Past Events

Patchworking with singularities (Section 2.4 of [IMS09])

Let a,b>0 be coprime integers. Assuming a conjecture on Hecke eigenvalues along binary cubic forms, we prove an asymptotic formula for the number of primes of the form ax^2+by^3 with x < X^(1/2) and y  < X^(1/3). The proof combines sieve methods with the theory of real quadratic…

Abstract: Heegaard Floer homology and instanton Floer homology are packages of invariants in low dimensional topology constructed via symplectic topology and gauge theory respectively. Kronheimer and Mrowka conjecture that appropriate versions of the two invariants are equivalent. I will discuss…

Many point configuration questions ask how large the Hausdorff dimension of a given compact set E in some d-dimensional Euclidean space must be in order to guarantee "lots" of occurrences of some point configuration of interest. One of the most well-known examples is the Falconer distance set…

Spin models on graphs are a source of many interesting questions in statistical physics, algorithms, and combinatorics. The Ising model is a classical example: first introduced as a model of magnetization, it can combinatorially be described as a weighted probability distribution on two-vertex…

Hecke operators play a fundamental role in understanding the arithmetic properties of modular and automorphic forms. Since the advent of the original Eichler-Shimura relation, it has been clear that the mod-p behavior of Hecke correspondences is crucial for such applications. However, one could…

We study the renormalization group method and its applications in probability theory.

Following a paper of Buckmaster, Shkoller, and Vicol, we consider the 2D isentropic compressible Euler equations. We give an elementary construction of a solution with smooth initial data that forms a shock and has O(1) vorticity at the shock.

We will continue our discussion of corks and Heegaard Floer theory.

If a Hilbert space is built from qubits, we may define complexity of a global unitary U by the minimal number of one- and two-qubit unitaries that comprise the global U. I will discuss three questions that can be posed using this complexity. (i) What quantum error correcting codes are there on D…