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In this talk, we give an overall description of the construction of the collapsed flying-wing-like steady gradient solitons, as well as the high dimension non-collapsed steady gradient solitons. In pa...
We study a Monge-Ampère type equation which interpolates the sigma_2-Yamabe equation in conformal geometry and the 2-Hessian equation. In dimension 4, we prove a corresponding Liouville’s theorem. Our...
I will give a review of the KP solitons based on Grassmannians. In the talk, I will also give several physical applications of KP solitons to shallow water wave phenomena, and discuss some initial val...
A matrix-based framework for the modeling, analysis and dynamics of Bayesian games are presented using the semi-tensor product of matrices. Static Bayesian games are considered first. A new conversion...
A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational po...
We go through Zimmer's book Chapter 2-3, making some preparations for Margulis super-rigidity theorem.
We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well.
In this talk, we address on the strong rigidity properties from joint integrability in the setting of Anosov diffeomorphisms on tori. More specifically, for an irreducible Anosov diffeomorphism with s...
Quasi-elliptic cohomology is closely related to Tate K-theory. It is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most elliptic c...
We prove sharp Lp estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their L2 norms on the boundary. We prove it by establishing Lp bounds for the harmonic extensi...
I will talk about affine Grassmannians for the exceptional group of type G_2. This group can be given as automorphisms of octonion algebras. I consider all maximal parahoric subgroups in G_2, and give...
A fundamental problem from computational learning theory is to well-reconstruct an unknown function on the discrete hypercubes. One classical result of this problem for the random query model is the l...
In this talk, I will introduce the methods for calculating the unstable homotopy groups of finite CW-complexes which builds on works of the relative James construction initiated by B. Gray in 1973 and...
For each central charge c\in (0,1], we construct a conformally invariant field which is a measurable function of the local time field \mathcal{L} of the Brownian loop soup with intensity c and i.i.d. ...
We propose a general framework of mass transport between vector-valued measures, which will be called simultaneous mass transport. The new framework is motivated by the need to transport resources of ...

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