Departement Mathematik

Zurich colloquium in mathematics

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Frühjahrssemester 2015

Datum / Zeit Referent:in Titel Ort
24. Februar 2015
17:15-18:15 		Prof. Dr. Bo'az Klartag
University of Tel Aviv
Details

Zurich Colloquium in Mathematics

Titel Needle decompositions and Ricci curvature
Referent:in, Affiliation Prof. Dr. Bo'az Klartag, University of Tel Aviv
Datum, Zeit 24. Februar 2015, 17:15-18:15
Ort KO2 F 150
Abstract Needle decomposition is a technique in convex geometry, which enables one to prove isoperimetric and spectral gap inequalities, by reducing an n-dimensional problem to a 1-dimensional one. This technique was promoted by Payne-Weinberger, Gromov-Milman and Kannan-Lovasz-Simonovits. In this lecture we will explain what needles are, what they are good for, and why the technique works under lower bounds on the Ricci curvature.
Needle decompositions and Ricci curvatureread_more
KO2 F 150
24. März 2015
17:15-18:15 		Prof. Dr. Blake Temple
University of California Davis
Details

Zurich Colloquium in Mathematics

Titel An instability creates the anomalous acceleration without dark energy
Referent:in, Affiliation Prof. Dr. Blake Temple, University of California Davis
Datum, Zeit 24. März 2015, 17:15-18:15
Ort KO2 F 150
Abstract We introduce a new asymptotic ansatz for spherical perturbations of the Standard Model of Cosmology (SM) which applies during the p = 0 epoch, and prove that these perturbations trigger an instability in the SM on the scale of the supernova data. The instability creates a large, central region of uniform under-density which expands faster than the SM, and this accelerated uniform expansion introduces into the SM precisely the same range of corrections to redshift vs luminosity as are produced by the cosmological constant in the theory of Dark Energy. A phase portrait of the instability places the Standard Model (SM) at a classic unstable saddle rest point, and universality is exhibited in the sense that all su?fficiently small perturbations evolve to a nearby stable rest point corresponding to Minkowski space. We then prove that this instability is triggered by a one parameter family of self-similar waves from the radiation epoch p = ((c^2)/3) rho,when the pressure drops to p = 0. The authors previously proposed this family as possible time-asymptotic wave patterns for perturbations of the SM at the end of the radiation epoch. Using numerical simulations, we calculate the unique wave in the family that accounts for the same values of the Hubble constant and quadratic correction to redshift vs luminosity as in a universe with seventy percent Dark Energy. A numerical simulation of the third order correction associated with that unique wave establishes a testable prediction that distinguishes this theory from the theory of Dark Energy. This explanation for the anomalous acceleration, based on instabilities in the SM together with simple wave perturbations from the radiation epoch that trigger them, provides perhaps the simplest mathematical explanation for the anomalous acceleration of the galaxies that does not invoke Dark Energy. (Joint work with Joel Smoller and Zeke Vogler.)
An instability creates the anomalous acceleration without dark energyread_more
KO2 F 150
14. April 2015
17:15-18:15 		Prof. Dr. Angelika Steger
ETH Zurich
Details

Zurich Colloquium in Mathematics

Titel The determinism of randomness and its use in combinatorics
Referent:in, Affiliation Prof. Dr. Angelika Steger, ETH Zurich
Datum, Zeit 14. April 2015, 17:15-18:15
Ort KO2 F 150
Abstract Many areas of science, most notably statistical physics, rely on the use of probability theory to explain key phenomena. The aim of this talk is to explore the role of probability in combinatorics. More precisely, I will address a wide range of topics which illustrates the various roles that probability plays within combinatorics: from just providing intuition for deterministic statements, like Szemerédi’s regularity lemma or the recent container theorems, to statements about random graphs with structural side constraints, all the way to neuroscience.
The determinism of randomness and its use in combinatoricsread_more
KO2 F 150
5. Mai 2015
17:15-18:15 		Prof. Dr. Ben Green
University of Oxford
Details

Zurich Colloquium in Mathematics

Titel Approximate algebraic structure
Referent:in, Affiliation Prof. Dr. Ben Green, University of Oxford
Datum, Zeit 5. Mai 2015, 17:15-18:15
Ort KO2 F 150
Abstract Abstract: What should we understand by an approximate group? An approximate field? An approximate polynomial? What can we say about these objects? What applications does this have? There are several answers to the last question ranging from results on expansion in groups to asymptotics for arithmetic progressions of primes. I will try and give a hint of one or two of these.
Approximate algebraic structureread_more
KO2 F 150

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