BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Google Inc//Google Calendar 70.9054//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
DESCRIPTION:One world numeration seminar seminar of IRIF
NAME:One world numeration seminar
REFRESH-INTERVAL:PT4H
TIMEZONE-ID:Europe/Paris
X-WR-CALDESC:One world numeration seminar seminar of IRIF
X-WR-CALNAME:One world numeration seminar
X-WR-TIMEZONE:Europe/Paris
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:DAYLIGHT
DTSTART:19700329T020000
RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=3
TZNAME:CEST
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
END:DAYLIGHT
BEGIN:STANDARD
DTSTART:19701025T030000
RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=10
TZNAME:CET
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
SUMMARY:On the smallest base in which a number has a unique expansion - Pi
eter Allaart\, University of North Texas
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20201110T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20201110T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1208
DESCRIPTION:For x>0\, let U(x) denote the set of bases q in (1\,2] such th
at x has a unique expansion in base q over the alphabet {0\,1}\, and let f
(x)=inf U(x). I will explain that the function f(x) has a very complicated
structure: it is highly discontinuous and has infinitely many infinite le
vel sets. I will describe an algorithm for numerically computing f(x) that
often gives the exact value in just a small finite number of steps. The K
omornik-Loreti constant\, which is f(1)\, will play a central role in this
talk. This is joint work with Derong Kong\, and builds on previous work b
y Kong (Acta Math. Hungar. 150(1):194-208\, 2016).
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:The carry propagation of the successor function - Jacques Sakarovi
tch\, IRIF\, CNRS et Télécom Paris
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20201117T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20201117T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1209
DESCRIPTION:Given any numeration system\, the carry propagation at an inte
ger N is the number of digits that change between the representation of N
and N+1. The carry propagation of the numeration system as a whole is the
average carry propagations at the first N integers\, as N tends to infinit
y\, if this limit exists. \n\nIn the case of the usual base p numeration s
ystem\, it can be shown that the limit indeed exists and is equal to p/(p-
1). We recover a similar value for those numeration systems we consider an
d for which the limit exists. \nThe problem is less the computation of the
carry propagation than the proof of its existence. We address it for vari
ous kinds of numeration systems: abstract numeration systems\, rational ba
se numeration systems\, greedy numeration systems and beta-numeration. Thi
s problem is tackled with three different types of techniques: combinatori
al\, algebraic\, and ergodic\, each of them being relevant for different k
inds of numeration systems. \n\nThis work has been published in Advances i
n Applied Mathematics 120 (2020). In this talk\, we shall focus on the alg
ebraic and ergodic methods. \n\nJoint work with V. Berthé (Irif)\, Ch. Fr
ougny (Irif)\, and M. Rigo (Univ. Liège).
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Rauzy fractal unbounded in all directions of the plane - Mélodi
e Andrieu\, Aix-Marseille University
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20201027T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20201027T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1210
DESCRIPTION:Until 2001 it was believed that\, as for Sturmian words\, the
imbalance of Arnoux-Rauzy words was bounded - or at least finite. Cassaign
e\, Ferenczi and Zamboni disproved this conjecture by constructing an Arno
ux-Rauzy word with infinite imbalance\, i.e. a word whose broken line devi
ates regularly and further and further from its average direction. Today\,
we hardly know anything about the geometrical and topological properties
of these unbalanced Rauzy fractals. The Oseledets theorem suggests that th
ese fractals are contained in a strip of the plane: indeed\, if the Lyapun
ov exponents of the matricial product associated with the word exist\, one
of these exponents at least is nonpositive since their sum equals zero. T
his talk aims at disproving this belief.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Distinct unit generated number fields and finiteness in number sys
tems - Tomáš Vávra\, University of Waterloo
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20201103T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20201103T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1212
DESCRIPTION:A distinct unit generated field is a number field K such that
every algebraic integer of the field is a sum of distinct units. In 2015\,
Dombek\, Masáková\, and Ziegler studied totally complex quartic fields\
, leaving 8 cases unresolved. Because in this case there is only one funda
mental unit u\, their method involved the study of finiteness in positiona
l number systems with base u and digits arising from the roots of unity in
K. \nFirst\, we consider a more general problem of positional representat
ions with base beta with an arbitrary digit alphabet D. We will show that
it is decidable whether a given pair (beta\, D) allows eventually periodic
or finite representations of elements of O_K. \nWe are then able to prove
the conjecture that the 8 remaining cases indeed are distinct unit genera
ted.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Representations for complex numbers with integer digits - Paul Sur
er\, University of Natural Resources and Life Sciences\, Vienna
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20201020T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20201020T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1213
DESCRIPTION:In this talk we present the zeta-expansion as a complex versio
n of the well-known beta-expansion. It allows us to expand complex numbers
with respect to a complex base by using integer digits. Our concepts fits
into the framework of the recently published rotational beta-expansions.
But we also establish relations with piecewise affine maps of the torus an
d with shift radix systems.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Representations of real numbers on fractal sets - Kan Jiang\, Ning
bo University
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20201013T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20201013T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1214
DESCRIPTION:There are many approaches which can represent real numbers. Fo
r instance\, the β-expansions\, the continued fraction and so forth. Repr
esentations of real numbers on fractal sets were pioneered by H. Steinhaus
who proved in 1917 that C+C=[0\,2] and C−C=[−1\,1]\, where C is the m
iddle-third Cantor set. Equivalently\, for any x ∈ [0\,2]\, there exist
some y\,z ∈ C such that x=y+z. In this talk\, I will introduce similar r
esults in terms of some fractal sets.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Finiteness and periodicity of continued fractions over quadratic n
umber fields - Francesco Veneziano\, University of Genova
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20201006T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20201006T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1215
DESCRIPTION:We consider continued fractions with partial quotients in the
ring of integers of a quadratic number field K\; a particular example of t
hese continued fractions is the β-continued fraction introduced by Bernat
. We show that for any quadratic Perron number β\, the β-continued fract
ion expansion of elements in Q(β) is either finite of eventually periodic
. We also show that for certain four quadratic Perron numbers β\, the β-
continued fraction represents finitely all elements of the quadratic field
Q(β)\, thus answering questions of Rosen and Bernat. \nBased on a joint
work with Zuzana Masáková and Tomáš Vávra.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Random matching for random interval maps - Marta Maggioni\, Leiden
University
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200929T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200929T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1216
DESCRIPTION:In this talk we extend the notion of matching for deterministi
c transformations to random matching for random interval maps. For a large
class of piecewise affine random systems of the interval\, we prove that
this property of random matching implies that any invariant density of a s
tationary measure is piecewise constant. We provide examples of random mat
ching for a variety of families of random dynamical systems\, that include
s generalised beta-transformations\, continued fraction maps and a family
of random maps producing signed binary expansions. We finally apply the pr
operty of random matching and its consequences to this family to study min
imal weight expansions. \nBased on a joint work with Karma Dajani and Char
lene Kalle.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multiscale Substitution Tilings - Yotam Smilansky\, Rutgers Univer
sity
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200922T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200922T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1217
DESCRIPTION:Multiscale substitution tilings are a new family of tilings of
Euclidean space that are generated by multiscale substitution rules. Unli
ke the standard setup of substitution tilings\, which is a basic object of
study within the aperiodic order community and includes examples such as
the Penrose and the pinwheel tilings\, multiple distinct scaling constants
are allowed\, and the defining process of inflation and subdivision is a
continuous one. Under a certain irrationality assumption on the scaling co
nstants\, this construction gives rise to a new class of tilings\, tiling
spaces and tiling dynamical system\, which are intrinsically different fro
m those that arise in the standard setup. In the talk I will describe thes
e new objects and discuss various structural\, geometrical\, statistical a
nd dynamical results. \nBased on joint work with Yaar Solomon.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lazy Ostrowski Numeration and Sturmian Words - Jeffrey Shallit\, U
niversity of Waterloo
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200915T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200915T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1218
DESCRIPTION:In this talk I will discuss a new connection between the so-ca
lled "lazy Ostrowski" numeration system\, and periods of the prefixes of S
turmian characteristic words. I will also give a relationship between peri
ods and the so-called "initial critical exponent". This builds on work of
Frid\, Berthé-Holton-Zamboni\, Epifanio-Frougny-Gabriele-Mignosi\, and ot
hers\, and is joint work with Narad Rampersad and Daniel Gabric.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some fractal problems in beta-expansions - Bing Li\, South China U
niversity of Technology
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200908T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200908T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1219
DESCRIPTION:For greedy beta-expansions\, we study some fractal sets of rea
l numbers whose orbits under beta-transformation share some common propert
ies. For example\, the partial sum of the greedy beta-expansion converges
with the same order\, the orbit is not dense\, the orbit is always far fro
m that of another point etc. The usual tool is to approximate the beta-tra
nsformation dynamical system by Markov subsystems. We also discuss the sim
ilar problems for intermediate beta-expansions.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hotspot Lemmas for Noncompact Spaces - Bill Mance\, Adam Mickiewic
z University in Poznań
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200901T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200901T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1220
DESCRIPTION:We will explore a correction of several previously claimed gen
eralizations of the classical hotspot lemma. Specifically\, there is a com
mon mistake that has been repeated in proofs going back more than 50 years
. Corrected versions of these theorems are increasingly important as there
has been more work in recent years focused on studying various generaliza
tions of the concept of a normal number to numeration systems with infinit
e digit sets (for example\, various continued fraction expansions\, the L
üroth series expansion and its generalizations\, and so on). Also\, highl
ighting this (elementary) mistake may be helpful for those looking to stud
y these numeration systems further and wishing to avoid some common pitfal
ls.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:On diophantine properties of generalized number systems - finite a
nd periodic representations - Attila Pethő\, University of Debrecen
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200714T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200714T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1221
DESCRIPTION:In this talk we investigate elements with special patterns in
their representations in number systems in algebraic number fields. We con
centrate on periodicity and on the representation of rational integers. We
prove under natural assumptions that there are only finitely many S-units
whose representation is periodic with a fixed period. We prove that the s
ame holds for the set of values of polynomials at rational integers.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Analogy of Lagrange spectrum related to geometric progressions - H
ajime Kaneko\, University of Tsukuba
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200707T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200707T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1222
DESCRIPTION:Classical Lagrange spectrum is defined by Diophantine approxim
ation properties of arithmetic progressions. The theory of Lagrange spectr
um is related to number theory and symbolic dynamics. In our talk we intro
duce significantly analogous results of Lagrange spectrum in uniform distr
ibution theory of geometric progressions. In particular\, we discuss the g
eometric sequences whose common ratios are Pisot numbers. For studying the
fractional parts of geometric sequences\, we introduce certain numeration
system. \nThis talk is based on a joint work with Shigeki Akiyama.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Continued fractions with two non integer digits - Niels Langeveld\
, Leiden University
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200630T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200630T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1223
DESCRIPTION:In this talk\, we will look at a family of continued fraction
expansions for which the digits in the expansions can attain two different
(typically non-integer) values\, named α1 and α2 with α1α2 ≤ 1/2 .
If α1α2 < 1/2 we can associate a dynamical system to these expansions wi
th a switch region and therefore with lazy and greedy expansions. We will
explore the parameter space and highlight certain values for which we can
construct the natural extension (such as a family for which the lowest dig
it cannot be followed by itself). We end the talk with a list of open prob
lems.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Univoque bases of real numbers: local dimension\, Devil's staircas
e and isolated points - Derong Kong\, Chongqing University
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200623T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200623T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1224
DESCRIPTION:Given a positive integer M and a real number x\, let U(x) be t
he set of all bases q in (1\,M+1] such that x has a unique q-expansion wit
h respect to the alphabet {0\,1\,...\,M}. We will investigate the local di
mension of U(x) and prove a 'variation principle' for unique non-integer b
ase expansions. We will also determine the critical values and the topolog
ical structure of U(x).
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Approximations of the Lagrange and Markov spectra - Carlos Matheus
\, CNRS\, École Polytechnique
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200616T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200616T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1225
DESCRIPTION:The Lagrange and Markov spectra are closed subsets of the posi
tive real numbers defined in terms of diophantine approximations. Their to
pological structures are quite involved: they begin with an explicit discr
ete subset accumulating at 3\, they end with a half-infinite ray of the fo
rm [4.52...\,∞)\, and the portions between 3 and 4.52... contain complic
ated Cantor sets. In this talk\, we describe polynomial time algorithms to
approximate (in Hausdorff topology) these spectra.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Equidistribution results for self-similar measures - Simon Baker\,
University of Birmingham
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200609T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200609T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1226
DESCRIPTION:A well known theorem due to Koksma states that for Lebesgue al
most every x>1 the sequence (x^n) is uniformly distributed modulo one. In
this talk I will discuss an analogue of this statement that holds for frac
tal measures. As a corollary of this result we show that if C is equal to
the middle third Cantor set and t≥1\, then almost every x in C+t is such
that (x^n) is uniformly distributed modulo one. Here almost every is with
respect to the natural measure on C+t.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linear repetition in polytopal cut and project sets - Henna Koivus
alo\, University of Vienna
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200602T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200602T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1227
DESCRIPTION:Cut and project sets are aperiodic point patterns obtained by
projecting an irrational slice of the integer lattice to a subspace. One w
ay of classifying aperiodic sets is to study repetition of finite patterns
\, where sets with linear pattern repetition can be considered as the most
ordered aperiodic sets. \nRepetitivity of a cut and project set depends o
n the slope and shape of the irrational slice. The cross-section of the sl
ice is known as the window. In an earlier work it was shown that for cut a
nd project sets with a cube window\, linear repetitivity holds if and only
if the following two conditions are satisfied: (i) the set has minimal co
mplexity and (ii) the irrational slope satisfies a certain Diophantine con
dition. In a new joint work with Jamie Walton\, we give a generalisation o
f this result for other polytopal windows\, under mild geometric condition
s. A key step in the proof is a decomposition of the cut and project schem
e\, which allows us to make sense of condition (ii) for general polytopal
windows.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergodic behavior of transformations associated with alternate base
expansions - Célia Cisternino\, University of Liège
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200526T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200526T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1228
DESCRIPTION:We consider a p-tuple of real numbers greater than 1\, beta=(b
eta_1\,…\,beta_p)\, called an alternate base\, to represent real numbers
. Since these representations generalize the beta-representation introduce
d by Rényi in 1958\, a lot of questions arise. In this talk\, we will stu
dy the transformation generating the alternate base expansions (greedy rep
resentations). First\, we will compare the beta-expansion and the (beta_1*
…*beta_p)-expansion over a particular digit set and study the cases when
the equality holds. Next\, we will talk about the existence of a measure
equivalent to Lebesgue\, invariant for the transformation corresponding to
the alternate base and also about the ergodicity of this transformation.
\nThis is a joint work with Émilie Charlier and Karma Dajani.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:On singular substitution Z-actions - Boris Solomyak\, University o
f Bar-Ilan
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200519T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200519T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1229
DESCRIPTION:We consider primitive aperiodic substitutions on d letters and
the spectral properties of associated dynamical systems. In an earlier wo
rk we introduced a spectral cocycle\, related to a kind of matrix Riesz pr
oduct\, which extends the (transpose) substitution matrix to the d-dimensi
onal torus. The asymptotic properties of this cocycle provide local inform
ation on the (fractal) dimension of spectral measures. In the talk I will
discuss a sufficient condition for the singularity of the spectrum in term
s of the top Lyapunov exponent of this cocycle. \nThis is a joint work wit
h A. Bufetov.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Preservation of normality by selection - Olivier Carton\, Universi
té de Paris
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200512T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200512T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1230
DESCRIPTION:We first recall Agafonov's theorem which states that finite st
ate selection preserves normality. We also give two slight extensions of t
his result to non-oblivious selection and suffix selection. We also propos
e a similar statement in the more general setting of shifts of finite type
by defining selections which are compatible with the shift.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ostrowski numeration and repetitions in words - Narad Rampersad\,
University of Winnipeg
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20200505T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20200505T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1231
DESCRIPTION:One of the classical results in combinatorics on words is Deje
an's Theorem\, which specifies the smallest exponent of repetitions that a
re avoidable on a given alphabet. One can ask if it is possible to determi
ne this quantity (called the repetition threshold) for certain families of
infinite words. For example\, it is known that the repetition threshold f
or Sturmian words is 2+phi\, and this value is reached by the Fibonacci wo
rd. Recently\, this problem has been studied for balanced words (which gen
eralize Sturmian words) and rich words. The infinite words constructed to
resolve this problem can be defined in terms of the Ostrowski-numeration s
ystem for certain continued-fraction expansions. They can be viewed as Ost
rowski-automatic sequences\, where we generalize the notion of k-automatic
sequence from the base-k numeration system to the Ostrowski numeration sy
stem.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rigid fractal tilings - Michael Barnsley\, Australian National Uni
versity
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20201201T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20201201T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1242
DESCRIPTION:I will describe recent work\, joint with Louisa Barnsley and A
ndrew Vince\, concerning a symbolic approach to self-similar tilings. This
approach uses graph-directed iterated function systems to analyze both cl
assical tilings and also generalized tilings of what may be unbounded frac
tal subsets of R^n. A notion of rigid tiling systems is defined. Our key t
heorem states that when the system is rigid\, all the conjugacies of the t
ilings can be described explicitly. In the seminar I hope to prove this fo
r the case of standard IFSs.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Limit theorems on counting large continued fraction digits - Tanja
Isabelle Schindler\, Scuola Normale Superiore di Pisa
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20201208T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20201208T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1243
DESCRIPTION:We establish a central limit theorem for counting large contin
ued fraction digits (a_n)\, that is\, we count occurrences {a_n>b_n}\, whe
re (b_n) is a sequence of positive integers. Our result improves a similar
result by Philipp\, which additionally assumes that bn tends to infinity.
Moreover\, we also show this kind of central limit theorem for counting t
he number of occurrences entries such that the continued fraction entry li
es between d_n and d_n (1+1/c_n) for given sequences (c_n) and (d_n). For
such intervals we also give a refinement of the famous Borel–Bernstein t
heorem regarding the event that the nth continued fraction digit lying inf
initely often in this interval. As a side result\, we explicitly determine
the first φ-mixing coefficient for the Gauss system - a result we actual
ly need to improve Philipp's theorem. This is joint work with Marc Kesseb
öhmer.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:The digits of n+t - Lukas Spiegelhofer\, Montanuniversität Leoben
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20201215T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20201215T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1262
DESCRIPTION:We study the binary sum-of-digits function s_2 under addition
of a constant t. For each integer k\, we are interested in the asymptotic
density δ(k\,t) of integers t such that s_2(n+t) - s_2(n) = k. In this ta
lk\, we consider the following two questions.\n\n(1) Do we have c_t = δ(0
\,t) + δ(1\,t) + ... > 1/2? This is a conjecture due to T. W. Cusick (201
1).\n\n(2) What does the probability distribution defined by k → δ(k\,t
) look like?\n\nWe prove that indeed c_t > 1/2 if the binary expansion of
t contains at least M blocks of contiguous ones\, where M is effective. Ou
r second theorem states that δ(j\,t) usually behaves like a normal distri
bution\, which extends a result by Emme and Hubert (2018). \n\nThis is joi
nt work with Michael Wallner (TU Wien).
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:alpha-odd continued fractions - Claire Merriman\, Ohio State Unive
rsity
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20210105T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20210105T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1269
DESCRIPTION:The standard continued fraction algorithm come from the Euclid
ean algorithm. We can also describe this algorithm using a dynamical syste
m of [0\,1)\, where the transformation that takes x to the fractional part
of 1/x is said to generate the continued fraction expansion of x. From th
ere\, we ask two questions: What happens to the continued fraction expansi
on when we change the domain to something other than [0\,1)? What happens
to the dynamical system when we impose restrictions on the continued fract
ion expansion\, such as finding the nearest odd integer instead of the flo
or? This talk will focus on the case where we first restrict to odd intege
rs\, then start shifting the domain [α-2\, α). \n\nThis talk is based on
joint work with Florin Boca and animations done by Xavier Ding\, Gustav J
ennetten\, and Joel Rozhon as part of an Illinois Geometry Lab project.
LOCATION:Online
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernoulli Convolutions and Measures on the Spectra of Algebraic In
tegers - Tom Kempton\, University of Manchester
DTSTART;TZID=Europe/Paris;VALUE=DATE-TIME:20210119T143000
DTEND;TZID=Europe/Paris;VALUE=DATE-TIME:20210119T153000
DTSTAMP;VALUE=DATE-TIME:20210128T090302Z
UID:1270
DESCRIPTION:
LOCATION:Online
END:VEVENT
END:VCALENDAR