### Homepage of Wushi Goldring

I am an Associate Professor at the Mathematics Department of Stockholm University, Sweden.

Department of Mathematics
Stockholm University
SE-10691 Sweden

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

Office: House 6, Room 110
Office Hours for exam week May 15-19: Mon 10-11, Wed 9:00-10:30, Fri 9:15-11:00

Joint KTH-Stockholm University Algebra and Geometry Seminar: KTH-SU-Algebra-and-Geometry-seminar
Stockholm Number Theory Seminar: https://people.kth.se/~kurlberg/ntseminar/vt17.html

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) Stratification of flag spaces and functoriality.

4. (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 waarXiv: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.

5. Stability of degenerate limits of discrete series under functoriality

## Publications (numbered chronologically):

#### 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 TheoremJ. Number Theory 135 (2014) pp. 151-154:

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 varietiesJ. 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.