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BEGIN:VEVENT
SUMMARY:Giovanni Panti (Università degli Studi di Udine)
DTSTART:20210114T153000Z
DTEND:20210114T164500Z
DTSTAMP:20260404T111106Z
UID:BODS/1
DESCRIPTION:Title: Slow continued fractions\, Minkowski functions and the joint spectral
radius\nby Giovanni Panti (Università degli Studi di Udine) as part o
f Bremen Online Dynamics Seminar\n\n\nAbstract\nEvery unimodular partition
of the real unit interval in m pieces gives\nrise to $2^m$ slow continued
fraction maps. Many such maps have names\n(Farey fractions\, ceiling frac
tions\, even/odd fractions\, ...)\, but most\nare nameless. Certain proper
ties are commonly shared (for example\, the\nvalidity of Lagrange's theore
m)\, while other features are more delicate\n(the validity of the Serret t
heorem\, the description of the unique a.c.\ninvariant measure\, the chara
cterization of purely periodic points\, ...).\n\nAny slow continued fracti
on map determines a Minkowski function\, namely\nthe distribution function
of the measure of maximal entropy. These\nMinkowski functions have a well
-defined average Holder exponent (studied\nby many authors\, and related t
o the dimension of the measure)\, as well\nas a least Holder exponent. The
latter has the form log(m)/2*log(r)\,\nwith r a quadratic irrational\, th
e joint spectral radius of the iterated\nfunction system given by the inve
rse branches of the map.\n\nIt is plausible that every IFS with maps in $\
\mathrm{GL}(2\,\\mathbb Z)$ has algebraic joint\nspectral radius\, but as
far as we know this issue has not been settled.\nWe show however\, in join
t work with Davide Sclosa\, that this is indeed\nthe case for IFSs over tw
o maps in $\\mathrm{SL}(2\,\\mathbb Z_{\\geq 0})$.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Mohammadi (UC San Diego)
DTSTART:20210128T153000Z
DTEND:20210128T164500Z
DTSTAMP:20260404T111106Z
UID:BODS/2
DESCRIPTION:Title: Geodesic planes in hyperbolic 3-manifolds\nby Amir Mohammadi (UC S
an Diego) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nLet M b
e a hyperbolic 3-manifold\, a geodesic plane in M is a\ntotally geodesic i
mmersion of the hyperbolic plane into M. In this talk\nwe will give an ove
rview of some results which highlight how geometric\,\ntopological\, and a
rithmetic properties of M affect the behavior of\ngeodesic planes in M. Th
is talk is based on joint works with McMullen\,\nOh and Margulis.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Springborn (TU Berlin)
DTSTART:20201126T153000Z
DTEND:20201126T164500Z
DTSTAMP:20260404T111106Z
UID:BODS/3
DESCRIPTION:Title: The hyperbolic geometry of Markov's theorem on Diophantine approximati
on and quadratic forms\nby Boris Springborn (TU Berlin) as part of Bre
men Online Dynamics Seminar\n\n\nAbstract\nMarkov's theorem classifies the
worst irrational numbers and the most non-zero quadratic forms. This talk
is about a new proof using hyperbolic geometry. The main ingredients are
a dictionary to translate between hyperbolic geometry and algebra/number t
heory\, and some very\nbasic tools borrowed from modern geometric Teichmü
ller theory. Simple closed geodesics and ideal triangulations of the modul
ar torus play an important role\, and so does the problem: How far can a s
traight line crossing a triangle stay away from the vertices?\n
LOCATION:https://stable.researchseminars.org/talk/BODS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Monk (IRMA\, Strasbourg)
DTSTART:20201112T153000Z
DTEND:20201112T164500Z
DTSTAMP:20260404T111106Z
UID:BODS/4
DESCRIPTION:Title: The geometry and spectrum of random hyperbolic surfaces\nby Laura
Monk (IRMA\, Strasbourg) as part of Bremen Online Dynamics Seminar\n\n\nAb
stract\nThe main aim of this talk is to present geometric and spectral\npr
operties of typical hyperbolic surfaces. More precisely\, I will:\n\n- int
roduce a probabilistic model\, first studied by Mirzakhani\, which is\na n
atural and convenient way to sample random hyperbolic surfaces\n\n- descri
be the geometric properties of these random surfaces: diameter\,\ninjectiv
ity radius\, Cheeger constant\, Benjamini-Schramm convergence...\n\n- expl
ain how one can deduce from this geometric information estimates\non the n
umber of eigenvalues of the Laplacian in an interval $[a\,b]$\,\nusing the
Selberg trace formula.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sören Petrat (Jacobs University)
DTSTART:20200604T143000Z
DTEND:20200604T154500Z
DTSTAMP:20260404T111106Z
UID:BODS/5
DESCRIPTION:Title: Effective Dynamics of the Mean-field Bose Gas\nby Sören Petrat (J
acobs University) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\
nThe quantum dynamics of N non-relativistic bosons is described\nby the Sc
hroedinger equation with pair interaction. The complexity of\nsolutions ge
nerally grow exponentially in the particle number\, so for\nlarge N coarse
-grained or effective descriptions are desirable. From a\nmathematical phy
sics point of view\, one aims at deriving effective\nequations in a rigoro
us way\, i.e.\, proving that their solutions converge\nto the solutions of
the Schroedinger equation in a suitable topology. In\nthis talk\, we will
consider the dynamics in the mean-field limit\, which\nhas been studied e
xtensively in the last two decades. I will present an\noverview about the
research goals and results\, and then specifically\ndiscuss recent results
of my collaborators and myself on a perturbative\nexpansion of solutions
to the Schroedinger equation.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keivan Mallahi-Karai (Jacobs University)
DTSTART:20200702T143000Z
DTEND:20200702T154500Z
DTSTAMP:20260404T111106Z
UID:BODS/6
DESCRIPTION:Title: Locally random groups\nby Keivan Mallahi-Karai (Jacobs University)
as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nGroups without n
on-trivial low dimensional representations\,\nnamed quasi-random by Gowers
\, have recently found many applications in\nstudying group theoretical p
roblems of combinatorial nature. Loosely\nspeaking\, non-existence of such
representations forces the product map\non the group mapping $(a\, b)$ to
their product $ab$ to have a certain mixing\nbehavior.\n\nIn this talk\,
after briefly recalling the notion of quasi randomness\, I\nwill discuss
a generalisation of this concept to the class of compact\ngroups. This pro
perty\, called local randomness\, is formulated in terms\nof unitary repre
sentations of the compact group $G$ and captures a similar\nmixing behavio
r at all scales. I will discuss a number of related\nresults including a
classification of locally random groups\, a mixing\ninequality\, and\, if
time allows\, connection to spectral gap.\n\nThe talk is based on a joint
work with Amir Mohammadi and Alireza Salehi\nGolsefidy.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Mitchell (University of Birmingham)
DTSTART:20210218T153000Z
DTEND:20210218T164500Z
DTSTAMP:20260404T111106Z
UID:BODS/7
DESCRIPTION:Title: Measure theoretic entropy of random substitutions\nby Andrew Mitch
ell (University of Birmingham) as part of Bremen Online Dynamics Seminar\n
\n\nAbstract\nRandom substitutions and their associated subshifts provide\
na model for structures that exhibit both long range order and positive\ne
ntropy. In this talk we discuss the entropy of a large class of ergodic\nm
easures\, known as frequency measures\, that arise naturally from random\n
substitutions. We introduce a new measure of complexity\, namely measure\
ntheoretic inflation word entropy\, and discuss its relationship to\nmeasu
re theoretic entropy. We also show how this new measure of\ncomplexity ca
n be used to provide a framework for the systematic study\nof the measure
theoretic entropy of random substitution subshifts.\n\nAs an application o
f our results\, we obtain closed form formulas for the\nentropy of a wide
range of random substitution subshifts and show that\nin many cases there
exists a frequency measure of maximal entropy.\nFurther\, for a class of r
andom substitution subshifts\, we show that this\nmeasure is the unique me
asure of maximal entropy.\n\nThis is joint work with P. Gohlke\, R. Leek\,
D. Rust\, and T. Samuel.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlangelo Liverani (U Roma „Tor Vergata“)
DTSTART:20210209T130000Z
DTEND:20210209T143000Z
DTSTAMP:20260404T111106Z
UID:BODS/9
DESCRIPTION:Title: Measurements in Dynamical Systems\nby Carlangelo Liverani (U Roma
„Tor Vergata“) as part of Bremen Online Dynamics Seminar\n\n\nAbstract
\nVery often a measurement of a physical system takes the form of a finite
\ntime average for some observable. For infinite time averages Birkhoff's\
ntheorem classifies all the possible outcomes in terms of the invariant\nm
easures of the system. The study of the\, much more realistic\, finite\nti
me averages is equivalent to investigating at which speed the limit is\nat
tained. This problem is only partially understood\, essentially we\nunders
tand few special cases. Yet\, our current knowledge shows that the\nbehavi
our depends drastically from the properties of the system. In the\nstudy o
f such a problem functional analysis\, probability theory\, and\ngeometry
play major roles. I will attempt to give an overview of the\nsubject.\n\nT
his is a joint event with the mathematical colloquium at the\nUniversity o
f Bremen\n
LOCATION:https://stable.researchseminars.org/talk/BODS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Schapira (Université Rennes 1)
DTSTART:20210315T143000Z
DTEND:20210315T154500Z
DTSTAMP:20260404T111106Z
UID:BODS/10
DESCRIPTION:Title: Strong positive recurrence for geodesic flows\nby Barbara Schapir
a (Université Rennes 1) as part of Bremen Online Dynamics Seminar\n\n\nAb
stract\nIn a recent paper with S Gouezel and S Tapie\, in the context of g
eodesic\nflows of noncompact negatively curved manifolds\, we propose thre
e\ndifferent definitions of entropy and pressure at infinity\, through\ngr
owth of periodic orbits\, critical exponents of Poincaré series\, and\nen
tropy (pressure) of invariant measures. We show that these notions\ncoinci
de. Thanks to these entropy and pressure at infinity\, we\ninvestigate tho
roughly the notion of strong positive recurrence in this\ngeometric contex
t. A potential is said strongly positively recurrent\nwhen its pressure at
infinity is strictly smaller than the full\ntopological pressure. We show
in particular that if a potential is\nstrongly positively recurrent\, the
n it admits a finite Gibbs measure. We\nalso provide easy criteria allowin
g to build such strong positively\nrecurrent potentials and many examples.
\n\nDuring the talk\, I will present some of these points\, to give to the
\naudience the flavour of this work.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Péter Koltai (FU Berlin)
DTSTART:20210419T133000Z
DTEND:20210419T144500Z
DTSTAMP:20260404T111106Z
UID:BODS/11
DESCRIPTION:Title: Coarse-graining of transport in non-autonomous systems\nby Péter
Koltai (FU Berlin) as part of Bremen Online Dynamics Seminar\n\n\nAbstrac
t\nThe decomposition of the state space of a dynamical system into almost\
ninvariant sets is important for understanding its essential macroscopic\n
behavior. The concept is reasonably well understood for autonomous\ndynami
cal systems\, and recently a generalization appeared for\nnon-autonomous s
ystems: coherent sets. Aiming at a unified theory\, in\nthis talk we will
first present connections between the\nmeasure-theoretic autonomous and no
n-autonomous concepts. We shall do\nthis by considering the augmented stat
e space. Second\, we will extend\nthe framework to finite-time systems\, a
nd show that it is especially\nwell-suited for manipulating the mixing pro
perties of the dynamics.\nThird\, we will show how this framework can be u
sed to identify the birth\nand death of coherent sets.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valérie Berthé (CNRS\, IRIF\, Université de Paris)
DTSTART:20210531T133000Z
DTEND:20210531T144500Z
DTSTAMP:20260404T111106Z
UID:BODS/12
DESCRIPTION:Title: Multidimensional continued fractions and symbolic codings of toral tr
anslations\nby Valérie Berthé (CNRS\, IRIF\, Université de Paris) a
s part of Bremen Online Dynamics Seminar\n\n\nAbstract\nIt has been a long
standing problem to find good symbolic codings for\nKronecker toral tra
nslations that enjoy the beautiful properties\nof Sturmian sequences like
low factor complexity and good local\ndiscrepancy properties. \nWe constr
uct such codings in terms of multidimensional continued fraction\nalgorith
ms that are realized by sequences of substitutions. In particular\,\ngiven
any strongly convergent continued fraction algorithm\, these sequences\nl
ead to renormalization schemes which produce symbolic codings and bounded\
nremainder sets at all scales in a natural way. Such sets \nprovide par
ticularly strong convergence properties of ergodic sums\, \nand are also
closely related to the notion of balance in word\ncombinatorics. \n As s
trong convergence of a continued fraction algorithm results in a Pisot\nty
pe property\, our approach provides a systematic way to confirm purely\ndi
screte \nspectrum results for wide classes of substitutions.\nThis is jo
int work with W. Steiner and J. Thuswaldner.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Gekhtman (Technion)
DTSTART:20210308T143000Z
DTEND:20210308T154500Z
DTSTAMP:20260404T111106Z
UID:BODS/13
DESCRIPTION:Title: Gibbs measures vs. random walks in negative curvature\nby Ilya Ge
khtman (Technion) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\
nThe ideal boundary of a negatively curved manifold naturally\ncarries two
types of measures.\nOn the one hand\, we have conditionals for equilibriu
m (Gibbs) states\nassociated to Hoelder potentials\; these include the Pat
terson-Sullivan\nmeasure and the Liouville measure. On the other hand\, we
have stationary\nmeasures coming from random walks on the fundamental gro
up.\n We compare and contrast these two classes.First\, we show that bot
h\nof these of these measures can be associated to geodesic flow invariant
\nmeasures on the unit tangent bundle\, with respect to which closed\ngeod
esics satisfy different equidistribution properties. Second\, we show\ntha
t the absolute continuity between a harmonic measure and a Gibbs\nmeasure
is equivalent to a relation between entropy\, (generalized)\ndrift and cr
itical exponent\, generalizing previous formulas of\nGuivarc’h\, Ledrapp
ier\, and Blachere-Haissinsky-Mathieu. This shows that\nif the manifold (o
r more generally\, a CAT(-1) quotient) is geometrically\nfinite but not co
nvex cocompact\, stationary measures are always singular\nwith respect to
Gibbs measures.\nA major technical tool is a generalization of a deviation
inequality due\nto Ancona saying the so called Green distance associated
to the random\nwalk is nearly additive along geodesics in the universal co
ver.\nPart of this is based on joint work with Gerasimov-Potyagailo-Yang a
nd\npart on joint work with Tiozzo.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Tiozzo (University of Toronto)
DTSTART:20210322T143000Z
DTEND:20210322T154500Z
DTSTAMP:20260404T111106Z
UID:BODS/14
DESCRIPTION:Title: The fundamental inequality for random walks on cocompact Fuchsian gro
ups\nby Giulio Tiozzo (University of Toronto) as part of Bremen Online
Dynamics Seminar\n\n\nAbstract\nSeveral stochastic processes are defined
on the hyperbolic plane H^2. For instance\, one can consider a Brownian mo
tion\, or a discretized version thereof\, when one performs a random walk
on the group of isometries of H^2. \n\nIt is a recurring question\, going
back to Furstenberg\, Guivarc’h\, Ledrappier\, Kaimanovich\, and others\
, \nwhether the measures obtained from the random walks coincide with meas
ures of geometric origin\, such as the Lebesgue measure. \n\nWe prove that
the hitting measure is singular with respect to Lebesgue measure for any
random walk on a cocompact Fuchsian group generated by translations on opp
osite sides of a symmetric hyperbolic polygon. This addresses a question o
f Kaimanovich-Le Prince. \n\nJoint with P. Kosenko.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rhiannon Dougall
DTSTART:20210517T133000Z
DTEND:20210517T144500Z
DTSTAMP:20260404T111106Z
UID:BODS/15
DESCRIPTION:Title: Comparison of entropy for infinite covering manifolds\, and group ext
ensions of subshifts of finite type\nby Rhiannon Dougall as part of Br
emen Online Dynamics Seminar\n\n\nAbstract\nA classical example of an Anos
ov flow is the geodesic flow associated to\na compact hyperbolic manifold
M\, for which the periodic orbits of the\nflow correspond to closed geodes
ics in M. In general\, Anosov flows are\nnot so well behaved: there may be
infinitely many periodic orbits in a\nfree homotopy class\, in contract t
o geodesic flows. In this talk we\ndiscuss the problem of counting periodi
c orbits in infinite covering\nmanifolds\, where we relate the exponential
growth rate of periodic\norbits in the cover to properties of the coverin
g group. One of the\ntools is a new result for non-symmetric group extensi
ons of subshifts of\nfinite type which includes a result on non-symmetric
random walks. I\nwill spend some time motivating the problems and give the
perspective of\nthe thermodynamical formalism.\n(Featuring joint work wit
h Richard Sharp.)\n
LOCATION:https://stable.researchseminars.org/talk/BODS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilka Agricola (Uni Marburg)
DTSTART:20210608T140000Z
DTEND:20210608T151500Z
DTSTAMP:20260404T111106Z
UID:BODS/16
DESCRIPTION:Title: What are spinors and what should they be?\nby Ilka Agricola (Uni
Marburg) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nRichard
Dedekind published in 1888 a paper entitled "Was sind und was sollen\ndie
Zahlen?"\, variously translated as "What are numbers and what should\nthey
be?". In analogy to this classic\, I shall investigate in this talk\nwhat
spinors (or\, in full term\, spinor fields) are\, what distinguishes\nthe
m from functions\, how they appear naturally in complex analysis and\ntheo
retical physics\, and\, finally\, why they are an object of intrinsic\nmat
hematical\ninterest. Doing so\, I will give a gentle introduction to spin
geometry\nand Dirac operators for the non-experts\, and I will provide an
overview of\ntypical problems and interesting links to other areas.\n\nThi
s is a joint seminar with the University of Bremen Mathematics Colloquium.
\n
LOCATION:https://stable.researchseminars.org/talk/BODS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vlad Vicol (NYU)
DTSTART:20210506T140000Z
DTEND:20210506T151500Z
DTSTAMP:20260404T111106Z
UID:BODS/17
DESCRIPTION:Title: Shock formation for the 3d Euler equations\nby Vlad Vicol (NYU) a
s part of Bremen Online Dynamics Seminar\n\n\nAbstract\nIn this talk\, I w
ill discuss the shock formation process for the 3d\ncompressible Euler equ
ations\, in which sounds waves interact with\nentropy waves to produce vor
ticity. Smooth solutions form a generic\nstable shock with explicitly comp
utable blowup time\, location\, and\ndirection. Our method establishes the
asymptotic stability of a generic\nshock profile in modulated self-simila
r variables\, controlling the\ninteraction of three distinct wave families
.\n\nThis is based on joint work with T. Buckmaster and S. Shkoller.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seonhee Lim (Seoul National University)
DTSTART:20210614T080000Z
DTEND:20210614T091500Z
DTSTAMP:20260404T111106Z
UID:BODS/18
DESCRIPTION:Title: Brownian motion in negative curvature\nby Seonhee Lim (Seoul Nati
onal University) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\n
Brownian motion in the hyperbolic space $H^n$ is rather\nwell-known with a
precise formula for the heat kernel\, which is the\nprobability density f
unction of the Brownian motion. In this talk\, we\nwill talk about the asy
mptotic formula for the heat kernel in a\nconnected simply connected negat
ively curved Riemannian manifold X whose\nmetric is lifted from a compact
manifold M.\n As time goes to infinity\, we show that the heat kernel $p(t
\,x\,y)$ is\nasymptotically $e^{-\\lambda_0} t^{-3/2} C(x\,y)$ where $\\la
mbda_0$ is the\nbottom of the spectrum of the geometric Laplacian. The pro
of uses the\nuniform Harnack inequality on the boundary $\\partial X$ as w
ell as the\nuniform mixing of the geodesic flow on the quotient manifold M
. (This is\na joint work with François Ledrappier.)\n
LOCATION:https://stable.researchseminars.org/talk/BODS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wael Bahsoun (Loughborough)
DTSTART:20210712T133000Z
DTEND:20210712T144500Z
DTSTAMP:20260404T111106Z
UID:BODS/19
DESCRIPTION:Title: Transfer operators and BV spaces: from classic to anisotropic\nby
Wael Bahsoun (Loughborough) as part of Bremen Online Dynamics Seminar\n\n
\nAbstract\nSmooth ergodic theory aims to analyse the long-term statistics
\nof chaotic dynamical systems. There are several analytic and\nprobabilis
tic tools that are used to answer such questions. Each of\nthese approache
s has its advantages and its shortcomings\, depending on\nthe system under
consideration. In this presentation\, I will focus on\ntransfer operator
techniques and spectral methods\, which are known to be\nvery powerful whe
n dealing with uniformly expanding\, or uniformly\nhyperbolic systems. The
first half of this talk will be rather\nintroductory\, aimed at non-exper
ts\, focusing on ideas behind this\napproach through simple\, yet importan
t examples. In the second half of\nthe talk\, I will discuss a recent join
t work with C. Liverani\, whose\nlong-term goal is to provide a good spect
ral picture for piecewise\nhyperbolic systems with singularities (e.g. bil
liard maps) in any\ndimension. In connection with this goal\, I will also
discuss a recent\njoint work with F. Sélley on coupled map lattices.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Folkmar Bornemann (TU München)
DTSTART:20210726T133000Z
DTEND:20210726T144500Z
DTSTAMP:20260404T111106Z
UID:BODS/20
DESCRIPTION:Title: Finite size effects: random matrices\, quantum chaos\, and Riemann ze
ros\nby Folkmar Bornemann (TU München) as part of Bremen Online Dynam
ics Seminar\n\n\nAbstract\nSince the legendary 1972 encounter of H. Montgo
mery and F.\nDyson at tea time in Princeton\, a statistical correspondence
of the\nnon-trivial zeros of the Riemann Zeta function with eigenvalues o
f\nhigh-dimensional random matrices has emerged. Surrounded by many deep\n
but notoriously intractable conjectures\, there is a striking analogy to\n
the energy levels of a quantum billiard system with chaotic dynamics.\nThe
statistical accuracy provided by an enormous dataset of more than\none bi
llion zeros reveals distinctive finite size effects. Using the\nphysical a
nalogy\, we discuss a precise prediction of these effects that\nhas been o
btained in terms of operator determinants and their\nperturbation series (
joint work with P. Forrester and A. Mays\, Melbourne).\n
LOCATION:https://stable.researchseminars.org/talk/BODS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Zelik (University of Surrey)
DTSTART:20210913T133000Z
DTEND:20210913T144500Z
DTSTAMP:20260404T111106Z
UID:BODS/21
DESCRIPTION:Title: Deterministic and random attractors for a wave equation with sign cha
nging damping\nby Sergey Zelik (University of Surrey) as part of Breme
n Online Dynamics Seminar\n\n\nAbstract\nWe discuss the long-time dynamic
s generated\nby weakly damped wave equations in bounded 3D domains where\n
the damping coefficient depends explicitly on time and may change sign.\nW
e show that in the case when the non-linearity is super-linear\, the\ncons
idered equation remains dissipative if the weighted mean value of\nthe dis
sipation rate remains positive and that the conditions of this type\nare n
ot sufficient in the linear case. Two principally different cases will be
\nconsidered. In the case when this mean is uniform (which corresponds\nto
deterministic dissipation rate)\, it will be shown that the considered sy
stem\npossesses smooth uniform attractors as well as non-autonomous expone
ntial\nattractors. In the case where the mean is not uniform (which\ncorre
sponds to the random dissipation rate\, for instance\, when this dissipati
on\nrate is generated by the Bernoulli process)\, the tempered random\natt
ractor will be constructed. In contrast to the usual situation\, this\nran
dom attractor is expected to have infinite Hausdorff \nand fractal dimens
ions. The simplified model example which demonstrates in\nfinite-dimensio
nality of the random attractor will also be presented.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Aaronson (Tel Aviv University)
DTSTART:20211129T143000Z
DTEND:20211129T154500Z
DTSTAMP:20260404T111106Z
UID:BODS/22
DESCRIPTION:Title: Renewal and ratio mixing properties of "nice" infinite ergodic transf
ormations\nby Jon Aaronson (Tel Aviv University) as part of Bremen Onl
ine Dynamics Seminar\n\n\nAbstract\nI'll discuss "ratio mixing" propertie
s\nof transformations preserving infinite measures ( e.g. as in Hopf's\n
1936 book) and also their "renewal properties"\n(occupation processes to s
ets of finite measure). Examples of "nice"\ntransformations considered inc
lude certain null-recurrent Markov\nchains\, - "intermittent" interval map
s\, - inner functions\, hyperbolic\ngeodesic flows on cyclic covers.\n\nIn
cludes joint work with Hitoshi Nakada\, Dalia Terhesiu & Toru Sera.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Hlushchanka (Utrecht University)
DTSTART:20220110T143000Z
DTEND:20220110T154500Z
DTSTAMP:20260404T111106Z
UID:BODS/23
DESCRIPTION:Title: Canonical decomposition of rational maps\nby Mikhail Hlushchanka
(Utrecht University) as part of Bremen Online Dynamics Seminar\n\n\nAbstra
ct\nThere are various classical and more recent decomposition results in m
apping class group theory\, geometric group theory\, and complex dynamics
(which include celebrated results by Bill Thurston). The goal of this talk
is to introduce a novel powerful decomposition of rational maps based on
the topological structure of their Julia sets. Namely\, we will discuss th
e following result: every postcritically-finite rational map with non-empt
y Fatou set can be canonically decomposed into crochet maps (these have ve
ry "thinly connected" Julia sets) and Sierpinski carpet maps (these have v
ery "heavily connected" Julia sets). If time permits\, I will discuss appl
ications of this result in various aspects of geometric group theory. Base
d on a joint work with Dima Dudko and Dierk Schleicher.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tushar Das (University of Wisconsin-La Crosse)
DTSTART:20220131T143000Z
DTEND:20220131T154500Z
DTSTAMP:20260404T111106Z
UID:BODS/24
DESCRIPTION:Title: Dimension theory for infinite-alphabet conformal iterated function sy
stem limit sets\nby Tushar Das (University of Wisconsin-La Crosse) as
part of Bremen Online Dynamics Seminar\n\n\nAbstract\nStudying the extreme
ly delicate geometric-measure-theoretic properties of dynamical limit sets
is often an endeavor beset with myriad challenges. In this vein\, we focu
s on the dimension-theoretic study of continued fraction Cantor sets -- a
rich seam inaugurated by the work of Jarník and Besicovitch in the 1920s.
I will report on two projects about such fascinating fractals. The first
considers small perturbations of a conformal iterated function system (CIF
S)\; while the second resolves two recent questions posed by Chousionis\,
Leykekhman\, and Urbański regarding the dimension spectrum of a CIFS (i.e
. the set of all Hausdorff dimensions of its various subsystem limit sets)
. We hope to present several interesting problems and directions that awai
t resolution and explorations by the brilliant Bremen dynamics group 🙂\
n
LOCATION:https://stable.researchseminars.org/talk/BODS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anja Randecker (University of Heidelberg)
DTSTART:20220117T143000Z
DTEND:20220117T154500Z
DTSTAMP:20260404T111106Z
UID:BODS/26
DESCRIPTION:Title: Interval exchange transformations and translation surfaces in genus 2
\nby Anja Randecker (University of Heidelberg) as part of Bremen Onlin
e Dynamics Seminar\n\n\nAbstract\nTranslation surfaces arise naturally in
many different contexts such as the theory of mathematical billiards\, of
Teichmüller spaces\, or of stability conditions of categories.\nA transla
tion surface can be described by finitely many polygons that are glued alo
ng edges which are parallel and have the same length.\n\nFrom a dynamical
system point of view\, it is interesting to study the geodesic flow on tra
nslation surfaces. These flows are strongly related to interval exchange t
ransformations.\n\nIn my talk\, I will explain this relation and give an e
xplicit description of translation surfaces of genus 2 where the horizonta
l geodesic flow is completely periodic. The talk is based on joint work in
progress with Binbin Xu.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Burrin (ETH Zurich)
DTSTART:20220214T143000Z
DTEND:20220214T154500Z
DTSTAMP:20260404T111106Z
UID:BODS/27
DESCRIPTION:Title: Windings of closed geodesics and number theory\nby Claire Burrin
(ETH Zurich) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nIn h
is 2006 ICM lecture\, Ghys made the following observation: the winding of
a closed geodesic around the cusp of the modular surface can be computed u
sing a function from the theory of modular forms\; the Rademacher function
. In joint work with Flemming von Essen\, we studied how and when generali
zations of the Rademacher function also encode the winding for closed geod
esics around the cusps of hyperbolic surfaces. For certain families of sur
faces\, we use a Selberg trace formula argument to obtain precise statisti
cal results on these winding numbers.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Ben-Artzi (Cardiff University)
DTSTART:20220523T133000Z
DTEND:20220523T144500Z
DTSTAMP:20260404T111106Z
UID:BODS/28
DESCRIPTION:Title: Dynamical systems lacking spectral gaps: functional inequalities and
convergence rates\nby Jonathan Ben-Artzi (Cardiff University) as part
of Bremen Online Dynamics Seminar\n\n\nAbstract\nOur world is neither comp
act nor periodic. It is therefore natural to consider dynamical systems on
unbounded domains\, where typically there is no spectral gap. I will pres
ent a (simple) method for studying the generators of such systems where a
spectral gap assumption is replaced with an estimate of the Density of Sta
tes (DoS) near zero. There are two main applications:\n\n1) Dissipative sy
stems: when the generator is non-negative\, an estimate of the DoS leads t
o a so-called "weak Poincaré inequality" (WPI). This in turn leads (in so
me cases) to an algebraic decay rate for the $L^2$ norm of the solution. F
or instance\, in the case of the Laplacian (generator of the heat equation
) the WPI is simply the Nash inequality which leads to the optimal decay r
ate of $t^{-d/4}$.\n\n2) Conservative systems: when the generator is skew-
adjoint\, an estimate of the DoS leads to a uniform ergodic theorem on an
appropriate subspace. Examples include the linear Schrödinger equation an
d incompressible flows in Euclidean space.\n\nBased on joint works with Am
it Einav (Durham) and Baptiste Morisse (formerly a postdoc at Cardiff).\n
LOCATION:https://stable.researchseminars.org/talk/BODS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shayan Alikhanloo (Uni Bielefeld)
DTSTART:20220321T143000Z
DTEND:20220321T154500Z
DTSTAMP:20260404T111106Z
UID:BODS/29
DESCRIPTION:Title: Self-adjoint Laplacians\, symmetric semigroups and diffusions on hype
rbolic attractors\nby Shayan Alikhanloo (Uni Bielefeld) as part of Bre
men Online Dynamics Seminar\n\n\nAbstract\nAnalysis on smooth manifolds\,
foliated spaces and fractals in terms of Dirichlet forms is well establish
ed. But such an analysis on hyperbolic attractors is yet to be explored. W
e use the core material and central results from the theory of hyperbolic
dynamical systems such as the stable manifold theorem and physical measure
s to introduce self-adjoint Laplacians\, symmetric Markov semigroups and s
ymmetric diffusions via Dirichlet forms. In particular\, this may be seen
as far-reaching extension of well-known classical analysis on geodesic flo
ws on manifolds of negative sectional curvature. This talk is based on a j
oint work with Michael Hinz.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Marchese ((University of Bologna))
DTSTART:20220718T133000Z
DTEND:20220718T144500Z
DTSTAMP:20260404T111106Z
UID:BODS/30
DESCRIPTION:Title: Transfer operators and dimension of bad sets for non-uniform fuchsian
lattices\nby Luca Marchese ((University of Bologna)) as part of Breme
n Online Dynamics Seminar\n\n\nAbstract\nThe set of badly approximable rea
l numbers admits an exhaustion in sets Bad(c) with c>0\, whose dimension g
oes to zero as c goes to zero. D. Hensley computed the asymptotic for the
dimension up to the first order in c\, via an estimate for the dimension o
f the set of real numbers whose continued fraction has partial quotiens bo
unded by a fixed parameter. We consider diophantine approximations by para
bolic fiwed points of any non-uniform lattice in PSL(2\,R) and the corresp
onding notion of badly approximable real numbers. We compute the dimension
of the set of such points up to the first order in c>0\, via the thermody
namic method of Ruelle and Bowen. Geometric good approximations are relate
d to a notion of bounded partial quotients for the Bowen-Series expansion.
This gives a family of Cantor sets and associated quasi-compact transfer
operators\, with simple and positive maximal eigenvalue. Then perturbative
analysis of spectra applies.\n
LOCATION:https://stable.researchseminars.org/talk/BODS/30/
END:VEVENT
END:VCALENDAR