*Academic mailing address: *

Department of Mathematics

Stockholm University

SE-10691 Sweden

* *

*Email Address: *wushijig* *(at) gmail (dot) com

Office: House 6, Room 110

Office Hours: By appointment -- please email me to set up a time if you want to meet.

Preprints (numbered from most recent to oldest):

1. (with Jean-Stefan Koskivirta) **Quasi-constant characters: Motivation, classification and applications**.

2. (with Jean-Stefan Koskivirta) **Automorphic vector bundles with global sections on G-Zip^Z-schemes.**

3. (with Jean-Stefan Koskivirta) **Strata Hasse invariants, Hecke algebras and Galois representations** .

*Notes: *Version of January 10, 2015 (replacing version of July 17, 2015, which was arXiv:1507.05032v1). In Section 1.3.1, footnote 2, reference is made to an email that George Boxer sent to David Geraghty and myself on October 13, 2013. Boxer's email may be found here.

4. **Stability of degenerate limits of discrete series under functoriality**

## Publications (numbered chronologically):

#### 1. **Dynamics of the $w$ function and primes**. *J. Number Theory ***119 **(2006) pp. 86-98:

#### 2. **Unifying Themes Suggested by Belyi's Theorem**. pp. 181--214 of *Number Theory, Analysis and Geometry *(Serge Lang Memorial Volume). D. Goldfeld, J. Jorgenson, P. Jones, D. Ramakrishnan, K. Ribet, J. Tate eds. Springer-Verlag, 2011*.*

3. **A new proof of Belyi's Theorem**. *J. Number Theory ***135 **(2014) pp. 151-154:

belyi new proof.pdf

4. **Galois Representations Associated to Holomorphic Limits of Discrete Series**. With an appendix by Sug Woo Shin. *Compositio Math. ***150 **(2014) pp.191-228

galois reps hlds.pdf

*Notes*: The above paper is an outgrowth of my thesis written at Harvard University under the supervision of Richard Taylor. I would like it noted for the record that I, like every graduate student at Harvard in recent years, was forced by Harvard University to pay ProQuest to publish my thesis (forced in the sense that, whether accurate or not, it was suggested to me by Harvard that should I fail to comply with this demand, I would not receive my PhD diploma). In my personal opinion, in this instance Harvard improperly used an unnecessary amount of power to pressure me to pay ProQuest, a for-profit organization which has previously been investigated by the SEC. As a result, I urge anyone interested in my thesis to read the above paper and to disregard any document on ProQuest which bears my name. Further, in the interest of preserving the integrity of scientific progress, I recommend that anyone who has the power to do so boycott ProQuest.

5. (with Marc-Hubert Nicole)** The $\mu$-ordinary Hasse invariant of unitary Shimura varieties**. *J. reine angew. Math.* 728 (2017), 137–151.* *

*Notes: *Revised version of December 2014 which merges our two previous preprints, "A \mu-ordinary Hasse invariant" (arXiv:1302.1614v2) and "The \mu-ordinary Hasse invariant of unitary Shimura varieties" (arXiv:1305.6956v1).

6.** An introduction to the Langlands correspondence**. pp. 333-367 of "Recent Advances in Hodge Theory: Period Domains, Algebraic Cycles, and Arithmetic". Proceedings of a conference held at the Pacific Institute for the Mathematical Sciences, Vancouver, Canada in June 2013. Matt Kerr and Gregory Pearlstein editors, Cambridge University Press, 2016. intro-langlands-vancouver-final.pdf *Notes: *Based on three expository lectures given at the above conference.

7. ** **(with Jean-Stefan Koskivirta) **Stratification of flag spaces and functoriality**. To appear in IMRN. zips_and_flags.pdf