User:HomotopyTheory/sandbox

Zhouli Xu (Chinese: 徐宙利; born 1987) is a Chinese mathematician specializing in topology. He is currently an Assistant Professor of Mathematics at the University of California, San Diego. Xu is known for computations of homotopy groups of spheres.

Xu earned both of his B.S. and M.S. in Mathematics from Peking University and his Ph.D. from University of Chicago in 2017 under the supervision of J. Peter May and Mark Mahowald.^{[1][2] [3]}

Xu was a C.L.E. Moore Instructor at Massachusetts Institute of Technology from 2017 to 2020. He has been a member of the mathematics faculty at University of California, San Diego since 2020.^[2]

He works in algebraic topology and focuses on classical, motivic and equivariant homotopy groups of spheres, with connections and applications to chromatic homotopy theory and geometric topology. ^[2]

His research accomplishments include his joint works with collaborators in proving that the 61-dimensional sphere has a unique smooth structure, proving a "10/8 + 4"-theorem on the geography problem in 4-dimensional topology, developing the motivic deformation method and the Chow t-structure, and computing the classical and motivic stable homotopy groups of spheres in the previously unknown range of dimensions. ^[4]

He was a recipient of the Plotnick Fellowship in 2015, and the William Rainey Harper Dissertation Fellowship in 2016, both by the University of Chicago. ^{[2] [5]}

In 2022, he is an invited speaker in the topology section at the International Congress of Mathematicians in St.Petersburg.^{[4] [6]}

• "The Strong Kervaire invariant problem in dimension 62", Geometry and Topology 20-3 (2016), 1611–1624.
• (with Guozhen Wang) "The triviality of the 61-stem in the stable homotopy groups of spheres", Annals of Mathematics 186(2) (2017), 501–580.
• (with Dan Isaksen, Guozhen Wang) "Stable homotopy groups of spheres", Proceedings of the National Academy of Sciences October 6, 2020 117 (40) 24757-24763.
• (with Michael J. Hopkins, Jianfeng Lin, XiaoLin Danny Shi) "Intersection forms of spin 4-manifolds and Pin(2)-equivariant Mahowald invariants", preprint.
• (with Dan Isaksen, Guozhen Wang) "More Stable Stems", preprint.
• (with Bogdan Gheorghe, Guozhen Wang) "The special fiber of the motivic deformation of the stable homotopy category is algebraic", Acta Mathematica Vol. 226, No. 2 (2021), 319–407.
• (with Tom Bachmann, Hana Jia Kong, Guozhen Wang) "The Chow t-structure on the ∞-category of motivic spectra", To appear in Annals of Mathematics.

Category:1987 births Category:Living people Category:Chinese science writers Category:University of Chicago alumni Category:University of California, San Diego faculty Category:21st-century Chinese mathematicians Category:Topologists Category:Peking University alumni