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TZID:Asia/Jerusalem
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BEGIN:VEVENT
UID:28@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230403T123000
DTEND;TZID=Asia/Jerusalem:20230403T133000
DTSTAMP:20230330T190555Z
URL:https://math.technion.ac.il/en/events/the-hidden-structure-in-aperys-p
roof/
SUMMARY:The hidden structure in Apery's proof
DESCRIPTION:Lecturer:Ofir David (Technion)\n Location:Amado 814\n In 1978\,
Apery proved the irrationality of the Riemann zeta value ζ(3) by utilizi
ng a fast converging sequence of rational approximations. However\, the de
tails of his proof remained difficult to comprehend. Since then\, many mat
hematicians have attempted to either elucidate Apery's approach or seek ou
t new proofs altogether.\n\nInspired by computer algorithms to find such a
pproximations\, an idea about a hidden mathematical structure behind the p
roof was beginning to formalize. This structure\, which we call the conser
vative matrix field\, not only clarifies some of Apery's proof but also of
fers a framework for Apery-like irrationality proofs and relates them to t
he broader themes of number theory and dynamics. In this talk\, we will ex
plore the properties of the conservative matrix field and discuss how it c
an be hopefully applied to prove irrationality for other mathematical cons
tants.\n\nThis research was done as part of the work in the Ramanujan Mach
ine group.\n\n
CATEGORIES:Faculty Events,Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:38@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230417T123000
DTEND;TZID=Asia/Jerusalem:20230417T133000
DTSTAMP:20230416T081259Z
URL:https://math.technion.ac.il/en/events/gdrt-seminar-approximation-of-di
agonally-invariant-measure-by-tori-measures/
SUMMARY:Approximation of diagonally invariant measure by tori measures
DESCRIPTION:Lecturer: Yuval Yifrach (Technion)\n Location:Amado 814\n \n\n\
nWe consider the family of periodic measures for the full diagonal action
on the space of unimodular lattices. This family is important and natural
due to its tight relation to class groups in number fields. We show that m
any natural families of measures on the space of lattices can be approxima
ted using this family (in the weak sense). E.g.\, we show that for any 0&l
t\;c\\leq 1\, the measure cm_{X_n} can be approximated this way\, where m_
{X_n} denotes the Haar probability measure on X_n. Moreover\, we show that
non ergodic measures can be approximated. Our proof is based on the equid
istribution of Hecke neighbors and on constructions of special number fiel
ds. We will discuss the results\, alternative ways to attack the problem\,
and our method of proof.\nThis talk is based on a joint work with Omri So
lan.\n\n\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:42@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230508T123000
DTEND;TZID=Asia/Jerusalem:20230508T133000
DTSTAMP:20230506T201615Z
URL:https://math.technion.ac.il/en/events/tba/
SUMMARY:Periodic approximations of substitution dynamical systems
DESCRIPTION:Lecturer:Lior Tenenbaum (Technion)\n Location:Amado 814\n \n\nI
n studying higher dimensional Schrödinger operators of quasicrystals\, i
t is advantageous to find periodic approximations\, given the known
theory for crystals. Namely\, we seek periodic operators such that
their spectrum converges as a set to the spectrum of the limiting operator
(of the quasi-crystal). To get such periodic approximations\, one needs
to study the convergence of the underlying dynamical systems.\n\n\n\n\nWe
treat dynamical systems which are based upon substitutions. We find natu
ral candidates of dynamical subsystems to approximate the substitutio
n dynamical system. We provide a characterization when these converg
e and estimates on the rate of convergence.\n\n\n\n\nSome well-known examp
les of 1-dimensional and 2-dimensional substitution systems are discuss
ed during the talk. These results also apply to non-commutative substitu
tion systems\, recently introduced in [1]. This is based on a joint wor
k with Ram Band\, Siegfried Beckus and Felix Pogorzelski.\n\n\n\n\n \;
\n\n\n\n\n[1] Siegfried Beckus\, Tobias Hartnick\, and Felix Pogorzelski
. Symbolic substitution systems\n\n\n\n\nbeyond abelian groups\, 2021. Ar
xiv: 2109.15210\n\n\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:67@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230515T123000
DTEND;TZID=Asia/Jerusalem:20230515T133000
DTSTAMP:20230509T105642Z
URL:https://math.technion.ac.il/en/events/tba-9/
SUMMARY:Universality for R^d flows
DESCRIPTION:Lecturer:Shrey Sanadhya (BGU)\n Location:Amado 814\n A dynamica
l system is called universal if any system with lower entropy can be embed
ded into it. In this talk\, we will discuss universality for R^d flows (d
>\; 1) both in\nergodic and Borel contexts. We will discuss a specificat
ion property that implies universality for R^d flows and provide an exampl
e of a tiling dynamical system with this specification\nproperty. This is
ongoing work with Tom Meyerovitch.\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:69@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230605T123000
DTEND;TZID=Asia/Jerusalem:20230605T133000
DTSTAMP:20230602T122427Z
URL:https://math.technion.ac.il/en/events/smb-equipartition-theorems-along
-almost-geodesics/
SUMMARY:Entropy equipartition along almost geodesics in negatively curved g
roups
DESCRIPTION:Lecturer:Felix Pogorzelski (Leipzig)\n Location:Amado 814\n The
classical Shannon-McMillan-Breiman (SMB) theorem states that for an ergod
ic measure preserving transformation on a probability space\, the rate of
uncertainty measured by mathematical entropy can be observed in almost eve
ry orbit of the system.\n\nWe explain how to use an abstract skew product
construction in order to prove such results for measure preserving actions
of negatively curved groups\, with refinements being taken along almost g
eodesics.\n\nJoint work with Amos Nevo\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:88@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230608T113000
DTEND;TZID=Asia/Jerusalem:20230608T123000
DTSTAMP:20230606T065124Z
URL:https://math.technion.ac.il/en/events/fighting-chaos-with-chaos/
SUMMARY:Fighting Chaos with Chaos (joint with the GDRT seminar)
DESCRIPTION:Lecturer:Hagai Perets (Technion\, Physics)\n Location:Amado 719
\n I will present a new approach of analytical statistical solutions to th
e three body problem (and other vegetables). No background will be assumed
.\n
CATEGORIES:Geometry and Topology Seminar,Groups, Dynamics and Related
Topics
END:VEVENT
BEGIN:VEVENT
UID:94@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230612T123000
DTEND;TZID=Asia/Jerusalem:20230612T133000
DTSTAMP:20230611T073503Z
URL:https://math.technion.ac.il/en/events/structure-theorems-for-the-host-
kra-characteristic-factors-and-inverse-theorems-for-the-gowers-norms/
SUMMARY:Structure theorems for the Host-Kra characteristic factors and inve
rse theorems for the Gowers norms
DESCRIPTION:Lecturer:Or Shalom (IAS)\n Location:Amado 814\n The Gowers unif
ormity k-norm on a finite abelian group measures the averages of complex f
unctions on such groups over k-dimensional arithmetic cubes. The inverse q
uestion about these norms asks if a large norm implies correlation with a
function of an algebraic origin. The analogue of the Gowers uniformity nor
ms for measure-preserving abelian actions are the Host-Kra-Gowers seminorm
s which are intimately connected to the Host-Kra-Ziegler factors of such s
ystems. The corresponding inverse question in the dynamical setting asks f
or a description of such factors in terms of systems of an algebraic origi
n. In this talk\, we survey recent results about the inverse question in t
he dynamical and combinatorial settings\, and in particular how an answer
in the former setting can imply one in the latter. This talk is based on j
oint works with Asgar Jamneshan and Terence Tao.\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:43@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230626T123000
DTEND;TZID=Asia/Jerusalem:20230626T133000
DTSTAMP:20230622T121845Z
URL:https://math.technion.ac.il/en/events/tba-2/
SUMMARY:Fourier decay for smooth images of self-similar measures
DESCRIPTION:Lecturer:Amir Algom (Haifa)\n Location:Amado 814\n Kaufman (198
4) and later Mosquera-Shmerkin (2018) showed that Bernoulli convolutions e
xhibit fast Fourier decay when perturbed by a smooth non-linear map. This
is remarkable\, since by a classical Theorem of Erdos (1939) many Bernoull
i convolutions don't have Fourier decay at all. We will present an extensi
on of this result to all self-similar measures: Any smooth non-linear pert
urbation of a self-similar measure enjoys fast (polynomial) Fourier decay
.\nJoint with Yuanyang Chang\, Meng Wu\, and Yu-Liang Wu.\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:134@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20231204T170000
DTEND;TZID=Asia/Jerusalem:20231204T180000
DTSTAMP:20231202T012222Z
URL:https://math.technion.ac.il/en/events/structure-theorems-for-the-host-
kra-characteristic-factors-and-inverse-theorems-for-the-gowers-uniformity-
norms/
SUMMARY:Structure theorems for the Host--Kra characteristic factors and inv
erse theorems for the Gowers uniformity norms
DESCRIPTION:Lecturer:Or Shalom (IAS)\n Location:https://technion.zoom.us/j/
96584779784\n The Gowers uniformity k-norm on a finite abelian group measu
res the averages of complex functions on such groups over k-dimensional ar
ithmetic cubes. The inverse question about these norms asks if a large nor
m implies correlation with a function of an algebraic origin.\nThe analogu
e of the Gowers uniformity norms for measure-preserving abelian actions ar
e the Host-Kra-Gowers seminorms\, which are intimately connected to the Ho
st-Kra-Ziegler factors of such systems. The corresponding inverse question
\, in the dynamical setting\, asks for a description of such factors in te
rms of systems of an algebraic origin.\nIn this talk\, we survey recent re
sults about the inverse question in the dynamical and combinatorial settin
gs\, and in particular how an answer in the former setting can imply one i
n the latter.\nThis talk is based on joint works with Asgar Jamneshan and
Terence Tao. This talk is aimed at a general audience. In particular\, no
prior knowledge in ergodic theory or additive combinatorics is required.\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:140@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20231227T123000
DTEND;TZID=Asia/Jerusalem:20231227T133000
DTSTAMP:20231224T091038Z
URL:https://math.technion.ac.il/en/events/on-the-denseness-of-horospheres-
in-higher-rank/
SUMMARY:On the denseness of horospheres in higher-rank
DESCRIPTION:Lecturer:Or Landsberg (Yale)\n Location:Amado 814\n In this tal
k I will discuss a necessary and sufficient condition for denseness of hor
opherical orbits in the non-wandering set of a higher-rank homogeneous spa
ce $G / \\Gamma$\, for a Zariski dense discrete subgroup $\\Gamma <\; G$
\, possibly of infinite covolume. In rank one this condition (established
in this setting by Eberlein and Dal'bo) implies in particular that the ho
rospherical subgroup acts minimally on the non-wandering set if and only i
f the discrete group $\\Gamma$ is convex co-compact. In contrast\, we show
that Schottky groups in higher-rank can support non-minimal horospherical
actions. This distinction between rank-one and higher-rank is due to the
role that Benoist's limit cone plays in the analysis. Based on joint work
with Hee Oh.\n https://technion.zoom.us/j/96584779784
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:141@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240101T123000
DTEND;TZID=Asia/Jerusalem:20240101T133000
DTSTAMP:20231226T093923Z
URL:https://math.technion.ac.il/en/events/fourier-quasicrystals-via-lee-ya
ng-polynomials/
SUMMARY:Fourier quasicrystals via Lee-Yang polynomials
DESCRIPTION:Lecturer:Lior Alon (MIT)\n Location:Amado 814\n The concept of
"quasiperiodic" sets\, functions\, and measures is prevalent in diverse ma
thematical fields such as Mathematical Physics\, Fourier Analysis\, and Nu
mber Theory. The Poisson summation formula provides a natural characteriza
tion of quasiperiodicity: a counting measure of a discrete set is a Fourie
r quasicrystal (FQ) if its Fourier transform is also a discrete atomic mea
sure\, together with some growth condition.\nRecently\, Kurasov and Sarnak
provided a method for constructing one dimensional FQs as the return time
s of a linear flow along an irrational slope on a torus to the zero set of
a multivariate Lee-Yang polynomial. In this talk\, I will show that\, in
fact\, every one dimensional FQ admits such a construction. I will also di
scuss the distribution of gaps in one dimensional FQs\, showing that they
are dense in an interval\, and the distribution is given explicitly in ter
ms of the slope and polynomial in the Kurasov-Sarnak construction. In the
last part I will talk about a generalization of their construction to any
dimension.\nThe talk is based on joint works with Alex Cohen\, Cynthia Vin
zant\, Mario Kummer\, and Pavel Kurasov.\n https://technion.zoom.us/j/9658
4779784
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:190@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240226T160000
DTEND;TZID=Asia/Jerusalem:20240226T170000
DTSTAMP:20240226T060718Z
URL:https://math.technion.ac.il/en/events/covering-radii-in-positive-chara
cteristic/
SUMMARY:Covering radius in positive characteristic
DESCRIPTION:Lecturer:Noy Soffer-Aranov\n Location:Amado 919\n Let L be a la
ttice and let C be any subset in R^d. The covering radius of L with respec
t to C is the infimum over all r >\; 0 such that L + rC = R^d is. It was
conjectured by Minkowski that if C is the set of all x satisfying |x_1 \\
cdots x_d| \\leq 1\, then the covering radius of any unimodular lattice L
with respect to C is at most 2^{-d}\, and this upper bound is obtained if
and only if L is in AZ^d\, where A is the group of diagonal matrices. In t
his talk I will discuss covering radii in the positive characteristic sett
ing. In particular\, I will talk about the surprising connections between
successive minima and covering radii with respect to convex sets\, and the
solution of the positive characteristic analogue of Minkowski’s conject
ure.\n https://technion.zoom.us/my/nesharim
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:235@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240520T123000
DTEND;TZID=Asia/Jerusalem:20240520T133000
DTSTAMP:20240513T221414Z
URL:https://math.technion.ac.il/en/events/diophantine-approximation-formal
-laurent-series-and-hankel-matrices/
SUMMARY:Diophantine approximation\, formal Laurent series and Hankel Matric
es
DESCRIPTION:Lecturer:Matan Ivgi (Technion)\n Location:Amado 814\n Diophanti
ne approximation in function fields gives rise to many combinatorial quest
ions. One interesting question is the computation of the Hausdorff dimensi
on of the set of badly approximable formal Laurent series. Those series ar
e tightly connected to Hankel matrices with specific properties. I will ta
lk about this connection and how I used it in order to solve this question
.\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:240@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240527T123000
DTEND;TZID=Asia/Jerusalem:20240527T133000
DTSTAMP:20240520T080222Z
URL:https://math.technion.ac.il/en/events/approximation-to-one-real-number
-revisited/
SUMMARY:Approximation to one real number revisited
DESCRIPTION:Lecturer:Nikolay Moshchevitin (TUW)\n Location:Amado 814\n We w
ill discuss various types of approximations to one real number by rational
s. We describe different irrationality measure functions and the related D
iophantine spectra\, such as Dirichlet spectrum\, spectra for the second b
est approximations\, Minkowski’s spectrum and resent results on the topi
c. Surprisingly there are unsolved problems related to some of these objec
ts and for some of them there is no ideas how to solve them. At the end we
will say a few words about multidimensional generalisations.\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:257@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240624T123000
DTEND;TZID=Asia/Jerusalem:20240624T133000
DTSTAMP:20240616T092003Z
URL:https://math.technion.ac.il/en/events/a-variant-of-kaufmans-measures-i
n-two-dimensions/
SUMMARY:A variant of Kaufman’s measures in two dimensions
DESCRIPTION:Lecturer:Manos Zafeiropoulos (Technion)\n Location:Amado 814\n
An old result of Kaufman showed that the set of badly approximable numbe
rs supports a family of probabilty measures with polynomial decay rate on
their Fourier transform. We show that the same phenomenon can be observed
in a two-dimensional setup: Consider the set of pairs (alpha\, gamma) in [
0\,1]^2 for which there exists c>\;0 such that all integers p\,q satisfy
\n| q alpha - p - gamma | >\; c.\nWe prove that it supports certain prob
ability measures with Frostman dimension arbitrarily close to $2$ and Four
ier transform with polynomial decay rate. This is joint work with S. Chow
and E. Zorin.\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:258@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240701T113000
DTEND;TZID=Asia/Jerusalem:20240701T123000
DTSTAMP:20240630T090359Z
URL:https://math.technion.ac.il/en/events/dynamics-over-the-quaternions/
SUMMARY:First steps in non-commutative dynamics over the Quaternions and th
e Octonions
DESCRIPTION:Lecturer:Solomon Vishkautsen (Tel-Hai)\n Location:Amado 919\n W
e present results on the dynamics of standard univariate polynomials over
Quaternions and Octonions from an algebraic point of view. We look at peri
odic and fixed points\, and emphasize the need to carefully define what we
mean by these terms when it comes to dynamics over non-commutative rings.
For quadratic monics over the Octonions\, we provide criteria for classif
ying fixed points as attracting\, repelling or "ambivalent"\, generalizin
g the complex case. This is a joint work with Adam Chapman from The Academ
ic College of Tel Aviv–Yaffo.\n
CATEGORIES:Geometry and Topology Seminar,Groups, Dynamics and Related
Topics
END:VEVENT
BEGIN:VEVENT
UID:286@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240715T123000
DTEND;TZID=Asia/Jerusalem:20240715T133000
DTSTAMP:20240712T152103Z
URL:https://math.technion.ac.il/en/events/sampling-methods-for-the-disk-an
d-for-3d-rotations/
SUMMARY:Sampling methods for the disk and for 3D rotations
DESCRIPTION:Lecturer:Rene Ruhr\n Location:Amado 814\n Generating random num
bers efficiently is a classical problem in computing.\nWe discuss two case
s: sampling the 2-dimensional disk and the space of 3D rotations.\nCommon
methods involve trigonometric functions or rejection approaches\, both of
which can be slow on some hardware.\nFirst\, we adapt the Lubotzky-Phillip
ps-Sarnak method for producing low discrepancy sequences which is based on
integers\, modifying it to trade quality for speed (keeping the spectral
gap).\nSecond\, we discuss von Neumann's method of rejection sampling for
the disk using conditional probability. By leveraging translation symmetry
and memory (Markov Chain)\, we can eliminate rejections.\nDiscussion on t
hese topics can already be found on https://rene.ruhr/gfx/.\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:259@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240722T123000
DTEND;TZID=Asia/Jerusalem:20240722T133000
DTSTAMP:20240712T150947Z
URL:https://math.technion.ac.il/en/events/indexing-periodic-trajectories-f
or-three-dimensional-flows/
SUMMARY:Indexing periodic trajectories for three-dimensional flows
DESCRIPTION:Lecturer:Eran Igra (Technion)\n Location:Amado 814\n Assume we
have a chaotic attractor in R^3\, generated by some smooth three-dimension
al flow -- can we say what makes it unique?\n\nThis question\, even though
intuitive\, is somewhat ill posed. Let us therefore consider a better pos
ed question: what can we say about the knot types of periodic trajectories
embedded inside the attractor? This question was answered for the case wh
en the dynamics are hyperbolic\, a result often termed as the "Birman-Will
iams Theorem". However\, most chaotic attractors are not known to be hyper
bolic (i.e.\, "Anosov")\, so in many interesting cases this question is st
ill wide open. In this talk\, we will show how using a topological invaria
nt known as the Orbit Index (originally due to K. Alligood\, J. Mallet-Par
et and J.A. Yorke) one can give a partial answer to this question for two
of the most famous chaotic dynamical systems: the Rössler and the Lorenz
attractors. Finally (and time permitting)\, inspired by the "Chaotic Hypot
hesis" due to G. Gallavotti and by the Thurston-Nielsen Classification The
orem for surface homeomorphisms\, we will discuss how our results can poss
ibly be generalized to a larger class of three-dimensional flows.\n \nBas
ed on work in progress.\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:293@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240729T123000
DTEND;TZID=Asia/Jerusalem:20240729T133000
DTSTAMP:20240721T114801Z
URL:https://math.technion.ac.il/en/events/classifying-stationary-measures-
on-s1-with-respect-to-the-action-of-fuchsian-groups/
SUMMARY:Classifying stationary measures on S^1 with respect to the action o
f Fuchsian groups
DESCRIPTION:Lecturer:Peter Kosenko (UBC)\n Location:Amado 814\n Through the
perspective of ergodic theory\, if one wants to study discrete dynamical
system on a nice space\, it is quite desirable to look for invariant measu
res and study ergodic/mixing properties. However\, this often does not wor
k even for nicest group actions on nice topological spaces. Our motivating
example will be the action of a non-elementary Fuchsian group on the hype
rbolic plane which induces the action on S^1. Such actions generally do no
t admit measures which are invariant with respect to the entire group.\nHo
wever\, given a measure mu on a Fuchsian group\, one might relax the invar
iance and ask whether a measure on S^1 is invariant "on average" with resp
ect to mu. Such measures are called mu-stationary\, and while one can show
the existence and uniqueness of the stationary measure for very general m
u\, there is still no satisfactory classification which tells us when the
stationary measure is singular/absolutely continuous wrt the Lebesgue meas
ure on S^1. We will discuss the classical results and the latest advances
related to this problem.\n
CATEGORIES:Groups, Dynamics and Related Topics
END:VEVENT
BEGIN:VEVENT
UID:294@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240805T123000
DTEND;TZID=Asia/Jerusalem:20240805T133000
DTSTAMP:20240722T144423Z
URL:https://math.technion.ac.il/en/events/irrationality-measure-functions/
SUMMARY:Irrationality measure functions
DESCRIPTION:Lecturer:Viktoria Rudykh (Technion)\n Location:Amado 814\n For
a real number x we define irrationality measure function as Ψ_x(t) = min_
{1≤q≤t} ||qx||\, where ||x|| is the distance to the nearest integer. K
an and Moshchevitin proved that for any x and y with x±y∉Z the differen
ce of two irrationality measure functions Ψ_x(t)-Ψ_y(t) changes its sign
infinitely many times as t↑∞. Later\, Moshchevitin showed that there
exists a constant C>\;0 such that |Ψ_x(t)-Ψ_y(t)|≥ C min{Ψ_x(t)\,Ψ
_y(t)} for infinitely many t. It was also shown that C is optimal when bot
h numbers are equal to the golden ratio up to a Möbius transformation wit
h integer coefficients. We prove that this constant can be significantly i
mproved when one of the numbers is not the golden ratio up to a Möbius tr
ansformation with integer coefficients. This is a joint work with Nikita S
hulga from La Trobe University. We will also give a generalisation of Kan-
Moshchevitin Theorem for $n >\; 2$ functions\n
CATEGORIES:Graduation Seminars,Groups, Dynamics and Related Topics
END:VEVENT
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