Title: Spectrum of Linial-Meshulam complex in thermodynamic regime Abstract: Linial-Meshulam complex, denoted by , is a random simplicial complex on vertices with a complete -dimensional skeleton and -simplices chosen independently with probability . Linial-Meshulam complex is one of the most studied generalizations of the Erdos-Renyi random…
Title: Permutation matrices, graph independence over the diagonal, and consequences Abstract: Often, one tries to understand the behaviour of non-commutative random variables or of von Neumann algebras through matricial approximations. In some cases, such as when appealing to the determinant…
Title: Limits of finite trees Abstract: Motivated by the work of Lovász, Szegedy and others on the convergence and limits of dense graph sequences, we investigate the convergence and limits of finite trees with respect to sampling in normalized distance.…
Title: The spectral edge of constant degree Erdős-Rényi graphs Abstract: Determining the spectrum and eigenvectors of the adjacency matrix of random graphs is a fundamental problem with applications in computer science and statistical physics. Often, the relevant model is…
Title: A new approach to proving strong convergence of random matrices Abstract. Friedman's celebrated 2004 result states that, as the number of vertices goes to infinity, random d-regular graphs are (with high probability) nearly optimal expanders, meaning that the top…
Title: ``Bi-Free Independence and the Asymptotics of Random Quantum Channels'' Abstract: It has been 10 years since the first paper on bi-free independence was published by Voiculescu. Since then, the theory of bi-free probability has been well developed. In this…
Title: ``Freeness for tensors'' Abstract: We pursue the current developments in random tensor theory by laying the foundations of a free probability theory for tensors and establish its relevance in the study of random tensors of high dimension. We give…
Title: ``Logarithmic correlation functions in 2D critical percolation'' Abstract: It is believed that the large-scale geometric properties of 2D critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic…
Title: ``Linear dependencies, polynomial factors in the Frankl-Furedi forbidden sunflower problem'' Abstract: We call a family of s sets \{F_1, …, F_s\} a sunflower with s petals if, for any distinct i, j \in , one has F_i \cap F_j…
Title: ``Limit shape of random polygons and lattice polygons: a survey'' Abstract. Assume K is a convex body in the plane and X is a (large) finite subset of K. How many convex polygons are there whose vertices belong to…
Title: ``An Introduction to the Theory of Rough Paths'' Abstract: The theory of rough paths, developed by Terry Lyons, provides a robust mathematical framework to analyze controlled differential equations driven by irregular signals, including those that are highly oscillatory or…
Title: ``Pitman's theorem and the quantum group SL2 in infinite curvature'' Abstract: Pitman's theorem states that a Brownian motion minus twice its current minimum is a Markov process. We will focus on two seemingly distinct approaches to this theorem: Biane's…