for Zoom access
Ricky Liu, contact for zoom access.
Lorena Bociu, contact for zoom access.
Advisor is Radmila Sazdanovic
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…
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…
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…
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…
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…
When studying Tensor Categories we want to understand what algebra objects can be found in those categories. After finding such objects it's natural to consider their A -modules and more importantly the category of A (bi)-modules. This talk will attempt to explain this concept and enlighten listeners with motivating examples. Zoom Meeting link: https://ncsu.zoom.us/j/92762214990?pwd=MnA1TnNVQUpzUlo3cTM5RmlNWVF4Zz09 Password:…
Deep learning method has emerged as a competitive mesh-free method for solving partial differential equations (PDEs). The idea is to represent solutions of PDEs by neural networks to take advantage of the rich expressiveness of neural networks representation. In this talk, we will explore the applicability of this powerful framework to the kinetic equation, which…