Seminar of the Mathematical Analysis Group.
Current
schedule available on www.math.uni.wroc.pl/analiza
Organizers: prof. Marek Bożejko
(the
main organizer), Piotr
Śniady
(technical organizer)
Topics:
commutative and
non-commutative
harmonic analysis, quantum groups, combinatorics, quantum probability,
free
probability, Young diagrams, random matrices, convolutions of
measures,....
Contact: Piotr Śniady
(piotr.sniady@math.uni.wroc.pl)
Past schedule:
October 4, 2004, Thursday, 11.30-13.00, room 311:
Piotr Śniady (Uniwersytet
Wrocławski):
Wolność wyższego rzędu (Higher order of freeness)
November 11, 2004, Thursday: no seminar (Independence Day)
November 17, 2004, Wednesday 11.00-12.45: Kenneth Dykema (Texas A&M): Microstate free entropy for DT-operators
November 18, 2004, Thursday,, 11.30-13.00, room 311:
Anna Krystek, Łukasz Wojakowski
(Uniwersytet
Wrocławski), Uwagi o r-splocie i
r-deformacji
(Remarks on r-convolution and r-deformation)
November 22, 2004, Monday, 17.15-19.00 room 604:
Akihito Hora: Noncommutative
Central
Limit Theorem and Asymptotic Representation Theory
for Symmetric Groups
November 24, 2004, Wednesday, 17.15-19.00 room 603:
Akihito Hora: Noncommutative
Central
Limit Theorem and Asymptotic Representation Theory
for Symmetric Groups
November 29, 2004, Monday, 17.15-19.00 room 604:
Akihito Hora: Noncommutative
Central
Limit Theorem and Asymptotic Representation Theory
for Symmetric Groups
In this series of lectures the topics treated will include
-- Noncommutative Kerov CLT
-- Noncommutative CLT and the Jack measure
-- Indecomposable Characters of a wreath product of the
infinite symmetric group.
November 25, 2004, Thursday 11.30-13.00, room 311:
Romuald Lenczewski: Discrete approximations of free
probability
December 2, 2004, Thursday, 11.30-13.00, room 311:
Anna Krystek, Łukasz Wojakowski (Uniwersytet
Wrocławski), New examples of
associative
convolutions arising from the conditionally free convolution
We define two families of deformations depending on the second free
cumulant
of the measure and new associative convolutions arising from
conditionally
free convolution.These deformations do not commute with dilation of
measures,
which means that the central limit theorem cannot be obtained as a
direct
application of the theorem for the conditionally free case.
Surprisingly,
for one of these deformations the central limit measure is not
symmetric
-- its third moment is not equal to zero. To our knowledge, the only
other
example of non--symmetric central limit measures come from the
universal convolution.
December 9, 2004, Thursday, 11.30-13.00, room 311:
Wojciech Matysiak (Politechnika
Warszawska): Procesy stochastyczne z
liniowymi regresjami
i kwadratowymi warunkowymi wariancjami
Tematyka procesow stochastycznych z liniowa warunkowa wartoscia
oczekiwana
pod warunkiem przeszlosci i przyszlosci (lacznie), wystepujacych w
literaturze
pod nazwa harness-ow, cieszy sie ostatnio sporym zainteresowaniem,
m.in.
ze wzgledu na zwiazki z niekomutatywna probabilistyka i matematyka
finansowa.
Celem wystapienia bedzie podstawowe opisanie rodziny harness-ow o (co
najwyzej)
kwadratowych drugich momentach warunkowych. Pokazemy, ze takie procesy
wyznaczone
sa przez kilka parametrow. Pokazemy takze rownanie q-komutacyjne dla
macierzy
wspolczynnikow rekurencji dla wielomianow martyngalowych. Prezentowane
wyniki
otrzymano wspolnie z W.Brycem (University of Cincinnati, USA) i
J.Wesolowskim
(Politechnika Warszawska).
December 16, 2004, Thursday, 11.30-13.00, room 311:
Piotr Sniady: Asymptotic theory of representations of
symmetric
groups and genus expansion
January 6, 2005, Thursday, 11.30-13.00, room 311:
Piotr Sniady: Asymptotic theory of representations of
symmetric
groups and genus expansion
Asymptotic theory of representations of symmetric groups asks questions
of
the following type: what is a typical shape of a Young diagram which
contributes
to a prescribed infinite series of representations of S_n? Let two
large
Young diagrams be given; what is the typical shape of a Young diagram
which
contributes to their outer product; or to a induced; or to a restricted
representation?
Usual combinatorial methods were unable to solve such questions.
In my talk I will show that for nearly all natural representations (and
constructions
on them) the fluctuations of Young diagrams around their limit shape
have
a Gaussian form; in this way I extend results of Kerov, Olshanski,
Biane
and others. The main tool is the genus expansion: a very universal
principle
which says that to any combinatorial object we should associate a
two-dimensional
surface such that its topology determines the asymptotic behavior of
the
considered object.
This talk is closely related to the series of lectures of Akihito Hora
(however
no previous knowledge is required and all necessary notions will be
introduces);
in particular we shall present a one-line proof of Kerov's central
limit
theroem for Plancherel measure.
January 13, 2005, Thursday, 11.30-13.00, room 311:
Janusz Wysoczanski: Monotoniczna niezaleznosc na zbiorach
czesciowo
uporzadkowanych
January 20, 2005, Thursday, 11.15-13.00, room 311:
Marek Bozejko: Najnowsze postepy w dyskretnej analizie
harmonicznej
January 26, 2005, Wednesday, 11.15-13.00, room 311:
Piotr Sniady: Permutation model for free random variables
February 16, 2005, Wednesday, 10.15-12.00, room ???:
Janusz Wysoczanski: Monotoniczna niezaleznosc zwiazana z
czesciowym
porzadkiem
March 2, 2005, Wednesday, 10.15-12.00, room 603:
Alexandre Nou:
Asymptotic
matricial models and QWEP for the q-Gaussian von Neumann algebras (part
1)
March 9, 2005, Wednesday, 10.15-12.00, room 603:
Alexandre Nou:
Asymptotic
matricial models and QWEP for the q-Gaussian von Neumann algebras (part
2)
March 16, 2005, Wednesday, 10.15-12.00, room
603:
Marek Bozejko:
Generalized q-Gaussian random variables (part 1)
March 23, 2005,
Wednesday, 10.15-12.00, room 603:
Artur Buchholz: Even
more generalized q-Gaussian random variables
April 6, 2005, Wednesday,
10.15-12.00, room 603:
Quanhua XU (Besancon, France)
Free Khintchine inequalities and applications
April 13, 2005, Wednesday,
10.15-12.00, room 603:
Marek Bożejko, Artur Jeż, Anna
Krystek, Łukasz Wojakowski, Piotr Śniady:
Wspomnienie z Oberwolfach (Souvenir from Oberwolfach)
April 20, 2005
(Wednesday),
10.15-12.00, room 603:
Marcin
Petrykowski:
Kombinatoryczne własności grup z miarami (Combinatorial properties of
groups with measures)
May
4, 2005 (Wednesday),
10.15-12.00, room 603:
Ilona Królak: Recent results of
Eric Ricard (part 1)
May 11, 2005 (Wednesday),
10.15-12.00, room 603:
Ilona Królak: Recent
results of
Eric Ricard (part 2)
May 18, 2005 (Wednesday),
10.15-12.00, room 603:
Jacek Wesołowski (Politechnika Warszawska): Wokół
twierdzenia Lukacsa na stożku Lorentza
May 25, 2005
(Wednesday),
10.15-12.00, room 603:
Benoit Collins: Jacobi random matrices and free probability.
Abstract:
we prove that the contraction of a random projection by a constant
projection is a Jacobi unitary ensemble. Motivated by this and the
asymptotic freeness results of Voiculescu, we study asymptotics of
Jacobi kernels with weights varying linearly with the degree. This
allows us to prove various universality results and reinforce results
predicted by free probability theory.
June 1, 2005
(Wednesday),
10.15-12.00, room 603:
Julia Reffy: Free transportation cost inequalities and
random matrices.
June 8, 2005
(Wednesday),
10.15-12.00, room 603:
Piotr Sniady: Representations of unitary groups and
random matrices.
People you may meet here: Marek Bożejko,
Artur
Buchholz, Ilona Królak, Anna Krystek, Romuald
Lenczewski
(Politechnika Wrocławska), Wojciech Młotkowski,
Rafał
Sałapata
(Politechnika Wrocławska), Piotr Śniady, Łukasz Wojakowski, Janusz Wysoczański
List of all seminars in the Institute of
Mathematics,
University of Wrocław
Please send remarks about this page to Piotr Śniady
