A promising route to quantum computing is the creation of electron quantum dots on a superconducting substrate. If such “valence” electrons are critically isolated, they behave as critically coherent multiplets—analagous to natural atoms together in a superposition of ionic and covalent bonds. De...

The classical estimate by Caffarelli shows that a strictly convex solution to the real Monge-Ampere equations has W^{2,p} regularity if the right hand side is close to a constant. We partially generalize this result to the complex version, when the underlying solution is close to a smooth strictly p...

Given a category of representations of some algebraic (geometric objects), there are many ways to attach algebraic varieties, so that the representations can be regarded as quasi-coherent sheaves on it, and then using the algebraic geometric method in turn to construct invariants of the representati...

Finding the mixed Nash equilibria (MNE) of a two-player zero sum continuous game is an important and challenging problem in machine learning. A canonical algorithm to finding the MNE is the (noisy) gradient descent ascent (GDA) method. In this talk, we will discuss the infinite particle limit of the...

Sir Simon Donaldson conjectured that there should exist a virtual fundamental class on the moduli space of surfaces of general type inspired by the geometry of complex structures on the general type surfaces. In this talk I will present a method to construct the virtual fundamental class on the modu...

High-dimensional interaction models have important applications in many scientific fields, especially in genetic research and medical studies. As in highdimensional main-effect models, feature selection is unavoidable in high-dimensional interaction models. However, feature-selection methods for hig...