In this talk, I will discuss the Real bordism spectrum and the theory of Real orientations. This is an equivariant refinement of the complex cobordism spectrum and the theory of complex orientations. The Real bordism spectrum and its norms are crucial in Hill--Hopkins--Ravenel's solution of the Kervaire invariant one problem in 2009. I will talk about their solution and explain how the Real bordism spectrum is further creating many connections between equivariant stable homotopy theory and chromatic homotopy theory. These newly established connections allow one to use equivariant machinery to attack classical computations that were long considered unapproachable. This talk contains joint work with Agnès Beaudry, Jeremy Hahn, Mike Hill, Guchuan Li, Lennart Meier, Guozhen Wang, Zhouli Xu, and Mingcong Zeng.

Xiaolin Danny Shi is a L.E. Dickson instructor in the Department of Mathematics at the University of Chicago (mentor: Peter May).  He obtained his Ph.D. in mathematics from Harvard University in 2019, advised by Michael Hopkins. His research interest is in algebraic topology, with an emphasis on equivariant homotopy theory and its connections to chromatic homotopy theory and geometric topology. 

Zoom Meeting ID：849 963 1368 
Passcode：YMSC