# Claus M. Sorensen
Department of Mathematics, UCSD
9500 Gilman Dr. #0112
La Jolla, CA 92093-0112 USA
Office: APM 6151
e-mail: csorensen at ucsd dot edu
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**Research interests: UCSD number theory seminar**
Number theory, representation theory, automorphic forms, arithmetic geometry.

**Current Teaching:**

**
The mod p Langlands program** (Math 205, Topics in Number Theory, Spring 2016)

**Taught (UCSD, Princeton, Caltech):**

Abstract & linear algebra, calculus, real & complex analysis, number theory,
Galois theory, class field theory, modular forms, Weil conjectures.

**Selected Preprints:**

Deformation rings and parabolic induction (with J. Hauseux
and T. Schmidt). In preparation.

**Selected Publications:**
A note on Jacquet functors and ordinary parts. Accepted in Math. Scand.
Strong local-global compatibility in the p-adic Langlands program for U(2) (with P. Chojecki). Rend. Semin. Mat. Univ. Padova 137, June 2017.
Weak local-global compatibility in the p-adic Langlands program for U(2) (with P. Chojecki). Rend. Semin. Mat. Univ. Padova 137, June 2017.
Locally algebraic vectors in the Breuil-Herzig ordinary part (with H. Gao). Manuscripta Mathematica, published online, DOI: 10.1007/s00229-016-0831-5
The local Langlands correspondence in families and Ihara's lemma for U(n). Journal of Number Theory 164 (2016) 127-165.
The Breuil-Schneider conjecture, a survey. Advances in the Theory of Numbers. Proceedings of the CNTA XIII.
Fields Institute Communications, Vol. 77. A. Alaca, S. Alaca, K. S. Williams (Eds.) 2015.
Eigenvarieties and invariant norms. Pacific Journal of Mathematics 275-1 (2015), 191-230.
A proof of the Breuil-Schneider conjecture in the indecomposable case.
**Annals of Mathematics** 177 (2013), 1-16.
Divisible motives and Tate's conjecture. Int. Math. Res. Not., Vol. 2012, No. 16, pp. 3763-3778
Galois representations and Hilbert-Siegel modular forms. Doc. Math. 15, 2010, 623-670.
A Patching Lemma. To appear in vol. 2 of "Stabilization of the trace formula, Shimura varieties, and arithmetic applications",
cf. the Paris
Book Project.
Potential level-lowering for GSp(4). J. Inst. Math. Jussieu, Volume 8, Issue 03, July 2009, pp. 595-622.
Level-raising for Saito-Kurokawa forms. Compos. Math., Volume 145, Issue 04, pp. 915-953.
Level-raising for GSp(4). Proc. of the 9th Number Theory Workshop in
Hakuba, Japan, 2006.
A generalization of level-raising congruences for algebraic modular forms. Ann. Inst. Fourier, 56, 2006, no. 6, 1735-1766.

**Recent talks:**
Munster, UCI, UCSC, Rutgers, Purdue, UIC, Urbana-Champaign, UCSD, McGill, Maryland, MIT, IAS, UCLA, Fields, Hopkins, Penn, Cornell, Columbia, BU.

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