## Localization and Thermalization in Highly-Excited Many-Body Quantum Systems

**ANALYSIS/MATHEMATICAL PHYSICS SEMINAR**

David Huse

Princeton University; Member, School of Mathematics

December 3, 2010

**ANALYSIS/MATHEMATICAL PHYSICS SEMINAR**

Steve Awodey

Institute for Advanced Study

December 3, 2010

In recent research it has become clear that there are fascinating connections between constructive mathematics, especially as formulated in the type theory of Martin-Löf, and homotopy theory, especially in the modern treatment in terms of Quillen model categories and higher-dimensional categories. This talk will survey some of these developments.

Ruochuan Liu

Institute for Advanced Study

December 2, 2010

Pierre Colmez

ational Center for Scientific Research; Member, School of Mathematics

December 2, 2010

December 1, 2010

Nigel Goldenfeld

University of Illinois at Urbana-Champaign

December 1, 2010

Can we use computational algorithms to make accurate predictions of physical phenomena? In this talk, intended for non-experts, I will give examples where complicated space-time phenomena can be exquisitely captured with simple computational algorithms, that not only produce patterns resembling those seen in experiment, but also make accurate predictions about probes of dynamics and spatial organisation, such as correlation functions. I use examples from condensed matter physics, as well as from geophysics.

Eric Babson

University of California at Davis

December 1, 2010

Jeremy Mason

Institute for Advanced Study

December 1, 2010

Paul Beame

University of Washington; Member, School of Mathematics

November 30, 2010

Dana Moshkovitz

Massachusetts Institute of Technology

November 29, 2010

We construct linear codes of almost-linear length and linear distance that can be locally self-corrected on average from a constant number of queries:

1. Given oracle access to a word $w\in\Sigma^n$ that is at least $\varepsilon$-close to a codeword $c$, and an index $i\in [n]$ to correct, with high probability over $i$ and over the internal randomness, the local algorithm returns a list of possible corrections that contains $c_i$.