Random constraint satisfaction problems: the statistical mechanics approach and results

Guilhem Semerjian
l'Ecole Normale Superieure
January 29, 2014
In the 90's numerical simulations have unveiled interesting properties of random ensembles of constraint satisfaction problems (satisfiability and graph coloring in particular). When a parameter of the ensemble (the density of constraints per variable) increases the probability of a satisfying instance drops abruptly from 1 to 0 in the large size limit. This threshold phenomenon has motivated a lot of research activity in theoretical computer science and in mathematics.

Tagged particle diffusion in one-dimensional systems with Hamiltonian dynamics

Abhishek Dhar
International Centre for Theoretical Sciences (TIFR), Bangalore, India
January 31, 2014
I will present results on the study of various temporal correlation functions of a tagged particle in a one-dimensional system of interacting particles evolving with Hamiltonian dynamics and with initial conditions chosen from thermal equilibrium.

Simplicial complexes as expanders

Ori Parzanchevski
Institute for Advanced Study; Member, School of Mathematics
February 4, 2014
Expanders are highly connected sparse graphs. Simplicial complexes are a natural generalization of graphs to higher dimension, and the notions of connectedness and expansion turn out to have interesting analogues, which relate to the homology and the spectral theory of the complexes. I will explain these notions, and discuss results and problems. No prior knowledge is assumed.

Malevich's Nervous System

Briony Fer
University of College London
February 4, 2014
In this lecture, Briony Fer, Professor of History of Art at University College London, will look at Malevich's systemic method, as it was elaborated in his work, writings, and teachings, and its ongoing relevance for subsequent generations of artists. Malevich's late work is examined as an intricate set of reflections on some of the problems raised by the systems that he set in the 1910s.

Malevich's Nervous System

Briony Fer
Professor of History of Art at University College London
February 4, 2014
In this lecture, Briony Fer, Professor of History of Art at University College London, will look at Malevich's systemic method, as it was elaborated in his work, writings, and teachings, and its ongoing relevance for subsequent generations of artists. Malevich's late work is examined as an intricate set of reflections on some of the problems raised by the systems that he set in the 1910s.

Motion of an invading heavy tracer particle in a Bose gas

Gang Zhou
California Institute of Technology
February 5, 2014
I will present recent results on a non-relativistic Hamiltonian model of quantum friction, about the motion of an invading heavy tracer particle in a Bose gas exhibiting Bose Einstein condensate. We prove the following observations: if the initial speed of the tracer particle is lower than the speed of sound in the Bose gas, then in large time the particle will travel ballistically; if the initial speed is higher than the speed of sound, the it will converge to the speed of sound. In both regimes the system will converge to some inertial states.

In search of explicit matrices that behave like random ones

Avi Wigderson
Institute for Advanced Study; Faculty, School of Mathematics
February 7, 2014
I will describe several properties (structural and/or computational) which are satisfied by random matrices almost surely, but for which we have no concrete examples of such matrices. My hope is that the audience will be intrigued and interested in generating such examples.

Cylindrical contact homology as a well-defined homology?

Joanna Nelson
Institute for Advanced Study; Member, School of Mathematics
February 7, 2014
In this talk I will explain how the heuristic arguments sketched in literature since 1999 fail to define a homology theory. These issues will be made clear with concrete examples and we will explore what stronger conditions are necessary to develop a theory without the use of virtual chains or polyfolds in 3 dimensions. It turns out that this can be accomplished by placing strong conditions on the growth rates of the indices of Reeb orbits.