Past Events
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…
Abstract: We extend the work of Székelyhidi to construct complete Calabi-Yau metrics on non-compact manifolds which are smoothings of an initial complete intersection Calabi-Yau cone $V_0$. The constructed Calabi-Yau manifold has tangent cone at infinity given by $\mathbb{C} \times V_0$. This…
The Erdös-Ginzburg-Ziv Problem is a classical extremal problem in discrete geometry. Given positive integers m and n, the problem asks about the smallest number s such…
We will discuss a new program of studying solitons using a geometric flow for a general tensor $q$. We begin by establishing a number of results for solitons to the geometric flow for a general tensor, $q$, examining both the compact and non-compact cases. From there, we will apply…
Sloan Math Corner
This talk has two goals. The first is a derivation of a time-inhomogeneous KPZ equation from fluctuations in a Ginzburg–Landau SDE in nonequilibrium. The method is a fluctuation-scale analog of Yau's method for hydrodynamic limits in nonequilibrium. The second is well-posedness of the limit KPZ…
Lower scalar curvature bounds on spin Riemannian manifolds exhibit remarkable extremality and rigidity phenomena determined by spectral properties of Dirac operators. For example, a fundamental result of Llarull states that there is no smooth Riemannian metric on the n-sphere which dominates the…
Abstract
Abstract: I will discuss propagation of singularities of the magnetic Hamiltonian with singular vector potentials, which is related to the so-called Aharonov--Bohm effect. In addition, I shall discuss a Duistermaat--Guillemin type trace formula and meromorphic continuation of the resolvent, as…
When M is the exterior of a knot K in the 3-sphere, Lin showed that the signature of K can be viewed as a Casson-style signed count of the SU(2) representations of pi_1(M) where the meridian has trace 0. This was later generalized to the fact that signature function of K on the unit circle…
Certain exact complex-symplectic manifolds, such as hypertoric varieties and Nakajima quiver varieties, play a prominent role in parts of geometric representation theory. I will talk about the wrapped Fukaya category of these manifolds. In particular, I will explain that the…