It is proved that the classical Laplace transform is a continuous valuation which is positively GL(n) covariant and logarithmic translation covariant. Conversely, these properties turn out to be sufficient to characterize this transform.

In 1999, Dar conjectured that there is a stronger version of the celebrated Brunn-Minkowski inequality. However, as pointed out by Campi, Gardner, and Gronchi in 2011, this problem seems to be open even for planar o-symmetric convex bodies. In this talk, we give a positive answer to Dar's conjecture for all planar convex bodies. Besides, we will introduce the development of the logarithmic Minkowski problem. Finally, the connection of these two problems and related results will be shown.

To study the impact of the sterile insect technique on the transmission dynamics of mosquito-borne diseases, we formulate continuous-time mathematical models for the interactive wild and sterile mosquitoes with or without stage structure. We incorporate different strategies for the releases of sterile mosquitoes in the models and investigate the model dynamics, including the existence of positive equilibria and their stability. We compare the dynamics of these models and also discuss mathematical modeling principles throughout the presentation.

We give explicit isomorphisms between simple modules of degenerate cyclotomic Hecke algebras defined via various cellular bases. A special case gives a generalized Mullineux involution in the degenerate case. This is a joint work with Linliang Song from HIT, Shenzhen.

In his plenary address to the 2002 International Congress of Mathematicians,former SIAM president,Professor D.N.Arnold stated, ''Four decades of searching for mixed finite elements for elasticity beginning in the 1960s did not yield any stable elements with polynomial shape functions.''Working with Professor Jun Hu of Peking University,we completely solved this problem,constructing optimally the conforming symmetric mixed finite elements on 2D and 3D triangular grids. Mainly for this work, Professor Jun Hu was awarded the Innovation Award by the Chinese Society of Computational Mathematics.

We know at least two ways to generalize multiple zeta(-star) values (MZ(S)Vs) which are q-analogue and t-interpolation. The q-analogue of MZVs was introduced by Bradley (2005), Zhao(2007), etc. On the other hand, polynomials interpolating MZVs and MZSVs using a parameter t were introduced by Yamamoto (2013). In this talk, we consider such two generalizations at the same time, that is, we compose polynomials interpolating q-MZVs and q-MZSVs using a parameter t which are reduced to q-MZVs as t=0 and t-MZVs as q to 1. Then we introduce algebraic setup and some relations for this new MZVs.

We propose new energy dissipative characteristic numerical methods for the approximation of the diffusive Oldroyd-B equations, that are based either on the finite element or finite difference discretization. We prove energy stability of both schemes and illustrate their behaviour on a series of numerical experiments. Using both the diffusive model and the logarithmic transformation of the elastic stress we are able to obtain methods that converge as mesh parameter is refined.This work has been done in the cooperation with M. Tabata, H. Notsu (Waseda University, Tokyo) and supported by the DFG International Reseach Training Group “Mathematical Fluid Dynamics”.

In this talk we will introduce (classical) multiple zeta values (MZVs) and relations among them. Our motivation to investigate relations among MZVs often comes from the dimension conjecture, which has been established by D. Zagier in 1994. We summarize several known relations by drawing a diagram for their implications. Moreover we give concrete statements of the derivation relation, the quasi-derivation relation, and the cyclic sum formula under the usual algebraic setup.