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Random phase approximation (RPA) was proposed by Bohm and Pines in four seminal papers during 1951-1953 to describe the correlation of fermions, namely the correction to the Hartree-Fock theory. While...
We present an algorithm for the vertex cover problem by combining the LP relaxation and the random edge-reductions. The algorithm has the expected approximation ratio of 1.344.
In this talk, we discuss the approximation and computation for the linear and nonlinear eigenvalue problems in photonic crystals. We discretize the shifted Maxwell operator with edge finite elements a...
A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Weitzman (1979) introduced the Pandora Box problem as a model for sequential search with inspection costs, and gave an elegant index-based policy that attains provably optimal expected payoff. In vari...
Nonconvex constrained optimization (NCO) has been one of the important research fields in optimization community. It has widely appeared in many application fields. However, challenges for solving NCO...
In this talk, I will discuss arithmetic purity of strong approximation : motivations and related results. Finally, for complete toric varieties, I will briefly explain my work on this topic.
Coherence distillation is a basic information-theoretic task in the resource theory of coherence. In this talk, I will report the framework of the approximate coherence distillation under strictly inc...
We study the performance of fixed-price mechanisms in the bilateral trade problem. We improve the approximation ratios of welfare-optimal mechanisms in several settings. In particular, when we have on...
Waves of all sorts, including electromagnetic waves, acoustic waves, and mechanical vibrations, play a role in shaping our world. In disordered systems, the transport of waves is hindered, resulting i...
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
In this talk we discuss a notion of $\psi$-Dirichlet in Diophantine approximation which concerns improving Dirichlet’s approximation theorem to a general approximating function $\psi$. This notion was...
Let $k$ be a field of characteristic 0 and let $C$ be the a smooth affine curve over $k$. We will first discuss applications of strong approximation to the theory of integral quadratic forms over $C$....
Two pillar theories in physics – general relativity and quantum mechanics – stand up well on their own, but are incompatible with each other.
Modeling non-commutative phenomena in finite dimensional matrix algebras is a central theme of the program Quantitative Linear Algebra. This workshop will focus on a variety of concrete questions aro...

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