Date  Speaker  Title (click for abstract, if available) 

Friday, January 27th 
LiCheng Tsai
University of Utah 
The variational principle, or the least action principle, offers a framework for the study of the Large Deviation Principle (LDP) for a stochastic system. The KPZ equation is a stochastic PDE that is central to a class of random growth phenomena. In this talk, we will study the FreidlinWentzell LDP for the KPZ equation through the lens of the variational principle. Such an approach goes under the name of the weak noise theory in physics. We will explain how to extract various limits of the most probable shape of the KPZ equation in the setting of the FreidlinWentzell LDP. We will also review the recently discovered connection of the weak noise theory to integrable PDEs. This talk is based in part on joint works with Pierre Yves Gaudreau Lamarre and Yier Lin. 
Friday, February 3th 
Xuan Wu
University of Chicago 
This talk presents the convergence of the KPZ equation to the directed landscape, which is the central object in the KPZ universality class. This convergence result is the first to the directed landscape among the positive temperature models. 
Friday, February 10th 
SungSoo Byun
Korea Institute for Advanced Study 
The study of products of random matrices has been proposed many decades ago by Bellman and by Furstenberg and Kesten with the motivation to understand the properties of the Lyapunov exponents in this toy model for chaotic dynamical systems. In this talk, I will discuss the real eigenvalues of products of random matrices with i.i.d. Gaussian entries. In the critical regime where the size of matrices and the number of products are proportional in the large system, I will present the mean and variance of the number of real eigenvalues. Furthermore, in the Lyapunov scaling, I will introduce the densities of real eigenvalues, which interpolates Ginibre's circular law with Newman's triangular law. This is based on joint work with Gernot Akemann. 
Friday, February 17th 
Shmuel Baruch
University of Rome, Tor Vergata 
We show that an irrelevance result reminiscent of Modigliani and Miller holds in a nonpublic setting of a startup owned by two entities (an entrepreneur and VC) with divergent roles, interests, and bargaining power. The startup always maximizes innovation efficiency and firm value.

Friday, February 24th 
Ofer Busani
University of Bonn 
The KPZ class is a very large set of 1+1 models that are meant to describe random growth interfaces. It is believed that upon scaling, the long time behavior of members in this class is universal and is described by a limiting random object, a Markov process called the KPZ fixedpoint. The (onetype) stationary measures for the KPZ fixedpoint as well as many models in the KPZ class are known  it is a family of distributions parametrized by some set I_ind that depends on the model. For k\in \mathbb{N} the ktype stationary distribution with intensities \rho_1,...,\rho_k \in I_ind is a coupling of onetype stationary measures of indices \rho_1,...,\rho_k that is stationary with respect to the model dynamics. In this talk we will present recent progress in our understanding of the multitype stationary measures of the KPZ fixedpoint as well as the scaling limit of multitype stationary measures of two families of models in the KPZ class: metriclike models (e.g. last passage percolation) and particle systems (e.g. exclusion process). Based on joint work with Timo Seppalainen and Evan Sorensen. 
Friday, March 3rd 
No seminar

No seminar 
Friday, March 17th 
Ken Alexander
USC 
First passage percolation may be viewed as a way of creating a random metric on the integer lattice. Random passage times (iid) are assigned to the edges of the lattice, and the distance from $x$ to $y$ is defined to be the smallest sum of passage times among all paths from $x$ to $y$. We consider geodesics (shortest paths) in this context; specifically, what is the probability that two closeby nearlyparallel geodesics are disjoint? More precisely, if the geodesics have endtoend distance $L$ and the endpoints are separated by distance $a$ at one end and $b$ at the other, how does the disjointness probability vary with $L,a,b$? We answer this question, at least at the level of the proper exponents for $L,a,$ and $b$. 
Friday, March 24th 
Vlad Margarint
CU Boulder 
In this talk, I will cover a study of the Loewner Differential Equation using Rough Path techniques, and beyond. The Loewner Differential Equation describes the evolution of a family of conformal maps. We rephrase this in terms of singular Rough Differential Equations (RDE). In this context, it is natural to study questions on the stability, and approximations of solutions of this equation. I will present a result on the continuity of the dynamics and related objects in the parameter kappa. The first approach will be based on Rough Path Theory, and the second approach will be based on a constructive method of independent interest: the squareroot interpolation of the Brownian driver of the Loewner Differential Equation. I will also touch on the second question, which is the approximation of solutions of this singular RDE. I will present another approximation method with some further applications to the simulations of the SLE traces. In the final part, I will touch on some recent results on the Multiple SLE with Dyson Brownian motion driver, as well as on future potential investigations in this direction. 
Friday, March 31st 
Hindy Drillick
Columbia University 
The tPNG model is a oneparameter deformation of the polynuclear growth model that was recently introduced by Aggarwal, Borodin, and Wheeler, who studied its fluctuations using integrable probability methods. In this talk, we will discuss how to use techniques from interacting particle systems to prove a strong law of large numbers for this model. To do so, we will introduce a new colored version of the model that allows us to apply Liggett's subadditive ergodic theorem to obtain the hydrodynamic limit. The tPNG model also has a close connection to the stochastic six vertex model. We will discuss this connection and explain how we can prove similar results for the stochastic six vertex model. This talk is based on joint work with Yier Lin. 
Friday, April 7th 
Nilanjan Chakraborty
Washington University in St. Louis 
This talk mainly concerns about a K sample high dimensional CLT over a class of hyperpolygons. This result finds an extremely useful application in the context of high dimensional MANOVA problems based on supremum type test statistics for the difference in means among the K groups. Here we can allow the number of groups (K) to diverge to infinity. The test procedure considered is free from any distribution and correlational assumptions which broadens its scope towards practical applications. The problem of generalized linear hypothesis testing has also been tackled using the previously mentioned CLT result. The asymptotic analysis of these tests in terms of controlling size and power has been theoretically validated. A detailed simulation study has been conducted which corroborates the findings done in the theoretical sections. 
Friday, April 14th 
Rodrigo Ribeiro
University of Denver 
In this presentation we will talk about a class of random walks that build their own domain. I.e., at each step of the random walk, the walker may add new vertices to the underlying graph according to some distribution. We will see that under the right conditions the walker might be either transient or recurrent. Additionally, in the transient regiment, the walker may exhibit ballistic behavior.

Friday, April 21st 
Scott Sheffield
MIT & IAS 
Although lattice YangMills theory is easy to rigorously define, the construction of a satisfactory continuum theory is a major open problem in dimension d ≥ 3. Such a theory should assign a Wilson loop expectation to each suitable collection L of loops in ddimensional space. One classical approach is to try to represent this expectation as a sum over surfaces having L as their boundaries. There are some formal/heuristic ways to make sense of this notion, but they typically yield an illdefined difference of infinities.
