Associate
Professor, Mathematics

Boston University

MCS 227

617-353-2560

`
jsweinst@math.bu.edu`

Here is my CV (pdf, updated October 2019).

- Spring 2021: MA 842, Algebra Seminar. The topic is the Mordell Conjecture.
- Previous courses

- On the Kottwitz conjecture for local shtuka spaces, with David Hansen and Tasho Kaletha. Updated May 2021. The smooth locus in infinite-level Rapoport-Zink spaces, with Alexander Ivanov. We show that each connected component of EL-type infinite-level Rapoport-Zink space is cohomologically smooth, once you remove the points with extra endomorphisms. To appear in Compositio Mathematica.
- Berkeley lectures on p-adic geometry, with Peter Scholze (updated March 2020). A book based on Scholze's 2014 course on perfectoid spaces, diamonds, and shtukas. To appear in Annals of Mathematics Studies, Princeton University Press.
- Reciprocity laws and Galois representations: recent breakthroughs. Bulletin of the AMS 53 (2016), No. 1, 1-39. An exposition of reciprocity laws, from 1640 to 2013.
- The Galois group of Q_p as a geometric fundamental group. Int. Math. Res. Not. (2016). We construct an object Z defined over an algebraically closed field, whose fundamental group equals the absolute Galois group of Q_p.
- Semistable models for modular curves of arbitrary level. Inventiones Mathematicae 205 (2016), No. 2, 459-526. We construct integral models for the tower of modular curves whose special fibers are all semistable, which means that the only singularities are normal crossings. For this it was necessary to work at infinite level, where the Lubin-Tate tower assumes the structure of a perfectoid space.
- Moduli of p-divisible groups, with Peter Scholze. Cambridge Journal of Mathematics 1, No. 2, 145-237, 2013. (2013). We prove that Rapoport-Zink spaces at infinite level are perfectoid spaces, and give a description of these spaces purely in terms of p-adic Hodge theory.
- Formal vector spaces over a field of positive characteristic, preprint. We introduce the notion of a "formal K-vector space", where K is the field of Laurent series in one variable over a finite field. The main result is that the infinite-level Lubin-Tate tower for K has a surprisingly simple description in terms of formal K-vector spaces.
- Maximal Varieties and the local Langlands correspondence for GL(n), with Mitya Boyarchenko. J. Amer. Math. Soc. 29 (2016), No. 1, 177-236. Wherein we compute the zeta function of a very unusual variety over a finite field, which has the maximum number of rational points relative to its topology. This variety appears as the reduction of an open affinoid subset of the Lubin-Tate tower at infinite level.
- On the computation of local components of a newform, with David Loeffler. Math. Comp. 81 (2012) 1179-1200. We present an algorithm for computing the p-components of the automorphic representation arising from a cuspidal newform, even at those primes p dividing the level more than once.
- Good reduction of affinoids on the Lubin-Tate tower. Documenta Mathematica 15 (2010) 981-1007. We find a family of analytic subspaces of the Lubin-Tate tower whose reduction is a rather curious nonsingular hypersurface; a conjecture on the L-functions of this hypersurface would link non-abelian Lubin-Tate theory to the theory of Bushnell-Kutzko types.
- Explicit non-abelian Lubin-Tate theory for GL_2, preprint (2009). Together with "Semistable models for modular curves of arbitrary level", this paper recovers the result of Deligne-Carayol that the tower of Lubin-Tate curves realizes the local Langlands correspondence for GL(2) in odd residue characteristic.
- The Local Jacquet-Langlands Correspondence via Fourier Analysis, Journal de Theorie de Nombres de Bordeaux, 22, No. 2, 2010. We give a new technique for passing between supercuspidal representations of GL_2 over a local nonarchimedean field with those of its inner twist.
- Hilbert Modular forms with Prescribed Ramification, Int. Math. Res. Not. (2009), No. 8. We find a formula for the number of hilbert modular forms over a totally real field K whose ramification is of a prescribed type. This is a strengthening of the first half of my thesis.
- Beyond Value at Risk: Forecasting Portfolio Loss at Multiple Horizons, with Lisa Goldberg and Guy Miller. Journal of Investment Management, Vol. 6, No. 2, (2008), pp. 1.26.
- Automorphic Forms with Local Constraints, my Berkeley dissertation.
- Adic spaces, notes for my lecture series at the 2017 Arizona Winter School in Tucson.
- Notes from Peter Scholze's revolutionary course on
*p*-adic geometry, Fall 2014. - Notes and slides for my talk
*Exploring the Galois group of the rational numbers: New breakthroughs*, at the Current Events Bulletin Session of the AMS-JMM Joint Meetings, San Antonio, January 2015. - A guest post on Frank Calegari's blog, about the fundamental curve of p-adic Hodge theory. See also the sequel, about the Galois group of Q_p as a geometric fundamental group.
- Modular curves at infinite level, notes for my lecture series at the 2013 Arizona Winter School in Tucson.
- A variety with many points over a finite field, slides for a talk given at the Arithmetic Geometry session of the 2012 Joint Meetings in Boston.
- Elliptic curves over the rational numbers, a SAGE worksheet I used for my lecture in the short course Computing with Elliptic Curves using SAGE at the 2012 Joint Meetings in Boston.
- The geometry of Lubin-Tate spaces, notes for a mini-course at the FRG/RTG Workshop on L-functions, Galois representations and Iwasawa theory, Ann Arbor, May 17-22, 2011. An introduction to formal groups, Dieudonné modules and the Lubin-Tate tower.
- Resolution of singularities on the tower of modular curves , slides from half of my talk at the Stanford Number Theory Seminar, Oct. 22, 2010. This is a graphical summary of my preprint on semistable models for modular curves.
- Deligne's letter to Piatetski-Shapiro. A latex transcription of Deligne's beautiful letter from 1973, in which he investigates the local behavior of Galois representations coming from modular forms.