## Eisenstein Congruences and Euler Systems

**GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR**

Eric Urban

Columbia University; Member, School of Mathematics

February 10, 2011

**GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR**

James Newton

Member, School of Mathematics

February 9, 2011

In this talk, I will describe a construction of a geometric realisation of a p-adic Jacquet-Langlands correspondence for certain forms of GL(2) over a totally real field. The construction makes use of the completed cohomology of Shimura curves, and a study of the bad reduction of Shimura curves due to Rajaei (generalising work of Ribet for GL(2) over the rational numbers). Along the way I will also describe a p-adic analogue of Mazur's principle in this setting.

Larry Guth

University of Toronto; Member, School of Mathematics

February 9, 2011

Rishi Saket

Princeton University

February 8, 2011

The Unique Games conjecture (UGC) has emerged in recent years as the starting point for several optimal inapproximability results. While for none of these results a reverse reduction to Unique Games is known, the assumption of bijective projections in the Label Cover instance seems critical in these proofs. In our work we bypass the UGC assumption in inapproximability results for two geometric problems, obtaining a tight NP-hardness result in each case. This talk shall focus on one of the problems as described below.

Edo Liberty

Yahoo! Research, Haifa, Isreal

February 7, 2011

Russell Impagliazzo

University of California, San Diego; Member, School of Mathematics

February 7, 2011

Guowu Meng

Hong Kong University of Science & Technology; Joint Member, School of Mathematics & Natural Sciences

February 4, 2011

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

Institute for Advanced Study

February 3, 2011

Christopher Skinner

Princeton University; Member, School of Mathematics

February 3, 2011

Jack Thorne

Harvard University

February 3, 2011

**GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR**