Conference: Representation Theory and Symplectic Algebraic Geometry

会议：表示论与辛代数几何

• 批准号: 1201580
• 负责人: Nicholas Proudfoot
• 金额: $ 4.72万
• 依托单位: University of Oregon Eugene
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-05-01 至 2014-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1201580&HistoricalAwards=false
• 关键词: Conference; Representation; Theory; Symplectic; Algebraic

The conference "Representation Theory and Symplectic Algebraic Geometry" will take place at the CIRM (Luminy) on the dates July 9-13, 2012. The appearance of symplectic algebraic varieties in representation theory has come primarily from two different directions. First, symplectic algebraic varieties admit quantizations, and there are many symplectic algebraic varieties whose rings of "quantized functions" are of independent algebraic interest. Second, they appear through the categorification program, also known as "higher representation theory." In many examples of categorification, the categories in questions have geometric interpretations involving sheaves on symplectic algebraic varieties. This grant will provide funding for U.S. researchers to participate in a conference that addresses both of these topics. More information about this conference can be found on the CIRM web page: http://www.cirm.univ-mrs.fr/index.html/spip.php?rubrique2&EX=info_rencontre&annee=2012&id_renc=637&lang=en.The central theme in algebraic geometry is the rich interplay between algebraic objects (called "rings" and "modules") and geometric objects (called "varieties" and "sheaves"). One of the goals of geometric representation theory is to exploit this interplay by using geometry to prove theorems about algebra. This approach has its roots in the early 1980s when it was used to prove the Kazhdan-Lusztig conjecture, an outstanding problem in algebra that, superficially, had nothing to do with geometry. The field has experienced enormous growth in the past decade, and this conference will allow researchers from around the world to keep abreast of recent work.

“表示理论与辛代数几何”会议将于2012年7月9日至13日在CIRM （Luminy）举行。表示理论中辛代数变分的出现主要来自两个不同的方向。首先，辛代数变量允许量化，并且有许多辛代数变量的“量化函数”环具有独立的代数意义。其次，它们通过分类程序出现，也被称为“高级表征理论”。在许多分类的例子中，所讨论的范畴都有几何解释，涉及辛代数变体上的束。这笔拨款将为美国研究人员参加讨论这两个主题的会议提供资金。关于这次会议的更多信息可以在CIRM网页上找到：http://www.cirm.univ-mrs.fr/index.html/spip.php?rubrique2&amp；EX=info_rencontre&annee=2012&id_renc=637&lang=en.The代数几何的中心主题是代数对象（称为“环”和“模块”）和几何对象（称为“品种”和“束”）之间丰富的相互作用。几何表示理论的目标之一是利用这种相互作用，用几何来证明代数定理。这种方法起源于20世纪80年代初，当时它被用来证明Kazhdan-Lusztig猜想，这是代数中的一个突出问题，表面上看，与几何无关。该领域在过去十年中经历了巨大的发展，这次会议将使来自世界各地的研究人员能够及时了解最新的工作。