Institutionen för matematik, KTH | Matematiska institutionen, Uppsala

DNA-seminariet (Dynamiska system, talteori, analys)

Tidigare seminarier:

våren 2009 (spring 2009)

15 januari 2009, Olof Sisask (University of Cambridge): The minimal and maximal number of three-term progressions in dense subsets of Z/pZ

Abstract. A famous theorem of Roth asserts that any dense subset of the integers {1, ..., N} must contain a three-term arithmetic progression provided N is large enough in terms of the density of the set. This turns out to be equivalent to the statement that a subset of {1 ,..., N} of positive density delta must actually contain a lot of three-term progressions: at least c(delta)N^2 of them, in fact, where c(delta) is some positive constant depending only on the density delta. Similar statements exist in Z/pZ, the integers modulo a prime p, and I shall discuss the analogous problem in this setting: how many three-term progressions must A contain if A is a subset of Z/pZ of density delta? In particular, I shall outline how one can obtain an exact answer for very large densities using some analytically-inspired ideas. Based on joint work Ben Green.

29 januari 2009, Pierre Berger (CRM, Barcelona): Abundance of one dimensional non uniformly hyperbolic attractors for surface endomorphisms

Abstract. We prove the existence of a non uniformly hyperbolic attractor for a positive set of parameters a in the family: \[(x,y)\mapsto (x^2+a+2y,0)+B(x,y)\] Where $B$ is fixed a $C^2$ small function. The proof uses the formalism of Yoccoz puzzle and analytical ideas of Benedicks-Carleson.

12 mars 2009, Thomas Kaijser (Linköpings universitet): Iterations of random functions. Contraction properties and limit theorems.

Abstract. (given as a pdf-file)

16 mars 2009, Alexander Fish (Ohio State University): Sumset phenomenon for amenable groups

Abstract. We prove a structure theorem for a sumset of two sets A and B of positive upper Banach density in any countable amenable group. More precisely, we prove that AB is "piecewise syndetic" which means that there exists a finite set K such that for any finite set F in G ("configuration") there exists an element g in G such that Fg is a subset of ABK. For abelian groups we prove even more, namely, if A and B have positive upper Banach density then there exists a finite set K in G such that A+B+K is a piecewise Bohr set (large pieces of almost periodic set -- contains a lot of structure). The latter implies that there exist C, D, E sets of positive upper Banach density such that C+D+E is a subset of A+B. (joint work with M.Beiglbock and V.Bergelson)

26 mars 2009, Jean-Pierre Conze (Institute of Mathematical Research of Rennes): Asymptotic laws for some sequential dynamical systems

Abstract. (given as a pdf-file)

2 april 2009, Giorgos Costakis (University of Crete): Dynamics of linear operators in finite and infinite dimensions

Abstract. (given as a pdf-file)

16 april 2009, Johan Andersson: Kloosterman sums and their applications in analytic number theory

Abstract. We will introduce the Kloosterman sums S(m,n;c) and discuss about some of their applications in analytic number theory, in particular applications on exponential sums and on the fourth power moment of the Riemann zeta-function (following Heath-Brown, Kuznetsov, Iwaniec and Motohashi).

4 maj 2009, Björn Winckler (KTH), Renormalization fixed points: one algorithm to find them all

Abstract. In this talk I will give an overview of the renormalization theory for unimodal maps. The focus will be on Marco Martens' proof of the existence of renormalization fixed points and how it naturally leads to an algorithm for constructing such fixed points (of any combinatorial type and critical exponent). Finally, I will outline a computer implementation of this algorithm.

7 maj 2009, Kristian Bjerkloev (KTH): Quasi-periodic perturbation of quadratic maps

Abstract. We consider quasi-periodic perturbations of a quadratic map exhibiting an attracting period-3 point. We will rigorously show that such a perturbation can create so-called Strange Nonchaotic Attractors, an object which lies between regularity and chaos.

8 maj 2009, Michael Benedicks (KTH): Kneading sequences for the Double Standard Map

Abstract. Maps from double standard map family f_a(x)=2x+a+(1/pi) sin(2 pi x) (mod~1), have the property that they are double covers of the circle onto itself with a unique inflexion point. They have been investigated most recently by M. Misiurewicz and A. Rodrigues. In particular one can say that they are hybrids between circle homeomorphims with inflexions and quadratic maps of the interval. The aim of the talk is to develop symbolic dynamics and kneading theory for these maps and discuss the behaviour in parameter space (chaotic behaviour, stable periodic orbits) comparing the situation to the more standard cases of circle homeomorphisms and quadratic interval maps. This is joint work with A. Rodrigues.

14 maj 2009, Elena Ushakova (UU): Kernel operators with variable limits of integration in Lebesgue spaces

Abstract. We study L^p-L^q boundedness and compactness of the operator f -> w(x) int_{a(x)}^{b(x)}k(x,y)f(y)v(y)dy with given weight functions w(x),v(y), differentiable strictly increasing border functions a(x),b(x) and a kernel k(x,y) satisfying some growth conditions. The results are applied for weighted L^p-L^q boundedness of geometric mean operator f -> exp[(b(x)-a(x))^(-1) int_a(x)^b(x) log f(y) dy] and other related problems. The talk is based on U.U.D.M. Reports 2008:30 and 2008:46.

15 maj 2009, Adrian Diaconu: Moments of quadratic Dirichlet L-functions

Abstract. This talk will present new developments in understanding the analytic continuation of certain Dirichlet series in several complex variables associated to moments of quadratic Dirichlet L-functions.

25 maj 2009, Emmanuel Breuillard (Univerité Paris-Sud, Orsay): Equidistribution of dense subgroups of nilpotent Lie groups

Abstract. The question of equidistribution of Gamma orbits on a homogeneous space X has been thoroughly studied in recent years from many perspectives. In this talk I will tackle this question for Gamma a nilpotent group and X a nilpotent Lie group and consider two types of averages: the word length average and the random walk average. Using unique ergodicity and precise geometric information on the shape of nilpotent balls I will show how to answer the equidistribution problem in that setting.

25 maj 2009, Uri Shapira (Hebrew University): Applying dynamics to number theory.

Abstract. I will present a recent joint work with Manfred Einsiedler and Lior Fishman in which we use rigidity results in dynamics to prove results in Diophantine approximations. We study how certain fractals intersect certain Diophantine classes. In particular I plan to concentrate on the following theorem regarding the intersection of the middle third Cantor set and the set of "Well Approximable" numbers: Theorem: Let a_n be a random sequence of the digits 0 and 2 (each digit appears with probability 1/2) and let x be the number in the unit interval having this sequence as its base three expansion. Then with probability one the coefficients in the continued fraction expantion of x, are unbounded.

25 maj 2009, Ben McReynolds (University of Chicago): Geometric spectra.

Abstract. In this talk, I will give a brief review of classical spectral geometry and the study of the geodesic length spectrum on a Riemannian manifold. I will then discuss some generalizations of the length spectrum and some results on how much of the geometry is encoded in other geometric spectra. This is joint work with Alan Reid.

2 juni 2009, Tom Sanders (Inst Mittag-Leffler): Modeling Roth's theorem on three term arithmetic progressions

Abstract. A beautiful theorem of K. F. Roth from the 50's asserts that any subset of the integers containing no three-term arithmetic progressions with non-zero common difference has density zero. In the 80's and 90's a beautiful model problem was considered: suppose that A \subset (\Z/3\Z)^n contains no affine line. Then |A|=O(3^n/n). A proof of this result (due to Meshulam) can be seen as a finite field version of Roth's proof of his aforementioned theorem, and in this setting the argument becomes much simpler. Despite this no improvement is known and any bound of the shape o(3^n/n) would be of considerable interest. In this talk we shall consider the analogous problem for (\Z/4\Z)^n where an improvement over Roth's argument is possible.

9 juli 2009, Carlos Vasquez: Stable ergodicity for partially hyperbolic attractors with positive central Lyapunov exponents.

Abstract. In this talk, we establish stable ergodicity for diffeomorphisms with partially hyperbolic attractors whose Lyapunov exponents along the center direction are all positive with respect to the physical measures.

9 juli 2009, Thomas Tucker (University of Rochester): Dynamical Mordell-Lang problems

Abstract. Let S be a group or semigroup acting on a variety V, let x be a point on V, and let W be a subvariety of V. What can be said about the structure of the intersection of the S-orbit of x with W? Does it have the structure of a union of cosets of subgroups of S? The Mordell-Lang theorem of Laurent, Faltings, and Vojta shows that this is the case for certain groups of translations (the Mordell conjecture is a consequence of this). On the other hand, Pell's equation shows that it is not true for additive translations of the Cartesian plane. We will see that this question relates to issues in complex dynamics, simple questions from linear algebra, and techniques from the study of linear recurrence sequences.

hösten 2008 (fall 2008)

26 augusti 2008, Bertrand Deroin (Université de Paris-Sud, Orsay): Polynomial ODEs in the complex domain; a probabilistic approach.

2 september 2008, Viviane Baladi (ENS, Paris): Linear response for piecewise expanding and smooth unimodal maps (joint with D. Smania)

11 september 2008, DUBBELSEMINARIUM
Roman Schubert (University of Bristol): Semiclassics and long time evolution: how compatible?
Oscar Marmon (Chalmers/GU): On the density of solutions to Diophantine equations

22 september 2008, Svetlana Jitomirskaya (University of California, Irvine): Quantitative Aubry duality, non-perturbative Eliasson theory and sharp properties of absolutely continuous spectral measures of 1D quasiperiodic operators

25 september 2008, Milagros Izquierdo (Linköping): Equisymmetric strata of the singular locus of the moduli space of Riemann surfaces of genus 4

16 oktober 2008, DUBBELSEMINARIUM
Håkan Hedenmalm (KTH): Heisenberg uniqueness pairs and the Klein-Gordon equation
Daniel Schnellmann (KTH): Almost Sure Equidistribution in Expansive Families

27 november 2008, Henrik Ueberschaer (University of Bristol): The trace formula for singular perturbations of the Laplacian on a hyperbolic surface

4 december 2008, Nikolai Proskurin (Steklov Institute): On the computation of L-series values with special reference to Rankin-Selberg convolutions of Maass wave forms

8-10 december 2008, "Automorphic forms, number theory, and computation" - workshop in honour of Dennis Hejhal on the occasion of his 60th birthday

18 december 2008, Juan Rivera-Letelier (PUC, Chile): Ergodic theory of ultrametric rational maps

våren 2008 (spring 2008)

27 mars 2008, Alexander Fish (Ohio State University): Rigidity of invariant measures under the action of a multiplicative semigroup of positive logarithmic density on T.

10 april 2008, Per Salberger (Chalmers): Counting solutions to Diophantine equations

8 maj 2008, Christopher Hughes (The University of York): Zeros and Derivatives

8 maj 2008, Tom Ward (University of East Anglia): Rigidity and entropy geometry

16 maj, Nalini Anantharaman (Ecole Polytechnique): Entropy and localization of eigenfunctions

20 maj, Jay Jorgenson (City College of New York, CUNY): Relating Maass forms to holomorphic one forms

21 maj, Mark Pollicott (Warwick University): Computing the Lyapunov exponent for random matrix products

29 maj, Florian Luca (Universidad Nacional Autonoma de Mexico): On the iterates of the Euler function

9 juni, Rafael de la Llave (University of Texas at Austin): Some geometric mechanisms of instability in Hamiltonian dynamical systems

1 juli, Yves de Cornulier (Université de Rennes I): on groups embedding quasi-isometrically into Hilbert spaces

1 juli, Romain Tessera (Vanderbilt University): Haagerup property, relative property T and expanders

hösten 2007 (fall 2007)

25 september 2007, kl 13.15-17.10, KTH, WORKSHOP "Group Actions and Arithmetic"
   Tsachik Gelander (Hebrew University): Property (T) and rigidity for actions on Banach spaces
   Richard Miles (KTH): Dirichlet series for finite combinatorial rank dynamics
   Rikard Olofsson (KTH): Large Hecke eigenfunctions of quantized cat maps
   Michael Björklund (KTH): Entropy of Algebraic Actions of the Discrete Heisenberg Group

1 november 2007, Morten Risager (University of Aarhus): Selberg's eigenvalue conjecture and poles of Eisenstein series

7 december 2007, Dennis Hejhal (Uppsala universitet): On Multi-variate Gaussians and Zeros of Linear Combinations of L-functions

13 december 2007, Magnus Aspenberg (Orsay): On rational Misiurewicz maps

våren 2007 (spring 2007)

29 januari 2007, Mitsuhiro Shishikura (Kyoto University, Japan): Parabolic renormalization and its application

20 februari 2007, Tatiana Smirnova-Nagnibeda (Université de Genève): Compactifying Outer space

7 maj 2007, Thomas Jordan (University of Warwick): The dimension of randomly perturbed self-affine sets

29 juni 2007, Nathan Jones (Centre de Recherches Mathematiques, Universite de Montreal): The square-free sieve and elliptic curve constants

12 juli 2007, Thomas J. Tucker (Rochester University): Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture

hösten 2006 (fall 2006)

4 september 2006, Fredrik Stromberg (Inst. of Theoretical Physics, TU-Clausthal, Germany), Transfer Operators for Hecke Triangle Groups

11 september 2006, Jens Marklof (University of Bristol, U.K.), Spectral Theta Series

21 september 2006, John Friedlander (University of Toronto, Canada), Hyperbolic Prime Number Theorem

11 december 2006, Francis Brown (Institut Mittag-Leffler), Arithmetic of zeta values and the irrationality of $\zeta(2)$ and $\zeta(3)$.

11 december 2006, Stephan Baier (IU Bremen, Germany), The Sato-Tate and Lang-Trotter conjectures about elliptic curves on average

18 december 2006, Tsachik Gelander (Hebrew University, Israel), On a conjecture by Margulis and Soifer

våren 2006 (spring 2006)

9 februari 2006, Moon Duchin (University of California, Davis): Random moves in the space of metrics

2 mars 2006, Jeffrey Steif (Chalmers): Statistical mechanical systems on complete graphs, infinite exchangeability and finite extensions

6 mars 2006, Michael Benedicks (KTH): Non uniformly hyperbolic attractors - invertible and non-invertible.

20 april 2006, Andrew Booker (University of Michigan): Convergent Hejhal-type algorithms

24 april 2006, Peter Storm (Stanford University): Topological lower volume bounds for hyperbolic 3-manifolds

2 maj 2006, Jean Lafont (Ohio State University): Simplicial volume of locally symmetric spaces of non-compact type

11 maj 2006, Mark Pollicott (Warwick University): Hausdorff dimension for randomly perturbed self-affine attractors

hösten 2005 (fall 2005)

12 september 2005, Anders Öberg (Uppsala): Uniqueness of $g$-measures

12 september 2005, Andreas Strömbergsson (Uppsala): Maass waveforms and Galois representations

3 oktober 2005, Dmitry Jakobson (McGill University): On nodal sets, critical points, and quasi-symmetry properties of eigenfunctions

17 oktober 2005, Andrew Booker (University of Michigan): On decidability of Artin's conjecture

12 december 2005, Yiannis Petridis (City University of New York, Lehman College): Distribution of closed geodesics with constraints

våren 2005 (spring 2005)

28 februari, Jörg Schmeling (Lund): Estimating the dimension of a model arising from horospherically tame Kleinian groups

14 mars, Stefan Lemurell (Chalmers): Deformations of Maass forms

14 mars, David Farmer (AIM): Derivatives of polynomials and L-functions

14 april, DNA Workshop: Number Theory and Quantum Chaos

18 april, Andreas Juhl (Humboldt-University, Berlin): Automorphic distributions, Selberg zeta functions and conformal geometry

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

2 maj, Peter Forrester (University of Melbourne): Sampling from eigenvalue distributions for matrix ensembles

9 maj, Peter Walters (Warwick Mathematics Institute): Cohomology for Shift Transformations

hösten 2004 (fall 2004)

20 september, Charles Favre (Université Denis Diderot): Equidistribution of points of small heights

27 september, Martin Olbrich (Technische Universität Clausthal and Georg-August-Universität Göttingen): Relations between length spectrum and topology of certain infinite volume hyperbolic manifolds

11 oktober, Dimitri Gioev (KTH): Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles

1 november, Torbjörn Lundh (Chalmers): DNA has not all the answers

15 november, Jens Marklof (University of Bristol): Recent developments in quantum chaos and number theory

29 november, Thomas Guhr (Matematisk fysik, LTH, Lunds universitet): Random Matrices in Physics and Supersymmetric Methods

29 november, Kurt Johansson (KTH): Determinantal processes and number variance saturation

20 december, Holger Then: Maass waveforms and an application to cosmology

våren 2004 (spring 2004)

5 april, Andreas Strömbergsson: On the values of a random linear form modulo one

19 april, Anders Karlsson: Metrics, isometries, and ergodic theory

3 maj, Mark Pollicott (University of Manchester): Zeta functions and hyperbolic dynamical systems

17 maj, Peter W. Jones (Yale University): Schwarzian derivatives for SLE mappings and approximation by Julia Sets

17 maj, Marco Martens (University of Groningen): Renormalization of Lorenz systems