Lattice valued vector systems have taken an important role in packing, coding, cryptography, and signal processing problems. In compressed sensing, improvements in sparse recovery methods can be reached with an […]
Tight frames in Euclidean spaces are widely used convenient generalizations of orthonormal bases. A particularly nice class of such frames is generated as orbits under irreducible actions of finite groups […]
Given integers $k,l$ and a graph $G$, how large can be the fraction of $k$-vertex subsets of $G$ which span exactly $l$ edges? The systematic study of this very natural […]
An agent comes to a fork in a road. There is a sign that says that one of the two roads leads to prosperity and another to death. The agent […]
Modular forms are ubiquitous in modern number theory. For instance, showing that elliptic curves are secretly modular forms was the key to the proof of Fermat's Last Theorem. In addition […]
Chebotarev's theorem on roots of unity says that every minor of a discrete Fourier transform matrix of prime order is nonzero. We present a generalization of this result that includes […]
In 1897, Indiana physician Edwin J. Goodwin believed he had discovered a way to square the circle, and proposed a bill to Indiana Representative Taylor I. Record which would secure […]
I will talk about a few graph-theoretic metrics then introduce the concept of refinements on a class of functions that include all metrics. As a case study, we will construct various […]
A Fibonomial is what is obtained when you replace each term of the binomial coefficients $ {n \choose k}$ by the corresponding Fibonacci number. For example, the Fibonomial $${ 6\brace […]
For centuries finding the determinant of a matrix was considered to be something that took $\Theta(n^3)$ steps. Only in 1969 did Strassen discover that there was a faster method. In […]
In this talk, I will try to give a fun introduction to tropical geometry and Hassett spaces, and show how tropical geometry can be used to compute the Chow rings […]
A triple of natural numbers (a,b,c) is an S-set if a+b=c. I. Schur used the S-sets to show that for n >3, there exists s(n) such that for prime p […]
