The Second Transatlantic Transchromatic Homotopy Theory Conference

这项国家科学基金会奖为美国的初级研究人员提供旅行资金，用于参加将于2020年8月2日至7日在德国雷根斯堡大学举行的“第二届跨大西洋泛色子同伦理论会议”。这个为期五天的活动将包括世界专家的演讲以及初级研究人员的演讲。本次会议的目的是将泛色同伦理论的专家，在该领域工作的初级研究人员和研究生，以及包括算术几何和微分几何在内的密切相关领域的专家聚集在一起。第二个目标是给非常早期的职业研究人员(例如，研究生和博士后)有机会以简短的谈话形式描述他们的研究。在这样做的过程中，不仅研究生会得到个人指导，而且该领域以外的数学家也会接触到变色同伦理论的进展。我们希望这将大大提高人们对已开发的技术和所面临的问题的认识。泛色同伦理论是色同伦理论中一个新兴的分支。色同伦理论通过将稳定同伦范畴分解成“色层”来组织稳定同伦范畴。在研究这些层的过程中，代数拓扑学家发现了同伦理论与代数几何、数论、高范畴论和超对称场论之间的深刻关系。为了将各色层的结果集合成关于稳定同伦范畴的全局结果，必须理解色层之间的关系。这是转色同伦理论的主要目标。自2017年6月在雷根斯堡大学召开的第一届跨大西洋泛色同伦理论会议以来，泛色同伦理论在其他领域的实际应用开始出现。特别是，转色同伦理论中的基本计算已经非常成功地应用于更好地理解等变稳定同伦范畴。本次会议的主要科学目的是描述该领域的前沿工作，解释在其他数学领域的应用，并从相关领域的专家那里获得意见。我们的演讲者包括在色同伦理论、算术几何、微分几何和群论方面的世界知名专家，他们的工作都在某种程度上与泛色同伦理论有关，以及正在迅速推动该领域发展的早期职业数学家。更多信息可在https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/SFB_transchromatic_2020.This上获得，该奖项反映了美国国家科学基金会的法定使命，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 National Science Foundation award provides travel funds for US based junior researchers to travel to "The Second Transatlantic Transchromatic Homotopy Theory Conference" that will take place at the University of Regensburg, Germany from August 2-7, 2020. This five day event will include talks by world experts as well as talks by junior researchers. The aim of this conference is to bring experts in transchromatic homotopy theory together with both junior researchers and graduate students working in the area as well as experts in closely associated fields including arithmetic geometry and differential geometry. A second aim is to give very early career researchers (i,e,. graduate students and postdocs) a chance to describe their research in the form of shorter talks. In doing this, not only will graduate students receive personal mentoring, but mathematicians outside of the field will be exposed to what is going on in transchromatic homotopy theory. We hope that this will significantly raise awareness of both the techniques that have been developed and also the problems that are faced.Transchromatic homotopy theory is a rapidly emerging subarea of chromatic homotopy theory. Chromatic homotopy theory organizes the stable homotopy category by decomposing it into "chromatic layers". In studying these layers, algebraic topologists have found deep relationships between homotopy theory and algebraic geometry, number theory, higher category theory, and supersymmetric field theories. To assemble results at each chromatic layer into global results about the stable homotopy category, the relationship between the chromatic layers must be understood. This is the primary goal of transchromatic homotopy theory. Since the first Transatlantic Transchromatic Homotopy Theory conference, which occurred at the University of Regensburg in June, 2017, real applications of transchromatic homotopy theory to other areas have begun to appear. In particular, fundamental calculations in transchromatic homotopy theory have been applied very successfully to better understand the equivariant stable homotopy category. The primary scientific aim of this conference is to describe work on the forefront of this area, explain applications to other mathematical areas, and also to get input from experts in related areas. Our speakers consist of established world experts in chromatic homotopy theory, arithmetic geometry, differential geometry, and group theory, all of whose work is related in some way to transchromatic homotopy theory, as well as early career mathematicians who are rapidly pushing the field forward. More information is available at https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/SFB_transchromatic_2020.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.