Mathematical Sciences: Explorations in Brownian Motion, Intrinsic Ultracontractivity, Martingales and Lancunary Series

巴纽艾洛斯 调查员将研究几个问题，其中位于交叉的概率和分析的各个领域。具体地说，主要研究领域包括：由平面单连通区域上布朗运动研究而产生的极值问题;某些类型平面单连通区域的内禀超压缩性的几何刻画;鞅不等式和T. Beurling-Ahlfors算子的Iwaniec不等式;缺项三角级数的零Khintchin不等式。 该奖项将提供资金，以进一步研究数学分析和概率论之间的相互关系。几个问题将被调查处理几何，运营商，系列和布朗运动。这将导致更好地理解这些数学领域，特别是当它们相互关联时。

Banuelos The investigator will study several problems which lie in the intersection of probability and various areas of analysis. Specifically, subject areas include extremal problems which are motivated from the study of Brownian motion in simply connected planar domains; a geometric characterization ofr intrinsic ultracontractivity for certain types of simply connected planar domains; martingale inequalities and a conjecture of T. Iwaniec for the Beurling-Ahlfors operator; and the zero Khintchin inequality for lacunary trigonometric series. This award will provide funding to further study the interrelationship between mathematical analysis and probability theory. Several problems will be investigated dealing with geometry, operators, series and Brownian motion. This should lead to a better understanding of these areas of mathematics, especially as they relate to one another.