Past Events
Let $\Omega(n)$ denote the number of prime factors of $n$, counted with multiplicity. Though the study of the asymptotic behavior of this sequence finds roots in analytic number theory, Bergelson and Richter introduced a dynamical perspective: in any uniquely ergodic system, $\Omega$-ergodic…
When waves propagate through weakly disordered, smoothly varying media whose correlation length is larger than the wavelength, they can exhibit a phenomenon known as branched flow. The wave energy becomes concentrated along narrow channels, or branches, which repeatedly split with increasing…
After very briefly recalling Guth-Manolescu's real Heegaard Floer homology, we will discuss an extension of the "hat" version of it to 3-manifolds with boundary and discuss what we know about using it for computations. This is joint work with Peter Ozsváth.
A theorem of Colin de Verdière shows that, on any closed manifold of dimension at least three, one can choose a Riemannian metric whose Laplace spectrum begins with any prescribed finite list of positive numbers. The proof is inherently one about discrete graphs: one first prescribes the…
A symplectophagy is a symplectic isotopy satisfying certain constraints reminiscent of the symplectic camel problem. In this talk, I will introduce this notion and basic examples, and present a new phenomenon of symplectic rigidity in the form of obstructions to the existence of…
We discuss a recent result which makes early progress towards understanding temperature chaos in the Kardar–Parisi–Zhang universality class. We show that the appropriately centered and scaled free energy of positive temperature Continuum Directed Random Polymers (CDRPs) at distinct temperatures…
Polylogarithms are analytic functions whose special values are related to Dedekind zeta functions. This suggests that special values of polylogarithms should come from motivic classes in algebraic K-theory. Such motivic classes, at least with some technical assumptions, were indeed first…