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In this talk, we introduce occupation fields for vertices and oriented edges and compute their distributions. More precisely, under the Markov loop measure, the expected number for crossings of an ori...
We considers the adaptive stabilization problem for a basic class of linear-quadratic non-cooperative stochastic differential games when the systems matrices are unknown to the regulator and the playe...
A Hénon map is a map of the form H(z, w) = (f(z) + aw, z). A main focus of interest are the Fatou sets and the Julia sets. In this lecture I will show that it is possible that the Fatou set and the Ju...
The Grobner basis for a zero-dimensional polynomial ideal comprises a univariate polynomial in the least variable. The elimination process in Buchberger's algorithm unnecessarily involves the least va...
In this talk, we give a proof of the conjecture of Hofer-Wysocki-Zehnder published in 2003 asserting that a smooth and autonomous Hamiltonian flow on R4 has either two or infinitely many simple period...
It is now known that the complement of any polynomially convex compact set K in C^n is an Oka manifold. In particular this holds if K is convex. I will discuss a recent result, joint with Forstneri?, ...
Recently, based on the classification of the second and third order homogeneous Hamitionan operators Lorenzoni and his collaborators classified compatible trios of two-component homogeneous Hamiltonia...
We report the work of Chen-Cheng on the existence of cscK metrics. In this talk I will mainly focus on the C0 estimate, which is derived using the ABP maximum principle.
We prove that if the Gauss map of a minimal surface immersed in Rm omits a generic hypersurface of large enough degree, then it must be constant.
The Prandtl equation introduced by Prandtl in 1904 is a basic equation describling the behavior of the fluid near the boundary at high Reynolds number regime. In this talk, I will first introduce some...
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.
Let K be a planar convex body with C^1 boundary. Consider a random line G intersecting K. In [1] Pleijel discovered an identity expressing the integral functional of the length of the chord G ∩ K in t...
The geometric considerations enter in a decisive way in many questions of harmonic analysis. For example, the estimation of the Fourier transform of surface-carried measure, which played a key role in...
Stability conditions on triangulated categories are introduced by Bridgeland. For 3-Calabi-Yau triangulated categories from quivers with potentials, the space of stability conditions on this triangula...
In this talk, we first recall classic projection theorem for closed convex subsets in a Hilbert space. Then we introduce two extensions of the projection theorem in the Banach space where one is estab...

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