Western Algebraic Geometry Seminar - Fall 2009

2009年10月24日和25日，西部代数几何研讨会(WAGS)将在加州大学洛杉矶分校举行。WAGS是一个周末会议，每年在美国西部和加拿大的多个机构举行两次，包括犹他大学、斯坦福大学、不列颠哥伦比亚大学、加州大学伯克利分校、科罗拉多州立大学、华盛顿大学，现在是科罗拉多大学和亚利桑那大学。该研讨会的起源可以追溯到1989年由H.Clemens、D.Gieseker、M.Green、J.Kollar和R.Lazarsfeld发起的犹他州-加州大学洛杉矶分校代数几何研讨会。WAGS目前的形式自2002年以来一直在运行，每个WAGS都有50多名参与者。UCLA-WAGS目前有55名注册研究生，约30名教师参与。WAGS为在美国西部建立一个充满活力的代数几何社区发挥了重要作用。它为研究人员在更广泛的地理区域内相互联系提供了重要的方式。这一点在西方尤为重要，因为许多代数几何学家只有他们系里的成员，而美国西部研究机构之间的地理距离意味着它们可能相对孤立。WAGS的一个重要特点是，它为他们提供了一个机会，让他们聚在一起，听取相当于一学期的研讨会，同样重要的是，他们彼此之间以及与年轻的研究人员进行了详细的会面。研究生有机会与资深教师见面，并对老年人有更广泛的认识，而不是只与他们的导师交谈。世界上许多目前领导代数几何领域的人都是通过世界代数几何系统发展起来的，这一事实突显了WAGS的成功。今年秋天的演讲者将讨论他们在代数几何领域的研究。代数几何涉及代数方程的解集，长期以来一直是数学中的一个中心学科，与现代数学的几乎每个方面都有着深刻而实质性的联系。除了与邻国的自然互动之外？数学领域，如数论、辛几何、拓扑学和交换代数，最近在代数几何和显然是外国的？之间出现了令人兴奋的联系。包括数学物理、生物、数字通信和机器人等领域。有许多不同的方法来研究代数几何，利用各种各样的技术工具；交换代数、复分析、层理论、上同调方法和组合技术都发挥着重要作用。代数几何仍然是一个非常活跃的研究领域。最近的一年尤其令人兴奋，因为古典音乐难道不能取得进展吗？问题的根源可以追溯到19世纪(例如最小模型程序)，以及新工具和技术的发展(例如吉文顿？S形式主义扩展到堆栈世界)。这种广泛而活跃的老年人在美国西部有着广泛的代表性。今年秋天WAGS的演讲者代表了该领域的广泛研究，以及知名人物和年轻活跃的研究人员的良好组合。组织者预计，加州大学洛杉矶分校的会议将继续促进美国西部代数几何社区的发展。

On October 24 and 25, 2009, the Western Algebraic Geometry Seminar(WAGS) will meet at the University of California at Los Angeles. WAGS is a weekend conference held twice a year at various institutions in the western part of the United States and Canada, including the University of Utah, Stanford University, the University of British Columbia, the University of California at Berkeley, Colorado State University, the University of Washington and now the University of Colorado and the University of Arizona. The seminar traces its roots back to the Utah-UCLA Algebraic Geometry Seminar started in 1989 by H. Clemens, D. Gieseker, M. Green, J. Kollar, and R. Lazarsfeld. In its current form WAGS has run since 2002, and every WAGS has had over 50 participants. For the UCLA-WAGS, currently there have been55 registered graduate students, and there are about 30 faculty participants.WAGS has been instrumental in building a vibrant algebraic geometry community in the western part of US. It provides an important way for researchers to connect to one another in the broader geographical area. This is especially important in the west since many algebraic geometers there are the only members of their department in the field, and the geographical distance between the research institutions in the western United States means they can be relatively isolated. A crucial feature of WAGS is that it provides an opportunity for them to come together and hear a semesters worth of seminars, and equally importantly, meet at length with each other and with younger researchers. Graduate students get the opportunity to meet senior faculty, and to get a broader sense of the field than they would get from speaking only with their advisor. The success of WAGS is underscored by the fact that many people around the world currently leading the field of algebraic geometry have come up through the WAGS system.The speakers this fall will discuss their research in the field of algebraic geometry. Algebraic geometry concerns the solution sets of algebraic equations, and has long been a central subject in mathematics with deep and substantial connections to almost every aspect of modern mathematics. Beyond the natural interactions with ?neighboring? mathematical fields such as number theory, symplectic geometry, topology, and commutative algebra, exciting connections have recently emerged between algebraic geometry and apparently ?foreign? fields including mathematical physics, biology, digital communications, and robotics. There are numerous different approaches to the study of algebraic geometry, utilizing a wide variety of technical tools; commutative algebra, complex analysis, sheaf theory, cohomological methods, and combinatorial techniques all play important roles. Algebraic geometry continues to be a very active area of research. The recent year has been particularly exciting, as significant progress was made on ?classical? problems with roots going back to the 19th century (such as the minimal model program), as well as on the development of new tools and techniques (for example the extension of Givental?s formalism to the world of stacks). This broad and active field is widely represented in the Western United States. The speakers at WAGS this fall represent a broad spectrum of research in the field and a good mix of established figures and young active researchers. The organizers expect that the conference at UCLA will continue to facilitate the development of the algebraic geometry community in the Western United States.