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BEGIN:VEVENT
SUMMARY:Giovanni Panti (Università degli Studi di Udine)
DTSTART;VALUE=DATE-TIME:20210114T153000Z
DTEND;VALUE=DATE-TIME:20210114T164500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/1
DESCRIPTION:Title: Slo
w continued fractions\, Minkowski functions and the joint spectral radius<
/a>\nby Giovanni Panti (Università degli Studi di Udine) as part of Breme
n-Oldenburg Dynamics Seminar\n\n\nAbstract\nEvery unimodular partition of
the real unit interval in m pieces gives\nrise to $2^m$ slow continued fra
ction maps. Many such maps have names\n(Farey fractions\, ceiling fraction
s\, even/odd fractions\, ...)\, but most\nare nameless. Certain properties
are commonly shared (for example\, the\nvalidity of Lagrange's theorem)\,
while other features are more delicate\n(the validity of the Serret theor
em\, the description of the unique a.c.\ninvariant measure\, the character
ization of purely periodic points\, ...).\n\nAny slow continued fraction m
ap determines a Minkowski function\, namely\nthe distribution function of
the measure of maximal entropy. These\nMinkowski functions have a well-def
ined average Holder exponent (studied\nby many authors\, and related to th
e dimension of the measure)\, as well\nas a least Holder exponent. The lat
ter has the form log(m)/2*log(r)\,\nwith r a quadratic irrational\, the jo
int spectral radius of the iterated\nfunction system given by the inverse
branches of the map.\n\nIt is plausible that every IFS with maps in $\\mat
hrm{GL}(2\,\\mathbb Z)$ has algebraic joint\nspectral radius\, but as far
as we know this issue has not been settled.\nWe show however\, in joint wo
rk with Davide Sclosa\, that this is indeed\nthe case for IFSs over two ma
ps in $\\mathrm{SL}(2\,\\mathbb Z_{\\geq 0})$.\n
LOCATION:https://researchseminars.org/talk/BODS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Mohammadi (UC San Diego)
DTSTART;VALUE=DATE-TIME:20210128T153000Z
DTEND;VALUE=DATE-TIME:20210128T164500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/2
DESCRIPTION:Title: Geo
desic planes in hyperbolic 3-manifolds\nby Amir Mohammadi (UC San Dieg
o) as part of Bremen-Oldenburg Dynamics Seminar\n\n\nAbstract\nLet M be a
hyperbolic 3-manifold\, a geodesic plane in M is a\ntotally geodesic immer
sion of the hyperbolic plane into M. In this talk\nwe will give an overvie
w of some results which highlight how geometric\,\ntopological\, and arith
metic properties of M affect the behavior of\ngeodesic planes in M. This t
alk is based on joint works with McMullen\,\nOh and Margulis.\n
LOCATION:https://researchseminars.org/talk/BODS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Springborn (TU Berlin)
DTSTART;VALUE=DATE-TIME:20201126T153000Z
DTEND;VALUE=DATE-TIME:20201126T164500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/3
DESCRIPTION:Title: The
hyperbolic geometry of Markov's theorem on Diophantine approximation and
quadratic forms\nby Boris Springborn (TU Berlin) as part of Bremen-Old
enburg Dynamics Seminar\n\n\nAbstract\nMarkov's theorem classifies the wor
st irrational numbers and the most non-zero quadratic forms. This talk is
about a new proof using hyperbolic geometry. The main ingredients are a di
ctionary to translate between hyperbolic geometry and algebra/number theor
y\, and some very\nbasic tools borrowed from modern geometric Teichmüller
theory. Simple closed geodesics and ideal triangulations of the modular t
orus play an important role\, and so does the problem: How far can a strai
ght line crossing a triangle stay away from the vertices?\n
LOCATION:https://researchseminars.org/talk/BODS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Monk (IRMA\, Strasbourg)
DTSTART;VALUE=DATE-TIME:20201112T153000Z
DTEND;VALUE=DATE-TIME:20201112T164500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/4
DESCRIPTION:Title: The
geometry and spectrum of random hyperbolic surfaces\nby Laura Monk (I
RMA\, Strasbourg) as part of Bremen-Oldenburg Dynamics Seminar\n\n\nAbstra
ct\nThe main aim of this talk is to present geometric and spectral\nproper
ties of typical hyperbolic surfaces. More precisely\, I will:\n\n- introdu
ce a probabilistic model\, first studied by Mirzakhani\, which is\na natur
al and convenient way to sample random hyperbolic surfaces\n\n- describe t
he geometric properties of these random surfaces: diameter\,\ninjectivity
radius\, Cheeger constant\, Benjamini-Schramm convergence...\n\n- explain
how one can deduce from this geometric information estimates\non the numbe
r of eigenvalues of the Laplacian in an interval $[a\,b]$\,\nusing the Sel
berg trace formula.\n
LOCATION:https://researchseminars.org/talk/BODS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sören Petrat (Jacobs University)
DTSTART;VALUE=DATE-TIME:20200604T143000Z
DTEND;VALUE=DATE-TIME:20200604T154500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/5
DESCRIPTION:Title: Eff
ective Dynamics of the Mean-field Bose Gas\nby Sören Petrat (Jacobs U
niversity) as part of Bremen-Oldenburg Dynamics Seminar\n\n\nAbstract\nThe
quantum dynamics of N non-relativistic bosons is described\nby the Schroe
dinger equation with pair interaction. The complexity of\nsolutions genera
lly grow exponentially in the particle number\, so for\nlarge N coarse-gra
ined or effective descriptions are desirable. From a\nmathematical physics
point of view\, one aims at deriving effective\nequations in a rigorous w
ay\, i.e.\, proving that their solutions converge\nto the solutions of the
Schroedinger equation in a suitable topology. In\nthis talk\, we will con
sider the dynamics in the mean-field limit\, which\nhas been studied exten
sively in the last two decades. I will present an\noverview about the rese
arch goals and results\, and then specifically\ndiscuss recent results of
my collaborators and myself on a perturbative\nexpansion of solutions to t
he Schroedinger equation.\n
LOCATION:https://researchseminars.org/talk/BODS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keivan Mallahi-Karai (Jacobs University)
DTSTART;VALUE=DATE-TIME:20200702T143000Z
DTEND;VALUE=DATE-TIME:20200702T154500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/6
DESCRIPTION:Title: Loc
ally random groups\nby Keivan Mallahi-Karai (Jacobs University) as par
t of Bremen-Oldenburg Dynamics Seminar\n\n\nAbstract\nGroups without non-t
rivial low dimensional representations\,\nnamed quasi-random by Gowers\, h
ave recently found many applications in\nstudying group theoretical probl
ems of combinatorial nature. Loosely\nspeaking\, non-existence of such rep
resentations forces the product map\non the group mapping $(a\, b)$ to the
ir product $ab$ to have a certain mixing\nbehavior.\n\nIn this talk\, afte
r briefly recalling the notion of quasi randomness\, I\nwill discuss a ge
neralisation of this concept to the class of compact\ngroups. This propert
y\, called local randomness\, is formulated in terms\nof unitary represent
ations of the compact group $G$ and captures a similar\nmixing behavior at
all scales. I will discuss a number of related\nresults including a clas
sification 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://researchseminars.org/talk/BODS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Mitchell (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20210218T153000Z
DTEND;VALUE=DATE-TIME:20210218T164500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/7
DESCRIPTION:Title: Mea
sure theoretic entropy of random substitutions\nby Andrew Mitchell (Un
iversity of Birmingham) as part of Bremen-Oldenburg Dynamics Seminar\n\n\n
Abstract\nRandom substitutions and their associated subshifts provide\na m
odel for structures that exhibit both long range order and positive\nentro
py. In this talk we discuss the entropy of a large class of ergodic\nmeasu
res\, known as frequency measures\, that arise naturally from random\nsubs
titutions. We introduce a new measure of complexity\, namely measure\nthe
oretic inflation word entropy\, and discuss its relationship to\nmeasure t
heoretic entropy. We also show how this new measure of\ncomplexity can be
used to provide a framework for the systematic study\nof the measure theo
retic entropy of random substitution subshifts.\n\nAs an application of ou
r results\, we obtain closed form formulas for the\nentropy of a wide rang
e of random substitution subshifts and show that\nin many cases there exis
ts a frequency measure of maximal entropy.\nFurther\, for a class of rando
m substitution subshifts\, we show that this\nmeasure is the unique measur
e of maximal entropy.\n\nThis is joint work with P. Gohlke\, R. Leek\, D.
Rust\, and T. Samuel.\n
LOCATION:https://researchseminars.org/talk/BODS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Rasmussen (Imperial College London)
DTSTART;VALUE=DATE-TIME:20210429T143000Z
DTEND;VALUE=DATE-TIME:20210429T154500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/8
DESCRIPTION:by Martin Rasmussen (Imperial College London) as part of Breme
n-Oldenburg Dynamics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BODS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlangelo Liverani (U Roma „Tor Vergata“)
DTSTART;VALUE=DATE-TIME:20210209T130000Z
DTEND;VALUE=DATE-TIME:20210209T143000Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/9
DESCRIPTION:Title: Mea
surements in Dynamical Systems\nby Carlangelo Liverani (U Roma „Tor
Vergata“) as part of Bremen-Oldenburg Dynamics Seminar\n\n\nAbstract\nVe
ry often a measurement of a physical system takes the form of a finite\nti
me average for some observable. For infinite time averages Birkhoff's\nthe
orem classifies all the possible outcomes in terms of the invariant\nmeasu
res of the system. The study of the\, much more realistic\, finite\ntime a
verages is equivalent to investigating at which speed the limit is\nattain
ed. This problem is only partially understood\, essentially we\nunderstand
few special cases. Yet\, our current knowledge shows that the\nbehaviour
depends drastically from the properties of the system. In the\nstudy of su
ch a problem functional analysis\, probability theory\, and\ngeometry play
major roles. I will attempt to give an overview of the\nsubject.\n\nThis
is a joint event with the mathematical colloquium at the\nUniversity of Br
emen\n
LOCATION:https://researchseminars.org/talk/BODS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Schapira (Université Rennes 1)
DTSTART;VALUE=DATE-TIME:20210315T143000Z
DTEND;VALUE=DATE-TIME:20210315T154500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/10
DESCRIPTION:Title: St
rong positive recurrence for geodesic flows\nby Barbara Schapira (Univ
ersité Rennes 1) as part of Bremen-Oldenburg Dynamics Seminar\n\n\nAbstra
ct\nIn a recent paper with S Gouezel and S Tapie\, in the context of geode
sic\nflows of noncompact negatively curved manifolds\, we propose three\nd
ifferent definitions of entropy and pressure at infinity\, through\ngrowth
of periodic orbits\, critical exponents of Poincaré series\, and\nentrop
y (pressure) of invariant measures. We show that these notions\ncoincide.
Thanks to these entropy and pressure at infinity\, we\ninvestigate thoroug
hly the notion of strong positive recurrence in this\ngeometric context. A
potential is said strongly positively recurrent\nwhen its pressure at inf
inity is strictly smaller than the full\ntopological pressure. We show in
particular that if a potential is\nstrongly positively recurrent\, then it
admits a finite Gibbs measure. We\nalso provide easy criteria allowing to
build such strong positively\nrecurrent potentials and many examples.\n\n
During the talk\, I will present some of these points\, to give to the\nau
dience the flavour of this work.\n
LOCATION:https://researchseminars.org/talk/BODS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Péter Koltai (FU Berlin)
DTSTART;VALUE=DATE-TIME:20210419T133000Z
DTEND;VALUE=DATE-TIME:20210419T144500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/11
DESCRIPTION:by Péter Koltai (FU Berlin) as part of Bremen-Oldenburg Dynam
ics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BODS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valérie Berthé (CNRS\, IRIF\, Université de Paris)
DTSTART;VALUE=DATE-TIME:20210531T133000Z
DTEND;VALUE=DATE-TIME:20210531T144500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/12
DESCRIPTION:by Valérie Berthé (CNRS\, IRIF\, Université de Paris) as pa
rt of Bremen-Oldenburg Dynamics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BODS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Gekhtman (Technion)
DTSTART;VALUE=DATE-TIME:20210308T143000Z
DTEND;VALUE=DATE-TIME:20210308T154500Z
DTSTAMP;VALUE=DATE-TIME:20210228T185305Z
UID:BODS/13
DESCRIPTION:Title: Gi
bbs measures vs. random walks in negative curvature\nby Ilya Gekhtman
(Technion) as part of Bremen-Oldenburg Dynamics Seminar\n\n\nAbstract\nThe
ideal boundary of a negatively curved manifold naturally\ncarries two typ
es of measures.\nOn the one hand\, we have conditionals for equilibrium (G
ibbs) states\nassociated to Hoelder potentials\; these include the Patters
on-Sullivan\nmeasure and the Liouville measure. On the other hand\, we hav
e stationary\nmeasures coming from random walks on the fundamental group.\
n We compare and contrast these two classes.First\, we show that both\no
f these of these measures can be associated to geodesic flow invariant\nme
asures on the unit tangent bundle\, with respect to which closed\ngeodesic
s satisfy different equidistribution properties. Second\, we show\nthat th
e absolute continuity between a harmonic measure and a Gibbs\nmeasure is e
quivalent to a relation between entropy\, (generalized)\ndrift and critic
al exponent\, generalizing previous formulas of\nGuivarc’h\, Ledrappier\
, and Blachere-Haissinsky-Mathieu. This shows that\nif the manifold (or mo
re generally\, a CAT(-1) quotient) is geometrically\nfinite but not convex
cocompact\, stationary measures are always singular\nwith respect to Gibb
s measures.\nA major technical tool is a generalization of a deviation ine
quality due\nto Ancona saying the so called Green distance associated to t
he random\nwalk is nearly additive along geodesics in the universal cover.
\nPart of this is based on joint work with Gerasimov-Potyagailo-Yang and\n
part on joint work with Tiozzo.\n
LOCATION:https://researchseminars.org/talk/BODS/13/
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