US-Mexico conference in representation theory and noncommutative algebra

这笔赠款将资助美国的参与-基于研究人员在美国-墨西哥会议上表示理论，分类，和非交换代数，将在墨西哥国立自治大学墨西哥城，2015年1月15日至18日和南加州大学，洛杉矶，2016年1月14日至17日。表示论是数学的一个主要分支，它研究物理理论和数学对象的对称性。表征理论中的主要对象往往只是更丰富结构的影子，这些结构是通过更深入的研究恢复的。非交换代数是代数学的另一个主要的相关分支，它研究在量子理论、表示论和几何中发现的交换对象的变形。会议的重点将是在代表性理论和非交换代数的接口的最新进展;在促进建立美国和墨西哥在这一研究领域之间的国际合作的环境;并在暴露研究生，博士后，和年轻的教师在这两个国家在该领域的当前发展。该系列会议有一个国际组成部分，由国际科学和工程科共同资助。PI将组织一个为期四天的会议，每学年将轮流在美国和墨西哥。会议系列的主要科学主题将是代数，几何和表示论，分类和非交换代数的同调方法。会谈将涵盖一些最新的趋势，包括：集群代数，量子群，monoidal和添加剂的代数，Calabi-Yau代数和范畴，以及非交换射影代数几何。

This grant will fund participation of U.S.-based researchers in the US-Mexico Conferences on Representation Theory, Categorification, and Non-Commutative Algebra that will take place at Universidad Nacional Autonoma de Mexico in Mexico City, January 15-18, 2015 and the University of Southern California, Los Angeles, January 14-17, 2016. Representation theory is a major branch of mathematics that studies symmetries of of physical theories and of mathematical objects. Often the main objects in representation theory are only the shadow of richer structures that are recovered through deeper study. Non-commutative algebra is another major, related branch of algebra that studies deformations of commutative objects found in quantum theories, representation theory, and geometry. The foci of the conferences will be on recent advances at the interface of representation theory and non-commutative algebra; on fostering an environment for the establishment of international collaborations between the US and Mexico in this research areas; and on exposing graduate students, post-docs, and young faculty in both countries to current developments in the field. The conference series has an international component and is co-funded by the International Science and Engineering Section.The PIs will organize one four-day conference each academic year that will alternate between the US and Mexico. The main scientific topics of the conference series will be algebraic, geometric and homological methods in representation theory, categorification, and non-commutative algebra. The talks will cover some of the most recent trends including: cluster algebras, quantum groups, monoidal and additive categorifications, Calabi-Yau algebras and categories, and non-commutative projective algebraic geometry.