Jared Weinstein

jaredw at ias dot edu

Jared Weinstein

As of July 2011, I have moved to Boston University. My new personal webage is here.

For the academic year 2010-2011, I am visiting the Institute for Advanced Study, where there is currently a special year in Galois representations and automorphic forms.

My old web page at UCLA.

Here is my CV (pdf format, updated Oct. 25, 2010).

On the stable reduction of modular curves, preprint (2010). We construct integral models for the tower of modular curves X_0(Np^n) whose special fiber mod p is stable, which means that the only singularities are normal crossings. There are interesting connections to the local Langlands correspondence, as well as the theory of Bushnell-Kutzko types.

On the computation of local components of a newform, with David Loeffler. To appear in Mathematics of Computation. 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 "On the semistable reduction of modular curves", this paper recovers the result of Deligne-Carayol that the tower of Lubin-Tate curves realizes the local Langlands correspondence for GL(2), but in a purely local manner.

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.

Other Writing

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.

Anomalous varieties and the local Langlands correspondence. These are expanded notes from a talk I gave at Don Blasius' birthday conference at IPAM in Los Angeles in November 2010. We discuss an interesting class of varieties over finite fields, which play a similar role for unipotent groups as the Deligne-Lusztig varieties play for Chevalley groups. We call them ``anomalous" because their zeta functions are (conjecturally) very simple. A connection is made to the local Langlands correspondence for GL(n).

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.