Time：10:00-11:00, Friday, May 20th, 2022
ZOOM ID：829 0049 9289
Passcode：264611
Host: Dr. Xing Gu, Institute for Theoretical Sciences, Westlake University
Speaker: Dr. Hana Jia Kong, Institute for Advanced Study, Princeton, USA
Title: Motivic image-of-J spectrum via the effective slice spectral sequence
Biography：
Dr Hana Jia Kong is a postdoc member at the IAS 2021-2023. She completed her Ph.D. in Spring 2021 at the University of Chicago, under the supervision of J. Peter May and Dan Isaksen. Her research interest is algebraic topology, with a particular emphasis on motivic and equivariant homotopy theory.
Abstract:
In classical homotopy theory, the J-homomorphism connects the homotopy groups of the orthogonal groups and spheres. It was defined geometrically, and its image detects an important family of classes in the stable homotopy groups. There is a spectrum j realizing the image of J-homomorphism, defined using K-theory and the Adams operations.
In the motivic stable homotopy category, there is an analogous spectrum, the motivic image-of-J defined by Bachmann--Hopkins. I will talk about this motivic analog and how to calculate its bigraded motivic homotopy groups using the effective slice spectral sequence. Over real numbers, the result captures a regular pattern in the bigraded homotopy groups of the motivic sphere. This is joint work with Eva Belmont and Dan Isaksen.
