## Future Seminar Talks

## Past Seminar Talks

For seminar talks in 2020, click here

## 1/26 Martin Hairer (Imperial College)

**Title:**The support theorem for singular SPDEs [Notes]

**We will present a generalization of the Stroock-Varadhan support theorem for a class of systems of subcritical singular stochastic PDEs driven by a noise that is either white or approximately self-similar. The main problem that we face is the presence of renormalisation which has the consequence that the "naive" guess for what the support should be turns out to be incorrect.**

****Abstract:## 2/9 Yilin Wang (MIT)

**Title:**SLE, energy duality, and foliations by Weil-Petersson quasicircles [Notes]

**The Loewner energy for Jordan curves first arises from the small-parameter large deviations of Schramm-Loewner evolution (SLE). It is finite if and only if the curve is a Weil-Petersson quasicircle, an interesting class of Jordan curves appearing in Teichmuller theory, geometric function theory, and string theory with currently more than 20 equivalent definitions. In this talk, I will show that the large-parameter large deviations of SLE gives rise to a new Loewner-Kufarev energy, which is dual to the Loewner energy via foliations by Weil-Petersson quasicircles and exhibits remarkable features and symmetries. Based on joint works with Morris Ang and Minjae Park (MIT) and with Fredrik Viklund (KTH).**

****Abstract:**2/23** **Ivan ****Nourdin** (University of Luxembourg)

**Nourdin**

**Title:**The Rosenblatt Process, old and new [Notes]

**In this talk, I will present recent and older results concerning the Rosenblatt process, which is a non-Gaussian generalization of the fractional Brownian motion.**

****Abstract:**3/23** Mickey Salins (Boston University)

**Title:**The stochastic heat equation with non-Lipschitz drift on an unbounded spatial domain [Slides]

**I prove the existence and uniqueness of mild solutions of a stochastic heat equations whose drift term is not globally, or even locally, Lipschitz continuous. Instead, the drift term is assumed to satisfy a "half-Lipschitz" condition, meaning that it can be written as the sum of a decreasing function and a line. The proof involves showing that the stochastic convolution terms grow slower than polynomially in space and that a certain solution map is Lipschitz continuous on polynomially weighted spaces of continuous functions.**

****Abstract:**4/6** Rene Carmona (Princeton University)

**Title:**Stochastic Differential Graphon Games and SDEs driven by a continuum of independent Brownian motions [Slides]

**We review several recent attempts at the introduction of a limit theory for stochastic differential games between a large number of players whose interactions are underpinned by a (possibly random) graph. We shall concentrate on dense graphs whose limits are given by graphons. In the limit, the formulations of the dynamics of the system and the forward backward systems characterizing the Nash equilibria, involve a continuum of stochastic differential equations driven by independent Brownian motions. We shall review the tools introduced by mathematical economists to address the measurability issues inherent in this set-up, in particular, the notion of Fubini’s extension and the exact law of large numbers. Finally, we shall illustrate their application to the solution of a simple model.**

****Abstract:Work done in collaboration with Alexander Aurell and Mathieu Lauriere.

**4/20** Jing Wang (Purdue University)

**Title:**Stiefel Brownian motion and related stochastic processes [Slides]

**We start with stochastic area processes and stochastic windings on some complex symmetric spaces of rank 1. Then we will discuss the generalized version of these processes in higher rank spaces such as Grassmannians, and study their large time asymptotic laws. The main tool is to use the Stiefel fibration to lift Brownian motions on a complex Grassmannian to ones on a complex Stiefel manifold. This talk is base on joint works with Fabrice Baudoin.**

****Abstract:**5/4** Ofer Zeitouni (Weizmann Institute & NYU Courant Institute)

**Title:**Disorder transition for random polymers and the SHE [Notes]

**The random polymer model weights the trajectories of a random walk \(S_n\) by the exponential of a random weight \(\beta \sum_{i=1}^n \omega(i,S_i)\) where \(\{\omega(i,x)\}_{i,x}\) are iid. The continuous analogue of this model is the (multiplicative) stochastic heat equation driven by mollified noise. The discrete model exhibits a transition from weak to strong disorder as function of \(\beta\), and by using a link with the theory of Gaussian multiplicative chaos, the same holds for the SHE. I will describe this link and then focus on questions of disorder transition for random walks on various graphs. The continuous analogue of the latter is largely unexplored.**

****Abstract: