Conference Proposal: Cluster Algebra and Mathematical Physics

该奖项支持参加将于2018年5月7日至11日举行的“集群代数和数学物理（CAMP）”会议。会议将在密歇根州东兰辛的密歇根州立大学（MSU）校园举行，由密歇根州立大学数学和理论物理研究所（IMTP）主办。这次会议将是一个机会，汇集了数学和物理界提出和合作研究在这个新的和令人兴奋的重叠领域。本次会议预计将有50-70名与会者。除了周一至周五丰富的讲座时间表外，还将为研究生和早期职业数学家提供额外的海报会议。为这些参与者预留了很大一部分资金。更多的信息可以在会议网站上找到：https://sites.google.com/site/campmay7may11/First由Fomin和Zelevinsky在2001年发明，用于研究正则基的正性，簇代数的研究领域从此起飞。簇代数在超对称杨-米尔斯理论的新发展中扮演了关键角色，也等价于微扰拓扑B模型弦理论和超规范理论，特别是膜拼接和塞伯格对偶。例如，在物理学家和数学家之间的合作中，正格拉斯曼的簇理论导致了振幅面体的定义。本次会议将重点关注这一领域的新发展以及类似技术在超对称理论之外的应用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports participation in the conference "Cluster Algebras and Mathematical Physics (CAMP)", to be held May 7th to 11th, 2018. The conference will take place on the Michigan State University (MSU) campus in East Lansing Michigan and hosted by the MSU Institute for Mathematical and Theoretical Physics (IMTP). The conference will be an opportunity to bring together both the mathematics and physics communities to present and collaborate on research in this new and exciting overlapping field. The conference is designed for 50-70 participants. In addition to the rich schedule of talks for Monday to Friday, there will be an additional poster session for graduate students and early career mathematicians. A substantial portion of the funding is being set aside for such participants. Further information can be found at the conference website: https://sites.google.com/site/campmay7may11/First invented by Fomin and Zelevinsky in 2001 to study positivity of canonical bases, the research field of cluster algebra has since taken off. Cluster algebras have played a key role in new developments in supersymmetric Yang-Mills theory, also equivalent to the perturbative topological B model string theory and quiver gauge theories, specifically brane tilings and Seiberg dualities. For example, in a collaboration between physicists and mathematicians, the cluster theory of positive Grassmannian resulted in the definition of the amplituhedron. This conference will focus on new developments in this area as well as applications of similar techniques beyond supersymmetric theories.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.