A number of ion channels are observed to be sensitive to the temperature changes. These temperature-gated ion channels can detect the temperature thus regulate the internal homoeostasis and disease-related processes such as the thermal adaptation and the fever response. In order to understand how the temperature affects the ion channel mechanics, we develop a Poisson--Nernst--Planck--Fourier (PNPF) system through the energetic variational approach. With given form of the free energy functional and the entropy production, we achieve the mechanical equations and a temperature equation, which satisfy the laws of thermodynamics automatically. From the energy point of view, we also develop the numeric scheme which satisfy the discrete energy dissipation.

Let A be a sequence of complex numbers. In this talk we present a new family of asymptotic formulas for of digamma function of sequence A. Then we apply it and use residue theorem to obtain a new family of identities for Dirichlet series. As applications of these relations, we establish some relations of Euler sums and hyperbolic series. Moreover, we give many explicit formulas for non-alternating Euler sums with weight ≤ 6 in terms of Riemann zeta values, and for alternating Euler sums with weight ≤ 10 in terms of Riemann zeta values and polylogarithms.

题目：数学的意义报告人：席南华 院士地点：综合楼410室时间：2018年7月1日 14：30-15:30报告人简介：席南华，中国科学院院士，现任中科院数学与系统科学研究院院长；曾获国家自然科学奖二等奖、陈省身数学奖、首届国家杰出青年基金等。主要从事代数群与量子群领域研究，并取得了一系列突出的研究结果，对仿射A型Weyl群证明了Lusztig关于基环的猜想，成为国际上很多后续工作的基础之一，对代数群理论有重要贡献。欢迎各位参加

This article is devoted to the exploration of finite element methods for magneto-heat coupling model, where the eddy current problem and the heat equation are coupled together with the heat convection and the radiation effects. Firstly, the decoupled scheme is established by applying backward Euler discretization in time and $N/acute{e}d/acute{e}lec$-Lagrange finite element in magnetic-temperature field, respectively. Secondly, the existence and uniqueness of the discretized scheme are proved by applying the theory of monotone operators. Then, under some regularity assumptions and time-step restriction

Voronoi formulas are Poisson-style summation formulas for automorphic forms (on GL(n)). They have been powerful tools in analytic number theory for a long time (with applications to the divisor problem, the circle problem, subconvexity of L-functions, etc). Firstly, we present a Voronoi formula for coefficients of a large class of L-functions, in the style of the classical converse theorem of Andre Weil. Our formula applies to full-level cusp forms, Rankin-Selberg convolutions, and isobaric sums. Secondly, we present the balanced Voronoi formula, with its both sides twisted by hyper-Kloosterman sums. Lastly, we will discuss how the formula will be generlized when the automorphic form has ramifications.

We will present the problem of bilinear controllability for Schrödinger equation in a bounded domain, i.e the possibility of controlling the equation by an action on a potential, with the difficulties and the few available results and methods up to now. We will then present a new result of local bilinear controllability in dimension 3 in a neighborhood of an eigenfunction corresponding to a simple eigenvalue and with a non-degeneracy condition of the normal derivative on a part of the boundary satisfying the geometric control condition.

Recently, we generalize the known DDVV-type inequalities for real (skew-)symmetric and complex (skew-)Hermitian matrices into arbitrary real, complex and quaternionic matrices. Inspired by the Erd/H{o}s-Mordell inequality, we establish DDVV-type inequalities for matrices in the subspaces spanned by a Clifford system or a Clifford algebra. We also generalize the B/"{o}ttcher-Wenzel inequality to quaternionic matrices. In this talk, we will briefly introduce the background, the new progress above, and some open questions.

Einstein metrics are natural Riemannian metrics on differentiable manifolds. In dimensions 2 and 3, they must have constant sectional curvature, while in dimension 4, they are much more complicated. For the complex setting, in 1990 Tian classified Kahler-Einstein four-manifolds with positive scalar curvature, and in 2012 LeBrun classified Hermitian, Einstein four-manifolds with positive scalar curvature. For the real setting, however less is known, even assuming a (strong) condition of positive sectional curvature.