## A Rigorous Renormalization Group Study of a p-Adic Quantum Field Theory

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

Abdelmalek Abdesselam

University of Virginia

November 12, 2010

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

George Dyson

November 12, 2010

This lecture was part of the Institute for Advanced Study’s celebration of its eightieth anniversary, and took place during the events related to the Schools of Historical Studies and Social Science.

Pierre Colmez

National Center for Scientific Research; Member, School of Mathematics

November 11, 2010

Michael Rapoport

University of Bonn

November 11, 2010

Picard moduli spaces parametrize principally polarized abelian varieties with complex multiplication by the ring of integers in an imaginary-quadratic field. The loci where the abelian varieties split off an elliptic curve in a controlled way are divisors on this moduli space. We study the intersection behaviour of these divisors and prove in the non-degenerate case a relation between their intersection numbers and Fourier coefficients of the derivative at s=0 of a certain incoherent Eisenstein series for the unitary group. This is joint work with Kudla.

Henri Carayol

University of Strasbourg

November 10, 2010

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR

Some automorphic forms, despite the fact they are algebraic, do not have any interpretation as cohomology classes on a Shimura variety: therefore nothing is known at present on their expected arithmetic properties. I shall explain how such forms appear to be related to more general objects (Griffiths-Schmid varieties) and discuss some related rationality questions.

Nikhil Srivastava

Institute for Advanced Study

November 9, 2010

We give an elementary proof of a generalization of Bourgain and Tzafriri's Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which it is well-invertible. Our proof gives the tightest known form of this result, is constructive, and provides a deterministic polynomial time algorithm for finding the desired subspace.

Sir Michael Atiyah

Institute for Advanced Study

November 8, 2010

Jacob Fox

Massachusetts Institute of Technology

November 8, 2010

Let H be a fixed graph with h vertices. The graph removal lemma states that every graph on n vertices with o(n^{h}) copies of H can be made H-free by removing o(n^{2}) edges. We give a new proof which avoids Szemeredi's regularity lemma and gives a better bound. This approach also works to give improved bounds for the directed and multicolored analogues of the graph removal lemma. This answers questions of Alon and Gowers.

Members of the Borromeo String Quartet

November 6, 2010

Listen to members of the Borromeo String Quartet discuss music with Institute Artist-in-Residence Derek Bermel.

Michael Damron

Princeton University

November 5, 2010

I will discuss the problem of determining the number of infinite-volume ground states in the Edwards-Anderson (nearest neighbor) spin glass model on $Z^D$ for $D \geq 2$. There are no complete results for this problem even in $D=2$. I will focus on this case and explain recent results which go some way toward proving that (with zero external field, so that ground states come in pairs, related by a global spin flip) there is only a single ground state pair (GSP).