Xinwen Zhu

Xinwen Zhu (born 1982 in Sichuan, China) is a professor of mathematics at the California Institute of Technology. His work deals primarily with geometric representation theory and in particular the Langlands program, tying number theory to number theory and quantum physics.^[1]

Zhu obtained his A.B. in mathematics from Peking University in 2004 and his Ph.D. in mathematics from the University of California, Berkeley in 2009 under the direction of Edward Frenkel.^[2] He taught at Harvard University as a Benjamin Peirce Lecturer and at Northwestern University as an assistant professor before joining the Caltech faculty in 2014. According to the American Mathematical Society, "[Zhu] studies the geometry and topology of flag varieties of loop groups and applies techniques from the geometric Langlands program to arithmetic geometry."^[3]

The awards Zhu has received include an AMS Centennial Fellowship in 2013 and a Sloan Fellowship in 2015.^[4] His research has been published in Annals of Mathematics and Inventiones mathematicae, among other mathematics journals. Zhu, Wei Zhang, Xinyi Yuan and Zhiwei Yun are frequent collaborators.^[5]

Publications (selected)

• (with Edward Frenkel) "Gerbal Representations of Double Loop Groups", Int. Math. Res. Not. IMRN 2012 (2012), No. 17, 3929-4013.
• (with George Pappas]) "Local models of Shimura varieties and a conjecture of Kottwitz", Invent. Math. 194 (2013), No. 1, 147–254.
• "On the coherence conjecture of Pappas and Rapoport", Ann. of Math. 180 (2014), No. 1, 1-85.
• (with Denis Osipov) "A categorical proof of the Parshin reciprocity laws on algebraic surfaces", Algebra Number Theory 5 (2011), No. 3, 289–337.
• "Affine Demazure modules and T-fixed point subschemes in the affine Grassmannian", Adv. Math. 221 (2009), No. 2, 570-600.
• "Affine Grassmannians and the geometric Satake in mixed characteristic", Ann. of Math., to appear in forthcoming issue.
• (with Edward Frenkel) "Any flat bundle on a punctured disc has an oper structure", Math. Res. Lett. 17 (2010), no. 1, 27–37.
• "The geometric Satake correspondence for ramified groups", Ann. Sci. Ec. Norm. Super. 48 (2015), no. 2, 409-451.
• (with Zhiwei Yun) "Integral homology of loop groups via Langlands dual groups", Represent. Theory 15 (2011), 347-369.
• (with An Huang, Bong H. Lian) "Period integrals and the Riemann–Hilbert correspondence", J. Differential Geom. 104 (2016), No. 2, 325-369.
• (with Tsao-Hsien Chen) "Geometric Langlands in prime characteristic", preprint.

References

1. "Prime Numbers, Quantum Fields, and Donuts: An Interview with Xinwen Zhu", Caltech. Retrieved on 3 December 2016.
2. "Xinwen Zhu", Caltech. Retrieved on 3 December 2016.
3. "Mathematics People", Notices of the AMS. Retrieved on 3 December 2016.
4. "Caltech Professors Awarded 2015 Sloan Fellowships", Caltech. Retrieved on 3 December 2016.
5. "Math Quartet Joins Forces on Unified Theory", Quanta Magazine. Retrieved on 3 December 2016.