个人简介
I received a bachelor degree in mathematics at Peking University, China, and finished my Ph.D in pure mathematics at MIT under the supervision of Kiran S. Kedlaya. After that, I was a Dickson Instructor at University of Chicago, and I later held faculty positions at University of California, Irvine, and at University of Connecticut.
Employment
2009.9-2013.2, Dickson Instructor, University of Chicago.
2013.3-2014.6, Assistant Professor, University of California, Irvine.
2014.8-2019.8, Assistant Professor, University of Connecticut, Storrs (tenured on 2019.8).
2019.8-present, Professor, Beijing International Center for Mathematical Research.
Education:
2005.9-2009.6 Ph.D., Massachusetts Institute of Technology (Advisor: Kiran S. Kedlaya)
2001.9-2005.7 B.S. in Mathematics, Peking University, China
Awards and grants:
NSF CAREER Grant: "Slopes of p-adic Modular Forms," 2018--2019 (DMS--1752703).
Research Excellence Program, 2018--2019, UConn.
NSA conference Grant: "Connecticut Summer School in Number Theory 2018," February 2018, Joint with Jennifer Balakrishnan, Keith Conrad, and Álvaro Lozano-Robledo)
NSF conference Grant: "Connecticut Summer School in Number Theory," August 2016, (DMS-1608789), Joint with Keith Conrad, Amanda Folsom, and Álvaro Lozano-Robledo)
NSF Grant: "Special fibers of modular varieties", 2015-2018, (DMS-1502147).
CORCL faculty research grant, UC Irvine, 2014.
Simons Foundation Collaboration Grants, 2013-2016.
NSF conference Grant: "Towards a local proof of local Langlands correspondence", May 2013 (DMS-1207440).
International Mathematics Olympiad: Gold medal, 2001.
研究领域
Geometry of Shimura varieties
p-adic automorphic forms
Slopes of Newton polygons
p-adic Hodge theory and (φ, Γ)-modules
Ramification theory
近期论文
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Slopes of modular forms and geometry of eigencurves, (with Ruochuan Liu, Nha Truong and Bin Zhao), arXiv:2302.07697.
A local analogue of the ghost conjecture of Bergdall-Pollack, (with Ruochuan Liu, Nha Truong and Bin Zhao), arXiv:2206.15372.
Deformation of rigid conjugate self-dual Galois representations, (with Yifeng Liu, Yichao Tian, Wei Zhang, and Xinwen Zhu), arXiv:2108.06998.
On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives, (with Yifeng Liu, Yichao Tian, Wei Zhang, and Xinwen Zhu), arXiv:1912.11942, Inventiones Mathematicae 228 (2022), 107–375.
Cycles on Shimura varieties via geometric Satake, Example, (with Xinwen Zhu),
Cycles on Shimura varieties via geometric Satake, (with Xinwen Zhu), arXiv:1707.05700
On the parity conjecture in finite-slope families, (with Jonathan Pottharst), arXiv:1410.5050.
Tate cycles on quaternionic Shimura varieties over finite fields, (with Yichao Tian), Duke Mathematical Journal, 168 (2019), 1551--1639. arXiv:1410.2321.
On vector-valued twisted conjugate invariant functions on a group, (with Xinwen Zhu), in Representation of Reductive Groups, Proceedings of Symposia in Pure Mathematics 101, 361--425. arXiv:1802.05299.
Unramfiedness of Galois representations arising from Hilbert modular surfaces, (with Matthew Emerton and Davide Reduzzi), Forum of Mathematics Sigma, 5 (2017), E29. arXiv:1410.6203
Tate cycles on some unitary Shimura varieties mod p, (with David Helm and Yichao Tian), Algebraic Number Theory 11 (2017), 2213--2288. arXiv:1410.2343
Slopes for higher rank Artin-Schreier-Witt Towers, (with Rufei Ren, Daqing Wan, and Myungjun Yu), Trans. Amer. Math. Soc. 370 (2018), 6411-6432. Journal arXiv:1605.02254.
The eigencurve over the boundary of weight space, (with Ruochuan Liu and Daqing Wan), Duke Mathematical Journal 166 (2017), 1739-1787. arXiv:1412.2584,
Slopes of eigencurves over boundary disks, (with Daqing Wan and Jun Zhang), Mathematische Annalen 369 (2017), 487-537. arXiv:1407.0279,
Partial Hasse invariants on splitting models of Hilbert modular varieties, (with Davide Reduzzi), Annales Scientifiques de l'ENS 50 (2017), 579-607. arXiv:1405.6349
Galois representations and torsion in the coherent cohomology of Hilbert modular varieties, (with Matthew Emerton and Davide Reduzzi) Journal für die reine und angewandte Mathematik 726 (2017), 93-127, arXiv:1307.8003,
On Goren-Oort stratification for quaternionic Shimura varieties, (with Yichao Tian), Compositio Mathematica 152 (2016), 2134--2220. arXiv:1308.0790
p-adic cohomology and classicality of overconvergent Hilbert modular forms, (with Yichao Tian), in Astérisque 382 (2016), 73-162. arXiv:1308.0779.
Newton slopes for Artin-Schreier-Witt towers, (with Christopher Davis and Daqing Wan), Mathematische Annalen 364 (2016), Issue 3, 1451-1468. arXiv:1310.5311,
Tensor being crystalline implies each factor being crystalline up to twists, (Appendix to "On automorphy of certain Galois representations of GO4-type", by Tong Liu and Jiu-Kang Yu, Jounal of Number Theory (special issue for Prof. Winnie Li) 161 (2016) 49-74, pdf.
Cleanliness and log-characteristic cycles of vector bundles with flat connections, Mathematische Annalen 362 (2015), Issue 1-2, 579-627. arXiv:1104.1224,
Gauss-Manin connections for p-adic families of nearly overconvergent modular forms, (with Robert Harron) Annales de l'institut Fourier 64 (2014), no.6, 2449-2464. arXiv:1308.1732,
Ramification of higher local fields, approaches and questions, (with Igor Zhukov), Algebra i Analiz, 26 (2014), issue 5, 1-40. reprinted in Proceedings of the 2nd International Conference on Valuation Theory. pdf
Cohomology of arithmetic families of (φ, Γ)-modules, (with Kiran S. Kedlaya and Jonathan Pottharst), Journal of American Mathematical Society 27 (2014), 1043-1115. arXiv:1203.5718,
On refined ramification filtrations in the equal characteristic case, Algebra and Number Theory 6 (2012), no. 8, 1579-1667. arXiv:0911.1802,
On ramification filtrations and p-adic differential equations, II: mixed characteristic case, Compositio Mathematica 148 (2012), no.2, 415-463. arXiv:0811.3792,
On ramification filtrations and p-adic differential equations, I: equal characterisitc case, Algebra and Number Theory 4 (2010), no.8, 969-1027. arXiv:0801.4962,
Differential modules on p-adic polyannuli, (with Kiran S. Kedlaya), Journal de l'Institut de Mathematiques de Jussieu 9 (2010), 155-201. arXiv:0804.1495
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