Complete embedded constant mean curvature (CMC) surfaces of fixed, finite topology comprise a finite-dimensional moduli space. In case of coplanar CMC surfaces of genus 0 with k ends, this moduli space can be identified with the space of holomorphic immersions from the plane to the 2-sphere whose Schwarzian derivative is a polynomial with degree depending on k. Can you guess which families of coplanar CMC surfaces correspond to the polynomials 0, or 1, or z?

In this talk, we consider the dual Minkowski problem, proposed by Huang-Lutwak-Yang-Zhang (Acta 2016), for the planar case and the index $q>0$, without any symmetry assumptions. If the prescribed measure has a density which is bounded between two positive constants, we show the existence of solutions to the problem. If the density is smooth, we show the smoothness of the solutions. Some other applications of our method will also be discussed. This is a joint work with Dr. Shibing Chen.

I will discuss some results on the classification of convex compact ancient solution to the generalized curve shortening flow (the speed of evolution is the curvature of the curve to some power). In particular, I will show that the only convex compact ancient solution to the affine curve shortening flow (also known as fundamental equation of image processing) is a shrinking ellipse.

An extension of the Lutwak projection inequality is established in the framework of Orlicz Brunn -Minkowski theory. This new result directly yields the Orlicz Brunn-Minkowski inequality for intrinsic volumes.

In this talk, I will first give an introduction on Tian's properness conjecture concerning on an analytic charactarization of the existence of canonical metrics in Kahler geometry. Then I will focus on compactifications of reductive Lie groups. The main results are criterion theorems of the properness of two important functionals——Ding functional and Mabuchi's K-energy on these manifolds. In particular, the existence of Kahler-Einstein metrics, Kahler-Ricci solitons and Mabuchi's generalized Kahler-Einstein metrics on Fano compactifications of reductive Lie groups can be established.

eaction-diffusion epidemic models are proposed in order to understand how spatial heterogeneity influences the transmission dynamics of infectious diseases. In this talk, I will first present our recent numerical studies of the seasonal influenza epidemics in Puerto Rico based on a diffusive susceptible-infected-recovered model. Our simulations demonstrate that even simple diffusive epidemic models have potential applications in real-world situations. Then I will present our theoretical investigations of a reaction-diffusion vector-host epidemic model.

By the super version of the Wedderburn Theorem, a finite dimensional complex simple (associative) superalgebras is isomorphic to either a (full) matrix superalgebra or a queer matrix superalgebra. This gives rise to two series Lie superalgebras: the general linear Lie superalgebra and the queer Lie superalgebra. In this talk, I am going to introduce the queer q-Schur superalgebras associated with the latter and discuss their fundamental structure. The Schur-Weyl-Sergeev duality involving the quantum queer supergroup and Hecke-Clifford superalgebra will also discussed.

Vector-borne infectious diseases may involve horizontal transmission between hosts in addition to transmission from infected vectors to susceptible hosts. In this talk, we develop a vector-borne disease model with general nonlinear incidence rates and continuous age structures in both infectious hosts and vectors. We first study the existence and local stability of steady states, which is completely determined by the basic reproduction number. With the assistance of the existence of a global attractor and the uniform persistence, a threshold dynamics is established by employing the Fluctuation Lemma and the approach of Lyapunov functionals.