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Spring Semester 2013

Date / Time Speaker Title Location
13 March 2013
15:45-16:45 		Zhiren Wang
Yale University
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Geometry Seminar

Title Global rigidity of abelian Anosov actions
Speaker, Affiliation Zhiren Wang, Yale University
Date, Time 13 March 2013, 15:45-16:45
Location HG G 43
Abstract As part of a more general conjecture, it was asked if all smooth Anosov $Z^r$-actions without rank-1 factor on tori and nilmanifolds are, up to smooth conjugacy, actions by automorphisms. Recently, Fisher, Kalinin and Spatzier showed this holds under the extra assumption that the action has at least one Anosov element in every Weyl chamber of the linearization action. We will verify that this assumption always holds, hence fully establish the statement above. This is a joint work with Federico Rodriguez Hertz.
Global rigidity of abelian Anosov actionsread_more
HG G 43
27 March 2013
15:45-16:45 		Rodolphe Richard
ETH Zürich
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Geometry Seminar

Title Local limit distributions of translated irrational orbits on S-arithmetic homogeneous spaces
Speaker, Affiliation Rodolphe Richard, ETH Zürich
Date, Time 27 March 2013, 15:45-16:45
Location HG G 43
Abstract (joint work Tomasz Zamojski, building on a joint work with Nimish Shah) I will describe a recent result on a problem of homogeneous dynamics where one studies the translates, in a lattice space, of an homogeneous orbit, from the point of view of measure theory: the asymptotic distribution of a given sequence of translates. More precisely: what are the possible limit distributions; along which sequences of translates does a limit distribution occur; how explicitly uniform distribution does occur ? This is a critical question in many of the applications of homogeneous dynamics to number theory problems. Thanks to recent technology developed on purpose, we are able to extend classical work of Dani-Margulis and Eskin-Mozes-Shah in several directions together, and to achieve the proof as it was originally meant.
Local limit distributions of translated irrational orbits on S-arithmetic homogeneous spacesread_more
HG G 43
17 April 2013
15:45-16:45 		Prof. Dr. Yakov Pesin
Penn State University
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Geometry Seminar

Title Coexistence phenomena in dynamics
Speaker, Affiliation Prof. Dr. Yakov Pesin, Penn State University
Date, Time 17 April 2013, 15:45-16:45
Location HG G 43
Abstract I will describe a very interesting and highly non-trivial phenomenon of essential coexistence of chaotic (highly complicated) and regular (relatively simple) behavior in dynamics. In the absence of general theory, the coexistence phenomenon has been shown in some particular cases. I will present the contemporary state of the art in this area with emphasis on some new examples in smooth conservative dynamics.
Coexistence phenomena in dynamicsread_more
HG G 43
24 April 2013
15:45-16:45 		Prof. Dr. Michael Farber
University of Warwick
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Geometry Seminar

Title Topology of random 2-dimensional complexes
Speaker, Affiliation Prof. Dr. Michael Farber, University of Warwick
Date, Time 24 April 2013, 15:45-16:45
Location HG G 43
Abstract A random two-dimensional simplicial complex Y is produced by starting with a complete graph on n vertices 1, 2,…, n and adding each two-simplex 1 \leq i,j < k \leq n with probability 0
Topology of random 2-dimensional complexesread_more
HG G 43
15 May 2013
15:45-16:45 		Alessandro Sisto
University of Oxford
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Geometry Seminar

Title Metric embeddings of relatively hyperbolic groups
Speaker, Affiliation Alessandro Sisto, University of Oxford
Date, Time 15 May 2013, 15:45-16:45
Location HG G 43
Abstract Relatively hyperbolic groups form a rich class of groups containing many examples coming from, e.g., 3-manifolds theory. I will discuss quasi-isometric embeddings of relatively hyperbolic groups in products of trees and a-bit-worse-than-quasi-isometric embeddings into real hyperbolic spaces with a collection of horoballs removed. Based on joint works with John MacKay.
Metric embeddings of relatively hyperbolic groupsread_more
HG G 43
22 May 2013
15:45-16:45 		Dr. Samuel Senti
UFRJ
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Geometry Seminar

Title Thermodynamical Formalism at the boundary of hyperbolicity for Henon maps
Speaker, Affiliation Dr. Samuel Senti, UFRJ
Date, Time 22 May 2013, 15:45-16:45
Location HG G 43
Abstract In this joint work with Hiroki Takahasi, we establish the existence and uniqueness of equilibrium measures for the geometric potential -t\log|df| for the Henon map at the first bifurcation parameter.
Thermodynamical Formalism at the boundary of hyperbolicity for Henon maps read_more
HG G 43
29 May 2013
15:45-16:45 		Prof. Dr. Manfred Einsiedler
ETH Zurich, Switzerland
Details

Geometry Seminar

Title Integer points on spheres and their orthogonal complement
Speaker, Affiliation Prof. Dr. Manfred Einsiedler, ETH Zurich, Switzerland
Date, Time 29 May 2013, 15:45-16:45
Location HG G 43
Abstract Consider the collection of all primitive integer vectors in $\mathbb{Z}^d$ of length $\sqrt{D}$. After dividing by $\sqrt{D}$ one gets for $D\to\infty$ an equidistributing family of points on $\mathbb{S}^{d-1}$ (if the set is non-empty and $d>2$.) The hardest case of this statement is the case $d=3$ and was obtained by Duke (after a breakthrough of Iwaniec and initial progress by Linnik). A related question is how the lattice in the orthogonal complement of the vector looks like. W. Schmidt showed that these lattices equidistribute if one considers all vectors up to a particular length (instead of just the vectors of a given length). We will show by using homogeneous dynamics (under mild conditions for $d=3,4,5$ and without additional conditions for $d\geq 6$) that the pair consisting of the normalized primitive vector of length $\sqrt{D}$ and the lattice in the orthogonal complement equidistribute in $\mathbb{S}^{d-1}$ times the moduli space of lattices (up to rotations and scalar multiplication). This is joint work with Menny Aka and Uri Shapira, and is related to a theorem of Mozes and Shah, the higher rank joining theorem by Lindenstrauss and myself, and ongoing joint work with Margulis, Mohammadi, and Venkatesh. As we will see, p-adic dynamics is needed.
Integer points on spheres and their orthogonal complementread_more
HG G 43

Organisers: Michael Björklund, Marc Burger, Manfred Einsiedler, Alessandra Iozzi, Urs Lang, Viktor Schröder

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09 SS 09

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