Past Events
A classic question in algebraic geometry asks what are the possible singularities for a plane curve of a given degree and genus. This turns out to be closely connected with the theory of symplectic embeddings of ellipsoids. In this talk I will explain how to construct various families of…
We give a general method that implies various on-diagonal heat kernel bounds, in particular, the lower bounds on stationary random media that may have long-range correlations. As an application, we determine the spectral dimension of simple random walk on the long-range percolation model in $Z^d…
For a compact subset K of a closed or geometrically bounded symplectic manifold one can consider the Hamiltonian Floer cohomology of the indicator function. This invariant is otherwise known as relative symplectic cohomology. At first sight, relative SH depends in an intractable way on both K…
I will speak about joint work with Vytautas Paškūnas and Gebhard Böckle which describes the space of lifts (to characteristic 0, for instance) of a representation (with mod p coefficients) of the absolute Galois group of a finite extension of the p-adic numbers. In the…
This is the story of understanding 'things' by asking 'what does a typical thing 'look like'. The things can be finite (permutations, elements of a finite group, graphs, or integers between 1 and N). They can also be infinite (random matrix theory asks about the eigenvalues of 'typical…
A link L is called a universal link, if every closed 3-manifold can be presented as the covering space of the 3-sphere with branch set L. We will discuss some techniques for defining branched coverings by link diagrams with colored arcs, and show that the Borromean rings is a universal…
In this talk, we will discuss techniques for explicitly describing the degenerations parametrized by the KSBA moduli space of surfaces and log pairs of general type. We will focus on specific examples, such as certain Horikawa surfaces and cubic surfaces, and how our techniques have been applied…
The problem of finding the smallest eigenvalue of a Hermitian matrix (also called the ground state energy) has wide applications in quantum physics. In this talk, I will first briefly introduce the mathematical setup of quantum algorithms, and discuss how to use textbook quantum algorithms to…