Periods and Special Values of L-functions

PI和他的合作者将继续研究周期和l函数的特殊值之间的关系。特别是关于Blochand Beilinson关于椭圆曲线的猜想和Borel关于数域的定理，以及它们与flaurent多项式的Mahler测度和双曲3流形几何的联系。PI的研究领域是数论，这是一个非常古老的学科，与数学和物理学的所有其他可想象的领域都有联系。在数论中，人们想要回答的问题类型是多么的引人注目，例如，我们能否把数字1写成两个有理数的立方的和？在费马（1600年）的时代，这些问题很可能对日常生活没有直接影响，但在今天已经演变成高度相关的问题。在当今的科技时代，数论在很多日常活动的安全背后起着重要作用，比如在网上购物。PI的具体研究涉及l函数，与上述问题相关的某些分析对象，这是现代数论的核心，人们期望并经常从中获得答案。

The PI and his collaborators, will continue their investigation of therelations between periods and special values ofL-functions. Specifically, those pertaining to the conjecture of Blochand Beilinson for elliptic curves and those implied by Borel's theoremfor a number field and their connection to the Mahler measure ofLaurent polynomials and the geometry of hyperbolic 3-manifolds.The PI's research area is in Number Theory, a very old subject withconnections to every other conceivable area of Mathematics as well asPhysics. It is remarkable how the type of questions one would like toanswer in Number Theory, for example, can we write the number 1 as thesum of the cubes of two rational numbers?, which at the time of Fermat(1600's) say, most likely had no direct implications to everyday life,have evolved into highly relevant issues today. In our currenttechnology age, Number Theory is behind much of the safety of commonactivities like, for example, shopping on the internet. The PI'sspecific research concerns L-functions, certain analytic objects oneassociates to questions like the one above, which are central tomodern Number Theory and from which one expects to, and often does,retrieve answers.