Tom Laetsch (U Conn)
A subRiemannian manifold $M$ is a connected smooth manifold such that the only smooth curves in $M$ which are admissible are those whose tangent vectors at any point are restricted to a subset $\mathcal{H} \subset TM$, called the horizontal distribution. Such spaces have several applications in physics and engineering, as well as in the study of hypoelliptic operators. In this talk we will construct a family of geometrically natural hypoelliptic Laplaciantype operators and discuss the trouble with defining one which is canonical. We will also attempt to construct a random walk on a subRiemannian manifold which converges weakly to a process whose infinitesimal generator is one of our hypoelliptic Laplaciantype operators.
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Tobias Hurth (Georgia Tech)
Consider a finite family of smooth vector fields on a finitedimensional smooth manifold $M$. For a fixed starting point on $M$ and an initial vector field, we follow the solution trajectory of the corresponding initialvalue problem for an exponentially distributed random time. Then, a new vector field is selected at random from the given family, and we start following the induced trajectory for another exponentially distributed time. Iterating this construction, we obtain a stochastic process $X$ on $M$. To $X$, we adjoin a second process $A$ that records the driving vector field at any given time. The twocomponent process $(X,A)$ is Markov. In the talk, I will present sufficient conditions for uniqueness and absolute continuity of its invariant measure. These consist of a Hörmandertype hypoellipticity condition that holds at a point on M that can be approached from all other points on the manifold. If $M$ is the real line, one can show that the densities of the invariant measure are smooth away from critical points. For analytic vector fields, we can derive the asymptotically dominant term of the densities at critical points. This is joint work with Yuri Bakhtin. top of page

Sneha Subramanian (U Penn)
We study the result of repeatedly differentiating a random entire function whose zeros are points of a Poisson process of intensity 1 on $\mathbb{R}$. For the first part of the talk, we shall discuss a toymodel based on a random polynomial, whose zeros are i.i.d. Rademacher random variables. For the second, we shall use our results from the first part as a poorism to discuss the main result regarding Poisson process. Based on joint work with Robin Pemantle. top of page
