### [YMSC-BIMSA Seminar in Analysis and Applications]Homogenization of Linear Elliptic Equations in Nondivergence-Form: Characterizations of Good Diffusion Matrices

In this talk, we discuss the periodic homogenization of linear elliptic equations of the form $-A(x/\varepsilon):D^2 u^{\varepsilon} = f$ subject to a Dirichlet boundary condition. We  characterize good diffusion matrices $A$, i.e., those for which the sequence of solutions  converges at a rate of $\mathcal{O}(\varepsilon^2)$ in the $L^{\infty}$-norm to the solution  of the homogenized problem. Such diffusion matrices are considered “good” as the optimal rate of convergence in the generic case is only $\mathcal{O}(\varepsilon)$. First, we provide a class of good diffusion matrices, confirming a conjecture posed by Guo and Tran in 2020.  Then, we give a complete characterization of diagonal diffusion matrices in two dimensions       and a systematic study in higher dimensions. This talk is based on joint work with Xiaoqin Guo (University of Cincinnati) and Hung V. Tran (University of Wisconsin Madison).

• ### [Seminar] [Applied Analysis Seminar] Stochastic homogenization for reaction-diffusion equations and G-equations

摘 要:Homogenization is a general phenomenon when physical processes in periodic or random environments exhibit homogeneous long time dynamics due to large space averaging of the variations in the environment. While this area of Mathematics saw a slew of remarkable developments in the last 20 years, the progress in the case of reaction-diffusion equations, which model many important physical ...

• ### [Seminar on Bioinformatics] The discussion on the Out of Africa hypothesis, OOAH and PPA (Progressive Phylogenetic Analysis), that identified the African human populations as paraphyletic

Abstract：The Out of Africa hypothesis, OOAH, was challenged recently in an extended mtDNA analysis, PPA (Progressive Phylogenetic Analysis), that identified the African human populations as paraphyletic, a finding that contradicted the common OOAH understanding that Hss had originated in Africa and invaded Eurasia from there. The results were consistent with the molecular Out of Eurasia hypoth...