Sept 4 , Monday, 2006, kl 13.15-14.15, Uppsala, rum 64119.
Speaker: Fredrik Stromberg, Inst. of Theoretical Physics, TU-Clausthal,
Germany
Title Transfer Operators for Hecke Triangle Groups
Abstract:
It is well-known that the classical geodesic flow on the modular surface
can be coded with the help of simple (Gauss) continued fractions and
that the reduction theory of binary quadratic forms can be used to establish
a connection between the transfer operator of the geodesic flow and the
Selberg zeta function of the surface. In this setting it is also
possible to relate eigenfunctions of the transfer operator directly to
Maass waveforms via functional equations and cohomology (Lewis-Zagier
theory of period functions).
I will talk about work by Tobias Mühlenbruch, Dieter Mayer and myself
aimed at generalizing these kinds of results from the Modular group to
Hecke triangle groups.
Detta är ett nytt gemensamt seminarium mellan KTH och Uppsala
som är tänkt att presentera nya resultat
och metoder inom gränsområdena mellan dynamiska system,
talteori och analys. Avsikten är att detta ska ses ur
ett brett perspektiv, så att även besläktade aspekter
av ergodteori, kvantkaos, statistisk mekanik,
sannolikhetsteori och matematisk fysik tas med.
Vi planerar för närvarande att seminariet ska hållas varannan
vecka. Målsättningen är att föredragen ska rikta
sig till en
bred publik, bland annat genom att tydligt peka på öppna problem.
Doktorander är särskilt välkomna att delta i seminariet.
The DNA seminar
(Dynamical systems, Number theory, Analysis)
This new joint seminar between KTH and Uppsala is
intended to highlight some of the recent
developments occurring at the intersection
of dynamics, number theory, and analysis.
We plan for the seminar to take a wide view, so
included here will also be related aspects of
ergodic theory, quantum chaos, statistical mechanics,
probability, and mathematical physics. We currently
anticipate the seminar will meet twice monthly.
The talks will be designed to appeal to a wide
audience, featuring for instance clear
indications of open problems. Graduate students
are especially invited to participate.
9 februari 2006, kl 13.15-14.15, KTH, Seminarierum 3721.
Moon Duchin (University of California, Davis): Random moves in the space of metrics
Abstract.
For a fixed topological surface, the Teichmuller space is a
parameter space for its possible metrics. These are considered up to
conformal equivalence and with a "marking" by a choice of curves. I will
discuss random walks in Teichmuller space where the moves are changes of
marking. Adapting a geometric strategy from work of Karlsson-Margulis, I
will show that sample paths for this random walk are tracked by geodesics
in the Teichmuller space, which have a nice description as metric
deformations.
2 mars 2006, kl 13.15-14.15, Uppsala, rum 3:513.
Jeffrey Steif (Chalmers): Statistical mechanical systems on complete
graphs, infinite exchangeability and finite extensions
Abstract.
We discuss the notion of infinite exchangeability in the context of
statistical mechanical systems. It turns out that many ferromagnetic systems
(like Ising, Potts and Heisenberg models)
can be extended to so-called infinite exchangeable processes.
For the antiferromagnetic Ising model, we obtain sharp
quantitative results on how much the system can be extended.
One approach for doing this is via a solution of a new type of moment
problem. This is joint work with Tom Liggett and Balint Toth.
6 mars 2006, kl 13.15-15.00, KTH, sal D35 (Två timmar!).
Michael Benedicks (KTH): Non uniformly hyperbolic attractors - invertible and non-invertible.
Abstract.
I will describe the theory of Hénon attractors and Hénon-like attractors
with chaotic behaviour and the corresponding ergodic theory:
existence of SRB measures and the description of their basins, decay of
correlation, stability under random perturbations.
The maps in Hénon- and Hénon-like case are diffeomorphims.
Recently, Pesin and Yurchenko have noticed similar phenomena for
non-inversible maps appearing from coupled map lattice models of certain
PDES. I will discuss an attempt to generalize the theory of Hénon- and
Hénon-like maps to certain non-invertible cases (work in progress).
20 april 2006, kl 13.15-14.15, Uppsala, rum 3:513.
Andrew Booker (University of Michigan):
Convergent Hejhal-type algorithms
Abstract.
There have been many numerical investigations of the
spectrum of the Laplace operator on non-compact, finite volume
hyperbolic surfaces. The algorithm of D. Hejhal has proven to be
robust and has yielded good results in many cases. However, there is
no rigorous proof of either the convergence of the algorithm or that
the results it gives are correct. In the talk I will give an overview
of Hejhal's algorithms for the case of the modular group, and discuss
some recent joint work with A. Strömbergsson and A. Venkatesh in which
we compute and prove correct the first few eigenvalues to high
precision. I will then show how to adapt the method to give
algorithms similar to those of Hejhal, but for which one can prove
convergence. If time permits I will discuss some related questions
concerning large eigenvalue computations.
24 april 2006, kl 13:15-14:15, KTH, sal 3721.
Peter Storm (Stanford University): Topological lower volume bounds for
hyperbolic 3-manifolds
Abstract.
I will outline some of the geometric and topological tools used to
obtain lower volume bounds for hyperbolic 3-manifolds with boundary.
I'll focus on a few specific examples which should elucidate the
origin of these lower bounds. The techniques are mostly based on
ideas of Besson-Courtois-Gallot. However, the recent work of Perelman
can be applied to yield strictly stronger results.
2 maj 2006, kl 15.15-16.15, KTH, sal 3733.
Jean Lafont (Ohio State University):
Simplicial volume of locally symmetric spaces of non-compact type.
Abstract.
I will define simplicial volume of a topological manifold, and
motivate the interest in the positivity of this invariant. I will then
outline a proof that the simplicial volume of locally symmetric spaces of
non-compact type is in fact positive. This was joint work with Ben Schmidt.
våren 2005 (spring 2005)
14 mars, David Farmer (AIM):
Derivatives of polynomials and L-functions
21 april, Carles Simó (Universitat de Barcelona):
Chaos and quasi-periodicity in diffeomorphisms of the solid torus
21 april, Robert MacKay (Warwick Mathematics Institute):
Coupled map lattices with non-unique phase
25 april,
Eric Bedford (Indiana University): Characterization of the
horseshoes in the Henon family
9 maj, Peter Walters (Warwick Mathematics Institute):
Cohomology for Shift Transformations
hösten 2004 (fall 2004)
våren 2004 (spring 2004)
3 maj, Mark Pollicott (University of Manchester):
Zeta functions and hyperbolic dynamical systems