Workshop: Towards a Local Proof of the Local Langlands Correspondence

组织者打算在芝加哥的伊利诺伊大学举行一个周末研讨会，针对研究生和年轻的研究人员，主题是当地的朗兰兹书信。最近的工作的特殊纤维的稳定约化的鲁宾-泰特塔的J.温斯坦使用p-adic霍奇理论和p-可分群似乎终于使一个纯粹的本地证明的对应。五位专家将被邀请就不同的相关主题进行演讲，这些主题将全面介绍当地信件背后的完整故事：介绍材料; Bushnell和P. Kutzko的类型理论; Strauch通过Lefschetz迹公式的Jacquet-Langlands对应; Weinstein上述关于Lubin-Tate塔稳定约化的结果，以及他与M. Boyarchenko讲述特殊纤维的几何形状。 研讨会将于2012年5月12日至13日举行。 更多信息可以在会议网站上找到：http://math.uchicago.edu/~lxiao/workshop_site/Number理论是纯数学的分支，致力于研究整数及其关系;一个特定的目标往往是了解给定的代数方程是否有整数解。这些问题表面上的简单掩盖了它们的复杂性，在过去的400年里，人们收集了一箱复杂的工具来解决这些问题。其中最主要的是R.朗兰兹在20世纪60年代提出了一种新的数学方法，一旦建立，数论家就可以利用其他各种看似无关的数学领域的方法。例如，300年前的问题“费马大定理”被A。怀尔斯在20世纪90年代通过建立朗兰兹通信的一部分。现在，虽然对应关系在一般情况下仍然是神秘的，但它可以被分成可以“一次一个素数”研究的部分，称为“局部对应关系”：因为素数是整数的原子，数论中的一种常见方法是一次解决一个素数问题。这些局部对应关系可以使用几何学进行研究，并且可以更好地理解;组织者的主要意图是举办一个周末研讨会，让研究生和年轻的研究人员可以了解该领域的最新发展。

The organizers intend to hold a weekend workshop at the University of Illinois at Chicago, aimed at graduate students and young researchers, on the subject of the Local Langlands Correspondence. Recent work on the special fiber of the stable reduction of the Lubin-Tate tower by J. Weinstein using p-adic Hodge theory and p-divisible groups appears finally to make possible a purely local proof of the correspondence. Five experts will be invited to give talks on different pertinent subjects, which in total present the complete story behind the local correspondence: introductory material; C. Bushnell and P. Kutzko's type theory; M. Strauch's Jacquet-Langlands correspondence via the Lefschetz trace formula; Weinstein's aforementioned results on the stable reduction of the Lubin-Tate tower, and his joint work with M. Boyarchenko on the geometry of the special fiber. The workshop will be held on May 12-13, 2012. More information can be found at the conference website: http://math.uchicago.edu/~lxiao/workshop_site/Number theory is the branch of pure mathematics devoted to the study of whole numbers and their relations; a particular goal is often to understand whether a given algebraic equation has a whole number solution. The apparent simplicity of such problems belies their complexity, and a box of intricate tools has been collected over the past 400 years to attack them. Chief among them is a 'correspondence' proposed by R. Langlands in the 1960s which, once established, would allow number theorists to exploit methods from a wide range of other, seemingly unrelated mathematical fields. For example, the 300 year old problem 'Fermat's Last Theorem' was successfully tackled by A. Wiles in the 1990s by establishing part of Langlands' correspondence. Now, although the correspondence remains mysterious in general, it can be split into pieces which can be studied 'one prime at a time', called 'local correspondences': since prime numbers are the atoms of the whole numbers, a common approach in number theory is to attack a problem one prime at a time. These local correspondences can be investigated using geometry and are much better understood; the main intent of the organizers is to host a weekend workshop where graduate students and young researchers can learn about the latest developments in the field.