The Second Transatlantic Transchromatic Homotopy Theory Conference

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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.