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 this talk I'll discuss his finding, how the Master Theorem for divide-and-conquer plays into it, and how it was shown that finding determinants, inverting matrices, […]
Abstract: "We present a general Bayesian statistical model for discrete time, discrete state space stochastic processes. Applications include the modeling of recurrent and episodic disease processes, such as episodes of illicit drug use, as well as social processes such as educational enrollment and employment. We also present Markov chain Monte Carlo inference algorithms for our […]
An important question in classical representation theory is when the tensor product of two irreducible representations has another representation as a factor. In this talk, I will introduce a quantum […]
TOPIC: Graphs, matrices, and recurrences Abstract: In mathematics, we are often surprised to find that problems that look very different are actually the same problem in a different guise! In […]
Abstract: Remember smoking? What’s the new public health problem? In the US, we are currently entangled within three converging and intertwined complex problems: Cancer, Obesity, Aging. There are over 16 million cancer survivors living in the US as we speak. Over 50% of our society is overweight and/obese. Our society is aging and the age […]
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 […]
Abstract: Mathematical modeling is an effective resource for biologists since it provides ways to simplify, study and understand the complex systems common in biology and biochemistry. Many mathematical tools can […]
Quandles are algebraic structures that play nicely with knots. The multiplicative structure of finite quandles gives us a way to "color" knot diagrams, and the number of such colorings for […]
Linear evolution equations, such as the heat equation, are commonly studied on finite spatial domains via initial-boundary value problems. In place of the boundary conditions, we consider “multipoint conditions”, where […]
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 > s(n), x^p + y^p = z^p (mod p) has a nontrivial solution. A (p,q)-graph G is said to be vertex Ho-Lee-Schur graph if there exists a bijection […]
Abstract: In this talk, a conformal mapping approach to shape optimization problems on planar domains will be discussed. In particular, spectral methods based on conformal mappings are proposed to solve Steklov eigenvalues and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov eigenvalue problem in the complex domain […]
Suppose K is an oriented knot in a 3-manifold M with regular neighborhood N (K). For each element γ ∈ π 1 (∂N (K)) we define a quandle Q γ (K; M) which generalizes the concept of the fundamental quandle of a knot. In particular, when γ is the meridian of K, we obtain the […]
