Given a link diagram L, one can apply a Skein relation to each crossing to yield a cube of resolutions. These skein relations come from the braiding in the category of Uq(sln) representations. When n2, we have the Khovanov cube of resolutions with edge maps defined by (co)pants conordisms. We may then apply a smooth…
In many modeling applications, the analytical structure of fundamental solutions to associated mathematical problems can be exploited to develop more efficient or robust numerical algorithms. I will present several examples of such approaches and techniques based on integral representations arising in the continuum modeling of materials. Some techniques to be discussed include asymptotic analysis, exploiting…
Integer matrices are often characterized by the lattice of combinations of their rows or columns. This is captured nicely by the Smith canonical form, a diagonal matrix of invariant factors, to which any integer matrix can be transformed through left and right multiplication by unimodular matrices. Algorithms for computing Smith forms have seen dramatic improvements…
Come relax with some free ice cream and AWM at our end of the year ice cream social! We will also be electing officers for next year at this event.
We associate to any quiver a family of symmetric functions, defined by creation operators which are generalizations of Jing's creation operators. For the cyclic quiver the coefficient polynomials were studied by Finkelberg and Ionov. Shoji has recently shown that the single variable specialization of the Finkelberg-Ionov polynomials agree with polynomials he studied in relation to…
This semester, the Duke University AMS and SIAM graduate student chapters will host the biannual Triangle Area Graduate Mathematics Conference (TAGMaC). The event will occur on Sunday April 23 in the Duke Physics Building. The plenary speaker will be new UNC Professor Dave Rose. The organizers are Hangjie Ji, Sarah Ritchey, Shan Shan, and Dmitry…
Multivalued matrix functions arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making…
Please join us for our last weekly brown bag lunch of the year! You bring your lunch, and we will bring a delicious treat. Everyone (not just women) is welcome to join or stop by for as long as they can!
Abstract: https://www.samsi.info/higham-lec Directions: https://www.samsi.info/for-visitors/directions-and-maps/
1. Ephraim Bililign Title: Measuring the temperature of granular systems Abstract: Granular systems, or collections of athermal mesoscale particles, are immune to temperature in the conventional sense. Thus, to describe the behavior of an jammed assortment of grains, we turn to a modified thermodynamics built on forces and volumes. I will discuss the experimental measurements…
In this talk, I will first introduce the Monge-Ampere eigenvalue problem on general bounded convex domains and related analysis. Then I will discuss the recent resolution, in joint work with Ovidiu Savin, of global smoothness of the eigenfunctions of the Monge-Ampere operator on smooth, bounded and uniformly convex domains in all dimensions. A key ingredient…
1. Beverly Setzer Title: Detecting Hidden Nodes in Neuronal Networks using Adaptive Filtering Abstract: The identification of network connectivity from noisy time series is of great interest in the study of network dynamics. This connectivity estimation problem becomes more complicated when we consider the possibility of hidden nodes within the network. These hidden nodes act…
Advised by Zhilin Li.
AMS will be hosting a special showing of Hidden Figures and provide pizza and other snacks.
We give a brief overview of factorization homology theory due to Ayala, Francis and Tanaka and explain how it leads to a (still mostly conjectural) generalization of graph homology to homotopy commutative algebras, and an efficient computation of knot invariants coming from factorization homology (at least for alternating links).