Assistant Professor, Mathematics

Boston University

MCS 227

617-353-2560

`
jsweinst@math.bu.edu`

Here is my CV (pdf format, updated Mar. 2014).

- Spring 2014: MA225, Multivariate Calculus, and MA512, Introduction to Analysis II.
- Fall 2013: MA843, Advanced Number Theory. The topic is Shimura Varieties.
- Spring 2013: MA442, Honors Linear Algebra.
- Fall 2012: MA541, Modern Algebra I, and MA711, Real Analysis.
- Spring 2012: MA746, Algebraic Geometry II.
- Fall 2011: MA843, Advanced Number Theory. The topic is Automorphic Representation Theory.

- The Galois group of Q_p as a geometric fundamental group, preprint. We construct an object Z defined over an algebraically closed field, whose fundamental group equals the absolute Galois group of Q_p.
- 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.
- Semistable models for modular curves of arbitrary level, preprint. (Latest version uploaded Feb. 16, 2014.) 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.
- 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), submitted, with Mitya Boyarchenko. (New version July 2013.) 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.
- 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.