**Feb 20 @ Penn: Cheyne Homberger (Maryland) **

*Permuted Packings and Permutation Breadth*

**Feb 13 @ Penn: Ewain Gwynne (MIT) **

*A mating-of-trees approach for graph distances and random walk on random planar maps*

**Jan 30 @ Penn: David Burstein (Swarthmore) **

*Tools for constructing graphs with fixed degree sequences*

**Jan 16 @ Penn: Jeffrey Kuan (Columbia) **

*Algebraic constructions of Markov duality functions*

**Dec 5 @ Penn: Konstantinos Karatapanis (Penn) **

*One dimensional system arising in stochastic gradient descent*

**Nov 14 @ Penn: Miklos Racz (Princeton)
**

*How fragile are information cascades?*

**Nov 7 @ Temple: Indrajit Jana (Temple)
**

* Spectrum of Random Band Matrices*

**Oct 24 @ Penn: Lisa Hartung (NYU)
**

* Extreme Level Sets of Branching Brownian Motion*

**Oct 17 @ Temple: Atilla Yilmaz (NYU)
**

* Homogenization of a class of 1-D nonconvex viscous Hamilton-Jacobi equations with random potential*

**Oct 10 @ Penn: Sourav Chatterjee (Stanford)
**

* Rigidity of the 3D hierarchical Coulomb gas*

**Oct 3 @ Penn: Stephen Melczer (Penn)
**

* Lattice Path Enumeration, Multivariate Singularity Analysis, and Probability Theory*

**Sep 26 @ Penn: Evita Nestoridi (Princeton)
**

* Cutoff for random to random*

**Sep 19 @ Penn: Marcus Michelen (Penn)
**

* Invasion Percolation on Galton-Watson Trees*

**Sep 12 @ Temple: Nicholas Crawford (Technion)
**

*Stability of Phases and Interacting Particle Systems*

**Sep 5 @ Penn: Allan Sly (Princeton)
**

* Large Deviations for First Passage Percolation*

**May 2 @ Penn: Milan Bradonjic (Rutgers)
**

* Percolation in Weighted Random Connection Model*

**Apr 25 @ Temple: Chris Sinclair (U. Oregon)
**

* An introduction to p-adic electrostatics*

**Apr 11 @ Penn: Patrick Devlin (Rutgers)
**

* Biased random permutations are predictable (proof of an entropy conjecture of Leighton and Moitra)*

**Apr 4 @ Penn: Tobias Johnson (NYU)
**

* Galton-Watson fixed points, tree automata, and interpretations*

**Mar 28 @ Temple: Arnab Sen (Minnesota)
**

* Majority dynamics on the infinite 3-regular tree
*

**Mar 21 @ Temple: Paul Bourgade (Courant)
**

* Local extrema of random matrices and the Riemann zeta function
*

**Feb 28 @ Temple: James Melbourne (Delaware)
**

*Bounds on the maximum of the density for certain linear images of independent random variables*

**Feb 21 @ Penn: Shirshendu Ganguly (Berkeley)
**

*Large deviation and counting problems in sparse settings*

**Feb 14 @ Temple: Mihai Nica (NYU)
**

*Intermediate disorder limits for multi-layer random polymers*

**Feb 07 @ Temple: Fabrice Baudoin (U. Conn)
**

*Stochastic areas and Hopf fibrations*

**Jan 31 @ Penn: Nina Holden (MIT)
**

*How round are the complementary components of planar Brownian motion?*

**Jan 24 @ Penn: Charles Burnette(Drexel University)
**

*Abelian Squares and Their Progenies*

**Dec 06 @ Penn: Hao Shen (Columbia)
**

*Some new scaling limit results on ASEP and Glauber dynamics of spin models*

**Nov 29 @ Temple: Jack Hanson (CUNY)
**

*Arm events in invasion percolation*

**Nov 15 @ Penn: Elliot Paquette (Ohio State)
**

*The law of fractional logarithm in the GUE minor process*

**Nov 08 @ Penn: Sébastien Bubeck (Microsoft)
**

*Local max-cut in smoothed polynomial time*

**Nov 01 @ Penn: Henry Towsner (Penn)
**

*Markov Chains of Exchangeable Structures*

**Oct 25 @ Penn: Alexey Bufetov (MIT)
**

*Asymptotics of stochastic particle systems via Schur generating functions*

**Oct 18 @ Penn: Sanchayan Sen (Eindhoven)
**

*Random discrete structures: Scaling limits and universality*

**Oct 11 @ Penn: Louigi Addario-Berry (McGill)
**

*The front location for branching Brownian motion with decay of mass*

**Oct 04 @ Temple: Ramon van Handel (Princeton)
**

*Chaining, interpolation, and convexity*

**Sep 27 @ Penn: Amanda Lohss (Drexel)
**

*Corners in Tree-Like Tableaux.*

**Sep 20 @ Temple: Wei Wu (NYU)
**

*Loop erased random walk, uniform spanning tree and bi-Laplacian Gaussian field in the critical dimension.*

**Sep 13 @ Penn: Yuri Kifer (Hebrew University)
**

*An Introduction to Limit Theorems for Nonconventional Sums*

**Sep 06 @ Penn: Jian Ding (Chicago)
**

*Random planar metrics of Gaussian free fields*

**May 05 @ Penn: Oren Louidor (Technion)
**

*Aging in a logarithmically correlated potential*

**Apr 26 @ Penn: Josh Rosenberg (Penn)
**

*The frog model with drift on R*

**Apr 19 @ Penn: Dan Jerison (Cornell)
**

*Markov chain convergence via regeneration*

**Apr 12 @ Penn: Zsolt Pajor-Gyulai (Courant)
**

*Stochastic approach to anomalous diffusion in two dimensional, incompressible, periodic, cellular flows*

**Apr 05 @ Penn: Boris Hanin (MIT)
**

* Nodal Sets of Random Eigenfunctions of the Harmonic Oscillator*

The purpose of this talk is to present several results about the expected volume of the zero set of a random Hermite function in both the allowed and forbidden regions as well as in a shrinking tube around the caustic. The results are based on an explicit formula for the scaling limit around the caustic of the fixed energy spectral projector for the isotropic harmonic oscillator. This is joint work with Steve Zelditch and Peng Zhou.

**Mar 29 @ Penn: John Pike (Cornell)
**

* Random walks on abelian sandpiles*

**Mar 22 @ Temple: Christian Benes (CUNY)
**

* The scaling limit of the loop-erased random walk Green's function*

**Mar 15 @ Temple: Philippe Sosoe (Harvard)
**

* The chemical distance in critical percolation*

**Mar 01 @ Penn: Sumit Mukherjee (Columbia)
**

* Mean field Ising models *

**Feb 16 @ Temple: Yuri Bakhtin (Courant)
**

* Burgers equation with random forcing*

**Feb 09 @ Penn: Nayantara Bhatnagar (Delaware)
**

* Limit Theorems for Monotone Subsequences in Mallows Permutations*

**Feb 02 @ Penn: Erik Slivken (UC Davis)
**

*Bootstrap Percolation on the Hamming Torus*

**Jan 26 @ Penn: Vadim Gorin (MIT)
**

* Largest eigenvalues in random matrix beta-ensembles: structures of the limit*

**Dec 01 @ Penn: Sivak Mkrtchyan (Rochester)
**

*The entropy of Schur-Weyl measures*

**Nov 17 @ Penn: Partha Dey (UIUC)
**

*Longest increasing path within the critical strip*

**Nov 10 @ Penn: Charles Bordenave (Toulouse)
**

*A new proof of Friedmanâs second eigenvalue Theorem and its extensions*

**Nov 03 @ Penn: Christian Gromoll (UVA)
**

*Fluid limits and queueing policies*

**Oct 27 @ Penn: Doug Rizzolo (U Delaware)
**

*Random pattern-avoiding permutations*

Abstract: In this talk we will discuss recent results on the structure of random pattern-avoiding permutations. We will focus a surprising connection between random permutations avoiding a fixed pattern of length three and Brownian excursion. For example, this connection lets us describe the shape of the graph of a random 231-avoiding permutation of {1,...,n} as n tends to infinity as well as the asymptotic distribution of fixed points in terms of Brownian excursion. Time permitting, we will discuss work in progress on permutations avoiding longer patterns. This talk is based on joint work with Christopher Hoffman and Erik Slivken.

**Oct 20 @ Penn: Tai Melcher (UVA)
**

*Smooth measures in infinite dimensions*

A collection of vector fields on a manifold satisfies H\"{o}rmander's condition if any two points can be connected by a path whose tangent vectors lie in the given collection. It is well known that a diffusion which is allowed to travel only in these directions is smooth, in the sense that its transition probability measure is absolutely continuous with respect to the volume measure and has a strictly positive smooth density. Smoothness results of this kind in infinite dimensions are typically not known, the first obstruction being the lack of an infinite-dimensional volume measure. We will discuss some smoothness results for diffusions in a particular class of infinite-dimensional spaces. This is based on joint work with Fabrice Baudoin, Daniel Dobbs, Bruce Driver, Nate Eldredge, and Masha Gordina.

**Oct 06 @ Penn: Leonid Petrov (UVA)
**

*Bethe Ansatz and interacting particle systems*

I will describe recent advances in bringing a circle of ideas and techniques around Bethe ansatz and YangâBaxter relation under the probabilistic roof, which provides new examples of stochastic interacting particle systems, and techniques to solve them. In particular, I plan to discuss a new particle dynamics in continuous inhomogeneous medium with features resembling traffic models, as well as queuing systems. This system has phase transitions (discontinuities in the limit shape) and Tracy-Widom fluctuations (even at the point of the phase transition).

**Sep 29 @ Temple: David Belius (Courant)
**

*Branching in log-correlated random fields*

This talk will discuss how log-correlated random fields show up in diverse settings, including the study of cover times and random matrix theory. This is explained by the presence of an underlying approximate branching structure in each of the models. I will describe the most basic model of the log-correlated class, namely Branching Random Walk (BRW), where the branching structure is explicit, and explain how to adapt ideas developed in the context of BRW to models where the branching structure is not immediately obvious.

**Sep 24 @ Penn: Steven Heilman (UCLA)
**

*Strong Contraction and Influences in Tail Spaces*

We study contraction under a Markov semi-group and influence bounds for functions all of whose low level Fourier coefficients vanish. This study is motivated by the explicit construction of 3-regular expander graphs of Mendel and Naor, though our results have no direct implication for the construction of expander graphs. In the positive direction we prove an L_{p} Poincar\'{e} inequality and moment decay estimates for mean 0 functions and for all 1 \less p \less \infty, proving the degree one case of a conjecture of Mendel and Naor as well as the general degree case of the conjecture when restricted to Boolean functions. In the negative direction, we answer negatively two questions of Hatami and Kalai concerning extensions of the Kahn-Kalai-Linial and Harper Theorems to tail spaces. For example, we construct a function $f\colon\{-1,1\}^{n}\to\{-1,1\}$ whose Fourier coefficients vanish up to level $c \log n$, with all influences bounded by $C \log n/n$ for some constants $0\lessc,C\less \infty$. That is, the Kahn-Kalai-Linial Theorem cannot be improved, even if we assume that the first $c\log n$ Fourier coefficients of the function vanish. This implies there is a phase transition in the largest guaranteed influence of functions $f\colon\{-1,1\}^{n}\to\{-1,1\}$, which occurs when the first $g(n)\log n$ Fourier coefficients vanish and $g(n)\to\infty$ as $n\to\infty$ or $g(n)$ is bounded as $n\to\infty$.. joint with Elchanan Mossel and Krzysztof Oleszkiewicz

**Sep 15 @ Penn: Toby Johnson (USC)
**

*The frog model on trees*

Imagine that every vertex of a graph contains a sleeping frog. At time 0, the frog at some designated vertex wakes up and begins a simple random walk. When it lands on a vertex, the sleeping frog there wakes up and begins its own simple random walk, which in turn wakes up any sleeping frogs it lands on, and so on. This process is called the frog model. I'll (mostly) answer a question posed by Serguei Popov in 2003: On an infinite d-ary tree, is the frog model recurrent or transient? That is, is each vertex visited infinitely or finitely often by frogs? The answer is that it depends on d: there's a phase transition between recurrence and transience as d grows. Furthermore, if the system starts with Poi(m) sleeping frogs on each vertex independently, for any d there's a phase transition as m grows. This is joint work with Christopher Hoffman and Matthew Junge.

**Sep 08 @ Penn: Matt Junge (U. Washington)
**

*Splitting hairs (with choice)*

Sequentially place n balls into n bins. For each ball, two bins are sampled uniformly and the ball is placed in the emptier of the two. Computer scientists like that this does a much better job of evenly distributing the balls than the "choiceless" version where one places each ball uniformly. Consider the continuous version: Form a random sequence in the unit interval by having the nth term be whichever of two uniformly placed points falls in the larger gap between the previous n-1 points. We confirm the intuition that this sequence is a.s. equidistributed, resolving a conjecture from Itai Benjamini, Pascal Maillard and Elliot Paquette. The history goes back a century to Weyl and more recently to Kakutani.