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Address: UCLA Department of Mathematics, 520 Portola Plaza, Los Angeles, CA 90095-1555
Office: MS 6931
email: xuzhouli12356125661@ucla.edu (delete all numbers)
I am a Professor in the Department of Mathematics at UCLA, starting November 2024.
From 2020 to 2024, I held the positions of Assistant Professor, Associate Professor with tenure, and Professor in the Department of Mathematics at UC San Diego.
Prior to that, from 2017 to 2020, I was a C.L.E. Moore Instructor in the Department of Mathematics at Massachusetts Institute of Technology, under the mentorship of Haynes Miller.
I received my Ph. D. from the University of Chicago in 2017,
mentored by J. Peter May, Daniel C. Isaksen, and Mark Mahowald.
Here is my CV.
I teach Math 225C in the spring quarter. See Canvas for more info.
On the Last Kervaire Invariant Problem (arXiv)
Theorem (Lin--Wang--Xu) The element $h_6^2$ survives to the $E_\infty$-page in the Adams spectral sequence.
Corollary There exist framed manifolds of Kervaire invariant one in dimension 126.
Adams charts on Weinan's website.
Minicourse given at eCHT.
I'm an Editor of Mathematische Zeitschrift. Submissions of papers in topology are welcome!
I'm an Associate Editor of Peking Mathematical Journal. Submissions of papers in topology are welcome!
I am deeply honored to have been named 2025-26 AMS Centennial Research Fellow.
I am deeply honored to have been named as a Fellow of the American Mathematical Society of class 2023.
I am deeply honored to receive the K-Theory Prize in 2022.
I am deeply honored to speak at the ICM 2022. Here is a link of my ICM talk with Guozhen Wang.
My research was partially sponsored by NSF Grant DMS 2105462 (2021-2024),
and NSF Grant DMS 1810638 (2018-2020), and DMS 2043485 (2020-2021).
My papers are on my research page. You may also find the videos of some of my talks on this page.
Here are some Adams charts of the computations of the classical and C-motivic stable homotopy groups of spheres that I have done with Daniel C. Isaksen and Guozhen Wang.
Research Interests:
Algebraic Topology -- more specifically, classical, motivic and equivariant stable homotopy groups of spheres, with connections and applications to algebraic geometry and geometric topology.
My collaborators:
Tom Bachmann, Agnès Beaudry, Mark Behrens, Eva Belmont, Prasit Bhattacharya, Irina Bobkova, Robert Burklund, Hood Chatham, Dominic Culver, Bogdan Gheorghe, Michael Hill, Michael Hopkins, Daniel C. Isaksen, Hana Jia Kong, Manuel Krannich, Achim Krause, Guchuan Li, Jianfeng Lin, Weinan Lin, Yunze Lu, Viet-Cuong Pham, Douglas Ravenel, XiaoLin Danny Shi, Matthew Stoffregen, Guozhen Wang, Shangjie Zhang, Yifei Zhu
Conferences I co-organized:
(Upcoming) Computations in stable homotopy theory. American Institute of Mathematics, Pasadena, California. October 2025.
(Upcoming) Workshop on Theory and Computation in Mathematical Physics and Topology. Tianyuan Mathematics Research Center, Kunming, China. September 2025.
(Upcoming) IWoAT 2025. Zhejiang University, Hangzhou, China, July 2025.
(Upcoming) Summer school on computations with the Adams spectral sequence and the Last Kervaire Invariant Problem. Westlake University, Hangzhou, China, July 2025.
Workshop on Stable Homotopy Theory. TSIMF. Sanya, China, March 2025.
IWoAT Special Conference in honor of Prof. J. Peter May. SUSTech, Shenzhen, China, March 2025.
IWoAT Symposium at SUSTech, Shenzhen, China, November 2024.
Computer-assisted research in geometry and topology Tianyuan Mathematics Research Center, Kunming, China. September 2024.
International Workshop on Algebraic Topology 2024. Shanghai Center for Mathematical Sciences (SCMS), Shanghai, China, July 2024.
IWoAT Summer School 2024: Motivic Stable Homotopy Theory Shanghai Center for Mathematical Sciences (SCMS), Shanghai, China, June 2024.
Special Session on Homotopy theory, Fall 2023 Sectional Meeting of the AMS Western Section. Creighton University, Omaha, NE.
IWoAT Summer School 2023 on “Operads, spectra, and multiplicative structures”, Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, China, August 14-19, 2023.
International Workshop on Algebraic Topology 2023 (IWoAT 2023), Beijing International Center for Mathematical Research (BICMR), Beijing, China, July 24-28, 2023.
Summer School on Chromatic Homotopy Theory and Higher (Infinity-Categorical) Algebra, Shanghai Center for Mathematical Sciences & School of Mathematical Sciences, Fudan University Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, August 15-26, 2022.
Summer School on Equivariant Homotopy Theory, Shanghai Center for Mathematical Sciences (SCMS), Shanghai, China, July 2021.
Summer School on Equivariant Homotopy Theory, Shanghai Center for Mathematical Sciences (SCMS), Shanghai, China, August 2019.
International Workshop on Algebraic Topology 2019 (IWoAT 2019), Shanghai Center for Mathematical Sciences (SCMS), Shanghai, China, August 2019.
International Workshop on Algebraic Topology 2018 (IWoAT 2018), SUSTech, Shenzhen, China, June 2018.
Midwest Topology Seminar, University of Chicago, Chicago, Illinois, May 2017.
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