李志远

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I am a mathematician currently at the SCMS of Fudan University as an associated professor. My research is primarily in Algebraic Geometry and related areas.


Publication and preprints 

 Unpolarized Shafarevich conjectures for hyper-Kähler varieties (with Lie Fu, Teppei Takamatsu, Haitao Zou), arXiv:2203.10391.

 Beauville-Voisin filtrations on zero cycles of moduli space of stable sheaves on K3 surfaces (with Ruxuan Zhang), Int Math Res Notices, rnac161.

 Algebraic reverse Khovanskii-Teissier inequality via Okounkov bodies (with Chen Jiang), arXiv:2112.02847. 

 Deligne-Beilinson cohomology of universal K3 surfaces  (with Xun Zhang), to appear in Forum of Mathematics, Sigma.

 Derived isogenies and isogenies for abelian surfaces  (with Haitao Zou)arXiv:2108.08710.

 A note on Fourier-Mukai Partners of abelian varieties over positive characteristic fields (with Haitao Zou), to appear in Kyoto J. Math. 

 Complement to tautological classes on moduli spaces of hyperkähler manifolds (with Nicolas Bergeron), to appear in Annales de la Faculté des Sciences de Toulouse.

 Supersingular O’Grady varieties (with Haitao Zou and Lie Fu), Int Math Res Notices, doi.org/10.1093/imrn/rnaa349.

 Chern classes of automorphic bundles on certain Shimura varieties (with Nicolas Bergeron), in preparation.

 P=W for Lagrangian fibrations and degenerations of hyper-Kähler manifolds (with Andrew Harder, Junliang Shen and Qizheng Yin), Forum of Mathematics, Sigma, Volume 9 , 2021 , e50

 Supersingular irreducible symplectic varieties (with Lie Fu),  "Rationality of Algebraic Varieties", Progress in Mathematics, Vol. 342, 191–244, (2021)

 Algebraic cycles on moduli space of polarized hyperkähler manifolds, Proceedings of ICCM, 2017, 19–49, Int. Press, Boston, MA, [2020]

 Asymptotic Chow stability of toric Del-Pezzo surfaces (with King-Leung Lee, Jacob Sturm and Xiaowei Wang ), Math. Res. Letter. Volume 26, Number 6, 1759–1787, 2019

 Tautological classes on moduli space of hyperkahler manifolds (with Nicolas Bergeron),  Duke. Math. 2019, vol 168,1179-1230

 Noether-Lefschetz conjecture and its generalizations (with Nicolas Bergeron, John Millson and Coellete Moeglin), Invent.math, (2017) Volume 208, Issue 2: 501-552.

 Integral Hodge classes on fourfolds fibered by quadric bundles (with Zhiyu Tian), Proc. Amer. Math. Soc. 144 (2016), no. 8, 3333-3345.

 Picard groups on moduli space of K3 surfaces (with Franscois Greer, Zhiyu Tian), Int Math Res Notices (2015) (16): 7238-7257

 On Rational Connectedness of Globally F-Regular Threefolds (with Yoshinori Gongyo, Zsolt Patakfalvi, Karl Schwede, Hiromu Tanaka, Hong R. Zong), Adv. Math. 280:47-78, 2015.

 Moduli space of quasi-polarized K3 surfaces of degree 6 and 8 (with Zhiyu Tian), Chin. Ann. Math. Ser. B  42(3), 2021, 427–450

 Modular forms and special cubic fourfolds (with Letao Zhang), Adv. Math., 245:315-326, 2013.

 Sections of Calabi-Yau threefolds with K3 fibrationTrans. Amer. Math. Soc., 366:6313-6328, 2014.

 Existence of HCMU metrics on higher genus Riemann surfaces, master thesis, 2007



Thesis:

 Density of rational points on K3 surfaces over function fileds, 2012

Useful Links:

 Online LaTeX Editor Overleaf

 Shanghai Center for Mathematical Science

 List of AG conferences in China

 Ravi Vakil’s list of AG conferences