中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人：时骁霖 博士（University of Chicago）
题 目：Complex cobordism, equivariant stable homotopy theory, and the Kervaire invariant
时 间：2021.07.01（星期四），10:00-11:00
地 点：数学院南楼N204室
腾讯会议：292 901 454
摘 要：I will talk about the complex cobordism spectrum and its role in studying the stable homotopy groups of spheres. Then, I will talk about the proof of the celebrated Kervaire invariant one problem by Hill—Hopkins—Ravenel using an equivariant refinement of the complex cobordism spectrum and equivariant stable homotopy theory. These newly established techniques allow one to use equivariant machinery to attack classical computations that were long considered unapproachable.
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报告人：时骁霖 博士（University of Chicago）
题 目：Real bordism, Real orientations, and Lubin--Tate spectra
时 间：2021.07.01（星期四），14:30-16:30
地 点：数学院南楼N902室
腾讯会议：875 302 456
摘 要：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.
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报告人：时骁霖 博士（University of Chicago）
题 目：The Slice Spectral Sequence of a $C_4$-equivariant height 4 Lubin—Tate theory
时 间：2021.07.02（星期五），09:30-11:30
地 点：数学院南楼N802室
腾讯会议：764 508 461
摘 要：I will talk about the slice spectral sequence of a $C_4$-equivariant spectrum. This spectrum is a variant of the detection spectrum that Hill-Hopkins-Ravenel used in the proof of the Kervaire invariant problem. After periodization and K(4)-localization, this spectrum is equivalent to a height-4 Lubin-Tate theory $E_4$ with $C_4$-action induced from the Goerss-Hopkins-Miller theorem. In particular, our computation shows that $E_4^{hC_12}$ is 384-periodic. This is joint work with Mike Hill, Guozhen Wang, and Zhouli Xu.
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