Seminars and Colloquia by Series

Shape optimization among convex bodies

Series
Math Physics Seminar
Time
Wednesday, July 13, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jimmy Lamboley – Dauphine –
Shape optimization is the study of optimization problems whose unknown is a domain in R^d. The seminar is focused on the understanding of the case where admissible shapes are required to be convex. Such problems arises in various field of applied mathematics, but also in open questions of pure mathematics. We propose an analytical study of the problem. In the case of 2-dimensional shapes, we show some results for a large class of functionals, involving geometric functionals, as well as energies involving PDE. In particular, we give some conditions so that solutions are polygons. We also give results in higher dimension, concerned with the Mahler conjecture in convex geometry and the Polya-Szego conjecture in potential theory. We particularly make the link with the so-called Brunn-Minkowsky inequalities.

Average Density of States for Hermitian Wigner Matrices

Series
Analysis Seminar
Time
Wednesday, June 15, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 05
Speaker
Dr Anna Maltsev – University of Bonn
We consider ensembles of $N \times N$ Hermitian Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. Assuming sufficient regularity for the probability density function of the entries, we show that the expectation of the density of states on arbitrarily small intervals converges to the semicircle law, as $N$ tends to infinity.

Hypersurfaces with a canonical principal direction

Series
Geometry Topology Seminar
Time
Monday, June 13, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gabriel Ruiz – National Autonomous University of Mexico
Given a non-null vector field X in a Riemannian manifold, a hypersurfaceis said to have a canonical principal direction relative to $X$ if theprojection of X onto the tangent space of the hypersurface gives aprincipal direction. We give different ways for building thesehypersurfaces, as well as a number of useful characterizations. Inparticular, we relate them with transnormal functions and eikonalequations. Finally, we impose the further condition of having constantmean curvature to characterize the canonical principal direction surfacesin Euclidean space as Delaunay surfaces.

Distances in the homology curve complex

Series
Geometry Topology Seminar
Time
Tuesday, May 31, 2011 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ingrid Irmer – U Bonn
In this talk a curve complex HC(S) closely related to the "Cyclic Cycle Complex" (Bestvina-Bux-Margalit) and the "Complex of Cycles" (Hatcher) is defined for an orientable surface of genus g at least 2. The main result is a simple algorithm for calculating distances and constructing quasi-geodesics in HC(S). Distances between two vertices in HC(S) are related to the "Seifert genus" of the corresponding link in S x R, and behave quite differently from distances in other curve complexes with regards to subsurface projections.

The 15th International Conference on Random Structures and Algorithms

Series
Other Talks
Time
Tuesday, May 24, 2011 - 08:00 for 8 hours (full day)
Location
Emory University
Speaker
Conference on Random Structures and Algorithms – Emory University
The 15th International Conference on Random Structures and Algorithms (RS&A) 2011 will be held at Emory University, May 24-28 (Tuesday-Saturday) 2011 and is co-organized by Emory University, Georgia Institute of Technology and Adam Mickiewicz University. The conference, organized biennially since 1983, brings together probabilists, discrete mathematicians and theoretical computer scientists working in probabilistic methods, random structures and randomized algorithms. The program will consist of one-hour plenary addresses by the invited speakers and parallel sessions of 25-minute contributed talks. It will begin on Tuesday morning and end on Saturday afternoon. The list of plenary speakers includes: Béla Bollobás [University of Cambridge and University of Memphis]; Jennifer Chayes [Microsoft Research New England, Cambridge]; Fan Chung [University of California, San Diego]; Jacob Fox [Massachusetts Institute of Technology]; David Gamarnik [Massachusetts Institute of Technology]; Jeff Kahn [Rutgers University]; Subhash Khot [Courant Institute]; Eric Vigoda [Georgia Institute of Technology]; Nick Wormald [University of Waterloo].

SHARP MIXING TIME BOUNDS FOR SAMPLING RANDOM SURFACES

Series
Other Talks
Time
Monday, May 23, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
KLAUS 1116W
Speaker
Fabio Martinelli – University of Rome 3, Rome, Italy
We analyze the mixing time of a natural local Markov Chain (Gibbs sampler) for twocommonly studied models of random surfaces: (i) discrete monotone surfaces in Z3 with ``almostplanar" boundary conditions and (ii) the one-dimensional discrete Solid-on-Solid (SOS) model.In both cases we prove the first almost optimal bounds O(L^2 polylog(L)) where L is the natural size of the system. Our proof is inspired by the so-called ``mean curvature" heuristic: on a large scale, the dynamics should approximate a deterministic motion in which each point of the surface moves according to a drift proportional to the local inverse mean curvature radius. Key technical ingredients are monotonicity, coupling and an argument due to D.Wilson in the framework of lozenge tiling Markov Chains together with Kenyon's results on the free Gaussian field approximation of monotone surfaces. The novelty of our approach with respect to previous results consists in proving that, with high probability, the dynamics is dominated by a deterministic evolution which, apart from polylog(L) corrections, follows the mean curvature prescription. Our method works equally well for both models despite the fact that their equilibrium maximal deviations from the average height profile occur on very different scales (log(L) for monotone surfaces and L^{1/2} for the SOS model).This is work in collaboration with PIETRO CAPUTO and FABIO LUCIO TONINELLI

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