2018.6.15-6.21 学术活动预告

2018.6.15-6.21 学术活动预告
2018/6/14 10:25:52 中国科学院数学与系统科学研究院

     Speaker:

     Terry Gannon, University of Alberta

     Title:

     Exceptional modular invariants are rare

     Time & Venue:

     2018.6.19 10:00-11:00 N212

     Abstract:

     Let g be a simple finite-dimensional Lie algebra and k be a positive integer. An old question is to identify all possible modular invariants for g at level k. The result for g=sl(2) is the famous ADE classification of Cappelli-Itzykson-Zuber from 1987. Understanding this ADE pattern at a deeper level was a crucial original motivation for Ocneanu's work. Somewhat later, the analogous classification for g=sl(3) was found; that classification is intimately connected to Jacobians for Fermat curves. Little else is known. However, recent work makes the analogous classification for all Lie groups up to rank 8 or so imminent. The key step is a bound K(g) which grows like the cube of the rank of g: when the level k is greater than K(g), the only modular invariants come from symmetries of the extended Dynkin diagram of g. My talk will describe the problem and explain the bound.

     Speaker:

     Zhengwei Liu, Harvard University

     Title:

     Picture language program

     Time & Venue:

     2018.6.20 15:00-16:00 N109

     Abstract:

     We discuss the appearance of pictures in mathematics. We emphasize a bi-directional process between picture language and mathematical concepts: abstraction and simulation. This provides a program to understand different subjects, using virtual and real mathematical concepts simulated by pictures.

     Speaker:

     Prof. Michael Roeckner, Bielefeld University and AMSS, CAS

     Title:

     Variational solutions to nonlinear stochastic differential equations in Hilbert spaces

     Time & Venue:

     2018.6.20 16:30-17:30 N613

     Abstract:

     One introduces a new variational concept of solution for the stochastic differential equation dX+A(t)Xdt+λXdt=XdW,t∈(0,T); X(0)=x in a real Hilbert space where A(t)=?φ(t), t∈(0,T), is a maximal monotone subpotential operator in H while W is a Wiener process in H on a probability space {Ω,,?}. In this new context, the solution X=X(t,x) exists for each x∈H, is unique, and depends continuously on x. This functional scheme applies to a general class of stochastic PDE not covered by the classical variational existence theory and, in particular, to stochastic variational inequalities and parabolic stochastic equations with general monotone nonlinearities with low or superfast growth to +∞.

     来源：中国科学院数学与系统科学研究院

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