US-Mexico conference in representation theory and noncommutative algebra

这笔赠款将资助美国研究人员参加美国-墨西哥会议，会议将于2015年1月15-18日在墨西哥城的墨西哥国立自治大学和2016年1月14-17日在南加州大学洛杉矶举行。表示论是数学的一个主要分支，研究物理理论和数学对象的对称性。通常，表征理论的主要对象只是通过更深入的研究恢复的更丰富结构的影子。非对易代数是另一个重要的、相关的代数分支，它研究在量子理论、表示理论和几何中发现的交换对象的变形。会议的焦点将集中在表示理论和非交换代数的界面上的最新进展；促进美国和墨西哥在这一研究领域建立国际合作的环境；以及让两国的研究生、博士后和年轻教师了解该领域的最新发展。该系列会议有一个国际部分，由国际科学和工程部共同资助。国际科学和工程部将在每个学年组织一个为期四天的会议，在美国和墨西哥之间轮流举行。会议系列的主要科学主题将是表示理论、分类和非交换代数中的代数、几何和同调方法。讲座将讨论一些最新的趋势，包括：簇代数，量子群，么半群和加性范畴化，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.