Previous Special Year Seminar

In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly-oriented copies of a molecule. The cryo-EM problem is to use the resulting set of noisy 2D projection images taken at unknown directions to reconstruct...

The study of the Gaussian limit of linear statistics of eigenvalues of random matrices and related processes, like determinantal processes, has been an important theme in random matrix theory. I will review some results starting with the strong...

What is the volume of the set of singular symmetric matrices of norm one? What is the probability that a random plane misses this set? What is the expected "topology" of the intersection of random quadric hypersurfaces? In this talk I will combine...

I discuss a renormalization group method to derive diffusion from time reversible quantum or classical microscopic dynamics. I start with the problem of return to equilibrium and derivation of Brownian motion for a quantum particle interacting with...

The quantum random energy model is a random matrix of Schroedinger type: a Laplacian on the hypercube plus a random potential. It features in various contexts from mathematical biology to quantum information theory as well as an effective...

We develop spectral theory for the generator of the \(q\)-Boson particle system. Our central result is a Plancherel type isomorphism theorem for this system; it implies completeness of the Bethe ansatz in infinite volume and enables us to solve...

In the early 1960's Dyson and Mehta found that the CSE relates to the COE. I'll discuss generalizations as well as other settings in random matrix theory in which \(\beta\) relates to \(4/\beta\).

An isolated quantum many-body system may be a reservoir that thermalizes its constituents. I will explore an example of the interplay of this thermalization and spontaneous symmetry-breaking, in the ferromagnetic phase of an infinite-range quantum...

Our goal is to explain how certain basic representation theoretic ideas and constructions encapsulated in the form of Macdonald processes lead to nontrivial asymptotic results in various `integrable'; probabilistic problems. Examples include dimer...

Our goal is to explain how certain basic representation theoretic ideas and constructions encapsulated in the form of Macdonald processes lead to nontrivial asymptotic results in various `integrable'; probabilistic problems. Examples include dimer...