US-Mexico conference in representation theory and noncommutative algebra

该奖项将资助美国研究人员参加将于2017年11月27日至12月1日在墨西哥城墨西哥国立自治大学举行的第三届美墨代表理论、范畴化和非交换代数会议。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；为美国和墨西哥在这一研究领域建立国际合作创造一个环境；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。自2015年1月以来，美国-墨西哥研究所每个学年都会在这个美国-墨西哥系列中组织为期一周的会议。这些会议在美国和墨西哥之间轮流举行。第三次会议的主要科学主题将是表示理论、范畴和表示以及非交换代数的理想结构中的代数、几何和同调方法。讲座将讨论一些最新的趋势，包括：簇代数，量子对称，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。会议的网址是https://sites.google.com/view/usmexico-2017/home.。

This award will fund the participation of US-based researchers in the third US-Mexico Conference on Representation Theory, Categorification, and Non-Commutative Algebra that will take place at Universidad Nacional Autonoma de Mexico in Mexico City, November 27-December 1, 2017. Representation theory is a major branch of mathematics that studies symmetries 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 conference 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 PIs have been organizing one week-long conference in this US-Mexico series each academic year since January 2015. These conferences alternate between the US and Mexico. The main scientific topics for the 3rd conference will be algebraic, geometric and homological methods in representation theory, categorification, and representations and ideal structure of non-commutative algebras. The talks will cover some of the most recent trends including: cluster algebras, quantum symmetries, monoidal and additive categorifications, Calabi-Yau algebras and categories, and non-commutative projective algebraic geometry. The website for the conference is https://sites.google.com/view/usmexico-2017/home.