Mathematical Sciences: Isoperimetric Inequalities and LowerBounds for Stochastic Processes

塔拉格兰德教授的研究将在三个主要领域进行。他将研究Bernoulli过程的下界，以期证明一个涉及结合两个Banach空间几何的范数的猜想。他将继续他在等周不平等方面的研究。他将研究Banach空间中的类型和余型的概念。这项研究涉及两个领域：概率论和无限维空间(Banach空间)的几何。概率论的思想对理解Banach空间很有用，反过来，对这些空间的理解又引出了一些新的、有趣的纯概率问题。

Professor Talagrand's research will be in three main areas. He will study lower bounds for Bernoulli processes with a view to proving a conjecture involving a norm incorporating the geometry of two Banach spaces. He will continue his research in isoperimetric inequalities. He will study the notion of type and cotype in Banach spaces. This research is at the interface of two fields: probability theory and the geometry of infinite dimensional spaces (Banach spaces). Probabilistic ideas are useful in understanding Banach spaces and conversely the quest to understand these spaces leads to new and interesting questions in pure probability.