I will discuss concordances of knots in 3-manifolds. In particular I will show that all the knots in the free homotopy class of $S^1\times pt$ in $S^1 \times S^2$ are concordant to each other. By Akbulut it turns out that many of these concordances are invertible.
We consider the no-flux initial-boundary value problem for the cross-diffusive evolution system which was introduced to describe the dynamics of urban crime. In bounded intervals I will first discuss the existence of global classical solutions for all reasonably regular non-negative initial data. Next I will address the issue of determining the qualitative behavior of solutions. Finally, I will conclude with some numerical simulations exploring possible effects…
Control systems impact our lives on a daily basis, whether it is from our thermostat controlling the temperature in our home to cruise control in our car to surfing the worldwide web. Feedback control systems is a type of dynamical system where it uses feedback from the system and an algorithm to determine an input…
Bryan Chu Title: Low Rank Randomized Standard Value Decomposition Abstract: The low rank randomized standard value decomposition is a fast, stable method of computing the dominant singular values of a real, large matrix A. For a large scale system we use a randomized matrix method, a so called, randomized SVD (rSVD). We improve the existing rSVD…
Tensors are closely related to secant varieties. In fact, the affine cone of the $r$th secant variety of the Segre variety is the set of tensors whose border rank is less than or equal to $r$. Similarly, we have a geometric interpretation of symmetric tensors. By studying the geometry of these secant varieties, we can…
Noether's theorem tells us that if a system is invariant under a group of symmetries, then we have quantities that are conserved. For example, if a system is invariant under translation, then momentum is conserved. If a system is invariant under rotation, then angular momentum is conserved. One of the challenges in numerical analysis is to make sure that these…
We will meet briefly to sign up for talks.
In my talk I will discuss some remarkable correspondence between symplectic varieties and vertex algebras, which has been discovered by physicists in the study of the four-dimensional N = 2 superconformal field theories. In the special class of the four-dimensional N = 2 superconformal field theories called the “theory of class S”, such correspondence is mathematically explained in terms of the…
You'll laugh, you'll cry, you'll probably consider planning a trip to Vegas. You can click here to watch a trailer of this cinematic masterpiece. We hope to see you all there! Your MGSA Secretary, Mallory
The Spring Departmental meeting will take place on Tuesday, January 16, 2018, 4:15PM-5:30PM in SAS 1102. Dean McGahan will be attending and will speak at the meeting. I solicit questions from the faculty that will be sent to the Dean ahead of the meeting so that she can address them when she comes. The Dean will be available for…
The Association for Women in Mathematics (AWM) will be hosting our weekly brown bag lunch. Attendees bring their own lunches, and have the opportunity to be in a casual discussion environment, while we provide a tasty treat! AWM is NOT exclusively for women, and we would like to emphasize that everyone is welcome join us…
Grid homology is a version of knot Floer homology in the 3-sphere that is entirely combinatorial and simple to define. Exploiting this, Ozsvath, Szabo, and Thurston defined a combinatorial invariant of transverse links in the 3-sphere using grid homology, which was then used to show that certain knot types are transversely non-simple by Ng, Ozsvath,…
The Finite Element Method(FEM) is one of many numerical methods to approximate solutions to ordinary and partial differential equations. FEM has been applied to numerous problems found in the fields of Fluid Mechanics, Electromagnetics, Lagrangian Mechanics, etc. While there are many approaches to the Finite Element Method, I will present the Galerkin approach. I will…
Suppose we lazily slice up the SUM series pizza. How many pieces can we make with just a few slices? What if we had a watermelon? Together we will try to answer this prob- lem and explore some of the beautiful geometry behind it. No background will be assumed and this talk should be ac-…
Phylogenetics is the branch of mathematical biology concerned with constructing evolutionary relationships between collections of species. These lectures will introduce these models, in particular emphasizing the ways that algebraic statistics can be used to analyze properties of the models. Viewed from the perspective of algebraic statistics, the corresponding algebraic varieties that arise are often familiar…