Tuesday, April 2, 2019
04/02/2019 - 4:00pm
Motivated by the study of sheaves of conformal blocks attached to affine Lie algebras, I will present in this talk an analogous geometric realization attached to vertex algebras. In particular, we will see how, thanks to the Virasoro uniformization theorem, it is possible to associate to certain representations of conformal vertex algebras, projectively flat sheaves on the moduli space of stable curves. Our construction extends the sheaves to nodal curves, and allows to explicitly compute the Atiyah algebra acting on these sheaves as in the prior case as well.This is joint work with Angela Gibney and Nicola Tarasca.
04/02/2019 - 4:15pm
Every pseudo-Anosov mapping class $\phi$ deﬁnes an associated veering triangulation $\tau_\phi$ of a punctured mapping torus. In joint work with S.J. Taylor and D. Futer, we show that generically, $\tau_\phi$ is not geometric. After defining the objects of interest, we will focus on an important lemma: for every surface $\Sigma$, there is a pseudo-anosov map on $\Sigma$ whose associated veering triangulation is non-geometric. Establishing this lemma boils down to finding mapping tori that fiber over many surfaces, and our approach will be to find examples for which we can describe the fibered faces of the Thurston norm unit ball. Although we do this by hand in this case, we will also briefly discuss recent work with S. Tillmann and D. Cooper that gives an algorithmic approach for computing the norm ball.
04/02/2019 - 6:00pm
Abstract: The method of graph regularity is an important tool in extremal combinatorics, allowing one to obtain good approximations of large graphs if one is willing to put up with terrible constants. Since the method only starts to say something meaningful when the graphs involved are far too large to write down, and since it is somewhat technical by nature, it can be hard to get an intuitive grasp of what the lemma states. In this talk, we’ll attempt to find this intuition anyway and get a big-picture overview of what graph regularity is actually doing, and we’ll see how to apply it to solve specific interesting problems in extremal graph theory.