[Turkmath:971] Talk by Poj Lertchoosakul at SU

[Canan Kasikci (Alumni)]

Degerli liste uyeleri,

Poj Lertchoosakul  (Polish Academy of Sciences) 8 Subat Pazartesi ve 10
Subat Carsmaba gunleri Sabanci Universitesi'nde iki konusma yapacaktir.
Asagida detaylarini bulacaginiz bu etkinlige katiliminiz bizi mutlu
edecektir.

iyi gunler dilegiyle

canan kasikci

Ulasim icin:
http://www.sabanciuniv.edu/en/transportation/shuttle-hours


*.......................................*

*Date/Time/Place: *
*8  February,  13:00 - 14:00,  FENS 2008*
*10 February, 13:00 - 14:00,  FENS 2008*

*Title: *Unique ergodicity and distribution functions for subsequences of
the van der Corput sequence

*Abstract: *Ergodic theory concerns with the behavior of a dynamical system
when it is allowed to run for a long time. The theory is a modern approach
in number theory which can be

used to study and characterize sets of numbers from a probabilistic or
measure-theoretic point of view. As it is the main tool in the talk, I will
first give a quick introduction to the main idea of the subject. In the
main talk, I would like to present a joint work, with R. Nair, on the
characterization
of unique ergodicity based on certain subsequences of the natural
numbers, called
Hartman uniformly distributed sequences. Then we shall see an application
of this characterization theorem on answering a question of O. Strauch, but
in a more general framework, regarding the limit distribution of
consecutive elements of the van der Corput sequence. Recently, C.
Aistleitner and M. Hofer calculated the asymptotic distribution function of
(Φb(n),Φb(n + 1),....,Φb(n + s -1))) n=0 to 1 on [0; 1)^s; where (Φb(n))n=0
to 1 denotes the van der Corput sequence in base b > 1; and showed that it
is a copula. In the talk, we shall see that this phenomenon extends not
only to a broad class of subsequences of the van der Corput sequence but
also to a more general setting in the a-adic numbers. Indeed, we shall use
the characterization of unique ergodicity, together with the fact that the
van der Corput sequence can be seen as the orbit of the origin under the
ergodic Kakutani-von Neumann transformation. Incidentally, we have
introduced the a-adic van der Corput sequence which significantly generalizes
the classical van der Corput sequence. I will go a bit further to present a new
joint work, with A. Jaššová and R. Nair, on extending the a-adic van der
Corput sequence to the Halton sequence in a generalized numeration system.
We shall see that it provides a wealth of low-discrepancy sequences, which
are very important in the quasi-Monte Carlo method. Note that some
knowledge of measure theory and some interest in uniform distribution theory
of sequences should be enough to follow the talk.



*Title:* On the metric theory of continued fractions in the field of formal
Laurent series over a finite field

*Abstract: *The fields of formal Laurent series over finite fields, or the
non-Archimedean local fields of positive characteristic, are considered to
be the true analogues of the real numbers. In this setting, I will
introduce the continued fraction algorithm, which is analogous to the
classical real case, and ask some metrical questions regarding the averages
of partial quotients of continued fraction expansion. In this talk, we
shall see that the continued fraction map in positive characteristic is
exact with respect to Haar measure. This fact of exactness implies a number
of strictly weaker properties. Indeed, we shall use weak mixing and
ergodicity, together with the point-wise subsequence ergodic theorems, to
answer our questions. This is a joint work with Radhakrishnan Nair. The
talk will be accessible to general maths audience.
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