Seminar

There is an impending doom that the undead will once again populate the Earth. In this talk, I will describe the mathematics behind this invasion. First, using scientific zombie data, I will discuss and analyze the population dynamics of zombie infestations and how it may be possible to overcome them. After, I will talk about some advances in the science of Vampirology with former Pitt math major Jackie Ruchti. In the presence of vampire killers, oscillations can emerge between the populations of vampires and their victims.

The history of the Hilbert-Waring problem dates back to Diophantus of Alexandria and his famous book Arithmetica.  It states that given a power $k\geq 2$, every positive integer $n$ can be written as a sum of $\mu_{k}$ $k$-powers, where $\mu_{k}$ depends on $k$; that is, $n=x_1^k+...+x_{\mu_k}^k$. I will discuss a short solution on a variation of this problem.

Abstract: Milnor fibers are invariants that arise in the study of hypersurface singularities. A major open conjecture predicts that for hyperplane arrangements, the Betti numbers of the Milnor fiber depend only on the combinatorics of the arrangement. I will discuss how tropical geometry can be used to study related invariants, the virtual Hodge numbers of a hyperplane arrangement’s Milnor fiber. This talk is based on joint work with Max Kutler.
 

Abstract: The algebra of conformal blocks is a commutative ring built from the spaces of conformal blocks of the Wess-Zumino-Novikov-Witten model of conformal field theory attached to a smooth projective curve and a simple Lie algebra. For algebraic geometers, these rings emerge naturally as the total coordinate rings of the moduli of principal bundles on the curve.