Zhouli Xu
Publications:
Stable homotopy groups of spheres: From dimension 0 to 90,
(previously called More stable stems),
(with Daniel C. Isaksen and Guozhen Wang).
Publications Mathématiques de l'IHÉS. 107-243 (2023). [arXiv:2001.04511], 137 pages.
Stable homotopy groups, (with Guozhen Wang).
European Mathematical Society Magazine. 128 (2023), pp. 23–29. 7 pages.
Stable homotopy groups of spheres and motivic homotopy theory,
(with Daniel C. Isaksen and Guozhen Wang).
Proceedings of the International Congress of Mathematicians 2022. PP. 2768-2790.
The topological modular forms of RP^2 and RP^2 smash CP^2,
(with Agnès Beaudry, Irina Bobkova, Viet-Cuong Pham).
Journal of Topology. 15(2022) 1864-1926. [arXiv:2103.10953], 63 pages.
The Chow t-structure on the infinite category of motivic spectra,
(with Tom Bachmann, Hana Jia Kong and Guozhen Wang).
Annals of Mathematics. Volume 195 (2022), Issue 2, 707-773. [arXiv:2012.02687], 67 pages.
Intersection forms of spin 4-manifolds and Pin(2)-equivariant Mahowald invariants,
(with Michael Hopkins, Jianfeng Lin and XiaoLin Danny Shi).
Communications of the American Mathematical Society, 2 (2022), 22-132. [arXiv:1812.04052], 111 pages.
The telescope conjecture at height 2 and the tmf resolution,
(with Agnès Beaudry, Mark Behrens, Prasit Bhattacharya and Dominic Culver).
Journal of Topology.14(2021): 1243-1320. [arXiv:1909.13379], 78 pages.
The special fiber of the motivic deformation of the stable homotopy category is algebraic,
(with Bogdan Gheorghe and Guozhen Wang).
Acta Mathematica. Vol. 226, No. 2 (2021), pp. 319-407. [arXiv:1809.09290], 89 pages.
Stable homotopy groups of spheres,
(with Daniel C. Isaksen and Guozhen Wang).
Proceedings of the National Academy of Sciences. October 6, 2020 117 (40) 24757-24763. [arXiv:2001.04247].
The slice spectral sequence of a C_4-equivariant height-4 Lubin-Tate theory,
(with Michael Hill, XiaoLin Danny Shi and Guozhen Wang).
Memoirs of the American Mathematical Society. [arXiv:1811.07960], 107 pages.
Mahowald square and Adams differentials,
Contemporary Mathematics. Homotopy Theory: Tools and Applications, vol. 729,
Amer. Math. Soc., Providence, RI, 2019, pp. 255-268. 14 pages.
Hurewicz images of real bordism theory and real Johnson-Wilson theories, (with Guchuan Li, XiaoLin Danny Shi and Guozhen Wang),
Advances in Mathematics. Volume 342, 21 January 2019, Pages 67-115. [arXiv:1707.03438], 48 pages.
Some extensions in the Adams spectral sequence and the 51-stem, (with Guozhen Wang),
Algebraic and Geometric Topology. 18 (2018), 3887–3906. [arXiv:1707.01620], 20 pages.
On the E_2-term of the bo-Adams spectral sequence,
(with Agnès Beaudry, Mark Behrens, Prasit Bhattacharya and Dominic Culver).
Journal of Topology. 13 (2020) 356-415. [arXiv:1702.00230], 60 pages.
The triviality of the 61-stem in the stable homotopy groups of spheres, (with Guozhen Wang),
Annals of Mathematics. Vol.186 (2017), Issue 2, 501-580. [arXiv:1601.02184], 80 pages.
Motivic stable homotopy and the stable 51 and 52 stems, (with Daniel C. Isaksen),
Topology and its Applications. 190 (2015) 31-34. [arXiv:1411.3447], 4 pages.
The Strong Kervaire invariant problem in dimension 62,
Geometry and Topology. 20-3 (2016),1611-1624. [arXiv:1410.6199], 14 pages.
arXiv preprints:
The Adams differentials on the classes h_j^3,
(with Robert Burklund).
[arXiv:2302.11869], 55 pages.
The reduced ring of the RO(G)-graded C_2-equivariant stable stems,
(with Eva Belmont and Shangjie Zhang).
[arXiv:2211.04611], 13 pages.
The algebraic Atiyah-Hirzebruch spectral sequence of the real projective space, (with Guozhen Wang).
[arXiv:1601.02185], 73 pages.
Survey article:
A Survey of Computations of Homotopy Groups of Spheres and Cobordisms. PDF.
(wrote with Guozhen when we were students at Peking University in 2010)
Papers in preparation:
Classical stable homotopy groups of spheres via F_2-synthetic methods, (with Robert Burklund and Daniel C. Isaksen).
Videos of some of my talks:
Monopole Floer Theory and Homotopy Theory, Pt 2, (joint with Jianfeng Lin, XiaoLin Danny Shi)
Introductory Workshop: Floer Homotopy Theory, MSRI, Sep 2022
Stable homotopy groups of spheres and motivic homotopy theory, (joint with Guozhen Wang)
International Congress of Mathematicians 2022, July 2022
Electronic Computational Homotopy Theory seminar, Nov 2018
Derived algebraic geometry and chromatic homotopy theory, Isaac Newton Institute for Mathematical Sciences, Cambridge, United Kingdom, Sep 2018
Chromatic Homotopy Theory: Journey to the Frontier, the University of Colorado, Boulder, Colorado, May 2018
Homotopy theory: tools and applications, University of Illinois at Urbana-Champaign, Urbana, Illinois, July 2017