
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
July
2013
Focus Program on Noncommutative Distributions in Free
Probability Theory
July
2226, 2013
Workshop on Analytic, Stochastic, and Operator Algebraic Aspects
of Noncommutative Distributions and Free Probability
Organizing
Committee:
Hari
Bercovici (Indiana),
Benoît Collins (Ottawa), James Mingo (Queen's)
Roland Speicher (Saarland),
DanVirgil Voiculescu (UC, Berkeley)



Monday July 22 
8:45  9:15

Onsite Registration 
9:15  9:30

Welcome and Introduction 
9:30  10:20

Ken Dykema, Texas A&M University (slides)
Quantum symmetric states on universal free product
C*algebras 
10:30  10:55

Michael Brannan, University of Illinois at UrbanaChampaign
(slides)
Strong asymptotic freeness for the generators of
free orthogonal quantum groups 
11:00  11:30

Coffee break 
11:30  12:20

Roland Vergnioux, Université de Caen BasseNormandie
On the adjoint representation of orthogonal free
quantum groups 
12:20  2:00

Lunch break 
2:00  2:50

Benoît Collins, University of Ottawa
Comparison of L^{p} norms and free compression
norms, and application to quantum information theory 
3:00  3:30

Coffee 
3:30  4:20

Todd Kemp, UC San Diego
The Large$\mathbb{N}$ Limit of Brownian Motion on
$\mathbb{GL_N}$

4:30  4:55

Moritz Weber, Saarland University (slides)
Partitions and Quantum Groups 
5:00  5:25

Stephen Avsec, University of Ottawa (slides)
New Examples of Exchangeable Noncommutative Brownian
Motions 
5:30  5:55

Guillaume Cébron, Université Pierre
et Marie Curie (Paris 6) (slides)
Transition operators for free convolution 
Tuesday July 23 
9:30  10:20

Franz Lehner, Graz University of Technology
Combinatorial relations between cumulants 
10:30  10:55

Wlodek Bryc, University of Cincinnati (slides)
CauchyStieltjes kernel families 
11:00  11:30

Coffee break 
11:30  12:20

Steen Thornbjørnsen, University of Aarhus
On the free Gamma distributions 
12:20  2:00

Lunch break 
2:00  2:50

Hiroaki Yoshida, Ochanomizu University
Applications of the time derivative of the Wasserstein
distance and the free entropy dissipation 
3:00  3:30

Coffee break 
3:30  4:20

Friedrich Götze, Bielefeld University
Asymptotic Approximation and Inverse Problems for
Sums of Free Variables 
4:30  4:55

Haowei Huang, Indiana University, Bloominton
(slides)
Supports of measures in a free additive convolution
semigroup 
5:00  5:25

Ping Zhong, Indiana University, Bloomington (slides)
Free convolution with a free multiplicative analogue
of the normal distribution 
5:30  5:55

Sheehan Olver, University of Sydney (slides)
Numerical Computation of Convolutions in Free Probability

Wednesday July 24 
9:30  10:20

Jesse Peterson, Vanderbilt University
Rigidity for characters on lattices and commensurators

10:30  11:20

Yoann Dabrowski, Université Lyon 1 (slides)
Time reversal of free Stochastic Differential
Equations and applications of nonmicrostates free entropy to von Neumann
algebras 
11:30  12:00

Coffee break 
12:00  12:50

Roland Friedrich, HumboldtUniversität zu Berlin
On Generalisations of Free Probability Theory
to Higher Dimensions 
7:30pm

Program Banquet, tickets $32 
Thursday July 25 
9:30  10:20

Victor Vinnikov, Ben Gurion University
Realization and interpolation for noncommutative
functions 
10:30  10:55

Paul Skoufranis, University of California, Los Angeles
(slides)
Distributions of Polynomials of Free Semicircular
Variables 
11:00  11:30

Coffee break 
11:30  12:20

Bill Helton, UCSD
Free Real Algebraic Geometry and Free Convexity 
12:20  2:00

Lunch break 
2:00  2:50

Serban Belinschi, Queen's University
Spectral and Brown measures of polynomials in free random variables 
3:00  3:30

Tea break 
3:30  4:20

John McKay, Concordia University
Some remarks on groups and cumulants 
4:30  4:55

John Williams, Texas A&M University
Analytic Function Theory for OperatorValued Free
Probability 
5:00  5:25

Mihai Popa, Queen's University
Hardy classes on some noncommutative unit balls 
5:30  5:55

Tobias Mai, Universite des Saarlandes (slides)
Operatorvalued free probability theory and the selfadjoint
linearization trick 
Friday July 26 
9:30  10:20

Yoshimichi Ueda, Kyushu University (slides)
Orbital free entropy and its dimension counterpart

10:30  10:55

Benjamin Hayes, University of California,
Los Angeles
An l^{ p}Version of von Neumann Dimension
For Representations of Equivalence Relations 
11:00  11:30

Coffee break 
11:30  12:20

V.S. Sunder, The Institute of Mathematical Sciences
Minimax theorems of Ky Fan and Wielandt 
12:20  2:00

Lunch break 
2:00  2:50

Thierry CabanalDuvillard, Université
René Descartes (slides)
A generalized MarchenkoPastur Theorem 
3:00  3:25

Daniel Redelmeier, Texas A&M University
(slides)
The Amalgamated Free Product of Semifinite Hyperfinite
von Neumann Algebras over Type I atomic Subalgebras 
3:30

Tea/Coffee break 
Speaker

Title
and Abstract 
Avsec,
Stephen
University of Ottawa 
New Examples of Exchangeable Noncommutative Brownian Motions
We will begin by recalling a definition of noncommutative
brownian motion due to Collins and Junge as well as a classification
theorem of such brownian motions which satisfy an exchangeability condition.
We will then discuss a couple of constructions which can be used to
produce new examples of such exchangeable brownian motions. This is
joint work with B. Collins and M. Junge.

Belinschi,
Serban
Queen's University

Spectral and Brown measures of polynomials in free random variables
The combination of a selfadjoint linearization trick due to
Greg Anderson with Voiculescu's subordination for operatorvalued free
convolutions and analytic mapping theory turns out to provide a method
for finding the distribution of any selfadjoint polynomial in free variables.
In this talk we will present the analytic machinery behind this process,
and show an extension that allows in principle the computation of Brown
measures of possibly nonselfadjoint polynomials in free variables.
We will also indicate some results on Brown measures of some sums and
products of free random variables. This talk is based on joint work
with Tobias Mai and Roland Speicher and ongoing joint work with Piotr
Sniady and Roland Speicher.

Brannan,
Michael
University of Illinois at UrbanaChampaign 
Strong asymptotic freeness for the generators of free orthogonal
quantum groups
It is a well known fact that as $N$ tends to infinity, the
standard coordinate functions over the $N \times N$ orthogonal group
$O_N$ converge in distribution with respect to the Haar measure (after
appropriate normalization) to a standard i.i.d. Gaussian family. In
this talk, I will discuss the analogous situation that occurs in the
large $N$ limit for Wang's free orthogonal quantum group $O_N^+$. In
this case, T. Banica and B. Collins have shown that the limiting distribution
of the normalized standard coordinate functions is Voiculescu's free
semicircular system. We will show that in the free case, the mode of
convergence to a free semicircular system is actually quite strong:
Given any noncommutative polynomial in the normalized coordinates over
$O_N^+$, not only does it converge in distribution to the corresponding
polynomial over a free semicircular system, but also the norm of the
polynomial converges to the norm of the limiting polynomial.

Bryc,
Wlodek
University of Cincinnati

CauchyStieltjes kernel families
The CauchyStieltjes kernel families are constructed from
a probability measure $\nu$ using the Cauchy kernel $x\mapsto 1/(1\theta
x)$ in a manner analogous to the celebrated exponential families that
are constructed using kernel $x\mapsto\exp(\theta x)$. There are numerous
similarities between the two families: both are parameterized by the
mean, both are uniquely determined by the variance function (and the
so called "domain of means"), and the variance function of
the CauchyStieltjes kernel family generated by the free convolution
power of the generating measure $\nu$ has the same form as the variance
function of the exponential family of the convolution powers.
There also some differences due to the fact that the exponential
kernel $\exp(\theta x)$ is always positive while the Cauchy kernel
$1/(1\theta x)$ might be negative, and due to the fact that the variance
of the CauchyStieltjes kernel family might not exist.
The material on CauchyStieltjes families comes from papers with
Raouf Fakhfakh, Abgelhamid Hassairi, and Mourad Ismail.

Thierry
CabanalDuvillard
Université René Descartes 
A generalized MarchenkoPastur Theorem
The wellknown MarchenkoPastur theorem gives the asymptotic
spectral distribution of sums of random, independent, rankone projections,
when their size tends to infinity. Its main hypothesis is that these
projections behave asymptotically as if they were uniformly distributed.
We propose a way to drop this delocalization assumption and we generalize
this theorem to a quite general framework, including random projections
whose corresponding vectors are localized, i.e. with some components
much larger than the other ones (joint work with Florent BenaychGeorges).

Cébron,
Guillaume
Université Pierre et Marie Curie (Paris 6) 
Transition operators for free convolution
By introducing a new universal space $\mathbb{C}\{X\}$ that
extends the space $\mathbb{C}[X]$ of polynomials, we define transition
operators which allows us to compute explicitly the conditional expectation
of $P(A+B)$ given $B$, if $A$ and $B$ are free variables and $P\in \mathbb{C}[X]$.
We investigate also the multivariate case and the multiplicative case.
We finally describe some applications related to the free SegalBargmann
transform introduced by Biane.

Collins,
Benoît
University of Ottawa 
Comparison of L^p norms and free compression norms, and application
to quantum information theory
We study and solve an optimization problem of the L^p norms
with respect to the free compression norms. The solution to this problem
clarifies and improves the violation of additivity for minimum output
entropy in quantum information theory. This is joint work with Serban
Belinschi and Ion Nechita.

Dabrowski,
Yoann
Université Lyon 1 
Time reversal of free Stochastic Differential Equations and applications
of nonmicrostates free entropy to von Neumann algebras
We show that solutions of free stochastic differential equations
(SDE) with regular drifts and diffusion coefficients, when considered
bacwards in time, still satisfy free SDEs for an explicit brownian motion.
From a von Neumann algebra viewpoint, this implies that important subspaces
of the L² space of the process, orthogonal to L²(W^*(X_t)),
considered as a bimodules over the algebra of variables at time t W^*(X_t)
are mixing and weakly contained in the coarse correspondence for almost
every t. We give applications to free entropy, combining this information
with previous joint results with Adrian Ioana using Popa's deformation/Rigidity
Theory. We especially prove that finite nonmicrostates entropy implies
nonGamma and that finite nonmicrostates mutual information and extra
assumptions (the main one being nonamenability of one algebra) implies
primness.

Dykema,
Ken
Texas A&M University 
Quantum symmetric states on universal free product C*algebras
(joint work with Claus Koestler and John Williams)
We study quantum symmetric states on universal free product C*algebras
of a unital C*algebra A with itself infinitely many times. This is
a generalization of the notion of quantum exchangeable random variables,
using the quantum permutation group of Wang. By extending and building
on the proof of the noncommutative de Finetti theorem of Koestler and
Speicher, we prove a de Finetti type theorem that characterizes quantum
symmetric states in terms of amalgamated free products, with amalgamation
over the tail algebra. This allows a convenient description of the set
of all quantum symmetric states and in particular of the extreme quantum
symmetric states. Finally, the sets of central quantum symmetric states
and central tracial quantum symmetric states are shown to be Choquet
simplexes.

Friedrich,
Roland
HumboldtUniversität zu Berlin 
On Generalisations of Free Probability Theory to Higher Dimensions
In this talk we will first discuss the algebraic structures
underlying Free Probability Theory. Then based on this, we will introduce
the generalisation of the Stransform to arbitrary dimensions. Whereas
in the onedimensional case it is abelian this is no longer true in
dimensions bigger or equal to two. This has some important consequences,
which we shall present, in particular also by examples from the analytic
category.

Götze,
Friedrich
Bielefeld University 
Asymptotic Approximation and Inverse Problems for Sums of Free Variables
We shall discuss higher order expansions of the Voiculescu
Entropy of sums of free variables under almost optimal moment conditions.
Furthermore, results related to classical inverse characterization questions
for linear forms of free variables are presented. This is joint work
with G. Chistyakov.

Hayes,
Benjamin
University of California, Los Angeles 
An l^{p}Version of von Neumann Dimension For Representations of
Equivalence Relations
Following our previous ideas on extending von Neumann for
Banach space representations of groups, we extend von Neumann dimension
to representations of an equivalence relation on a Banach space. This
extended dimension is defined in an "entropic" way, counting
size of a certain set of microstates for the action of the equivalence
realtion. Applications will include a way to define l^{p}Betti numbers
for equivalence relation, as well as giving some insight to the cost
versus l^{2}Betti number problem.

Helton,
Bill
University of California, San Diego

Free Real Algebraic Geometry and Free Convexity
Real Algebraic Geometry concerns polynomial inequalities
and equalities. Say p >0 where q>0, then there is a algebraic
relationship between p and q which is equivalent to this happening.
Within the last decade there has been an effort to extend this sort
of "algebraic certificate" to polynomials in (free) matrix
variables. One important inequality a polynomial can satisfy is convexity.
By now there is considerable theory of free convexity which continues
to develop.
The talk will give an overview and describe the status of some parts
of these two areas.

Huang,
Haowei
Indiana University, Bloominton 
Supports of measures in a free additive convolution semigroup
Any Borel probability measure $\mu$ on $\mathbb{R}$ generates
a discrete free additive convolution semigroup {$\mu^{\boxplus n}: n
\in \mathbb{N}$}, which can be continuously imbedded into a partially
defined semigroup {$\mu^{\boxplus n}: t \geq 1$}, as proposed by Bercovici
and Voiculescu in their study of the free central limit theorem. In
this talk, the supports and densities of measures in the continuous
semigroup will be analyzed. More precisely, we will explain how the
supports of the measures in the semigroup {$\mu^{\boxplus n}: t >
1$}vary when t increases. Moreover, motivated by the free central limit
theorem we will give equivalent conditions so that the measure $\mu^{\boxplus
n}$ has only one component in the support for sufficiently large t.
An example of $\mu$ such that there are infinitely many components in
the support of $\mu^{\boxplus n}$ for all t > 1 will be given as
well.

Kemp,
Todd
University of California, San Diego 
The Large$N$ Limit of Brownian Motion on $GL_N$
The Brownian motion on the Unitary group $U_N$ has a large$N$
limit: the free unitary Brownian motion, introduced by Philippe Biane
in 1997 and used extensively in free probability since then. In the
same 1997 paper, Biane introduced a complex multiplicative free Brownian
motion (as the solution of a free SDE) that he conjectured is the large$N$
limit of the Brownian motion on $GL_N$. In this talk, I will discuss
my recent work proving this conjecture, as well as classifying the large$N$
limits of a class of diffusion processes on $GL_N$ that are invariant
with respect to the real subgroup $U_N$ in a strong sense. The techniques
rely, in part, on my recent joint work with Bruce Driver and Brian Hall
on the large$N$ limit of the unitary SegalBargmann transform; time
permitting, I will discuss this as well.

Lehner,
Franz
Graz University of Technology 
Combinatorial relations between cumulants
We discuss combinatorial relations between various cumulants
(classical, free, boolean and monotone) which we found in joint work
with O.Arizmendi, T.Hasebe and C.Vargas.

Mai,
Tobias
Universität des Saarlandes 
Operatorvalued free probability theory and the selfadjoint linearization
trick
The linearization trick in its selfadjoint version by G.
Anderson provides in many situations and particularly in free probability
theory a powerful tool to deal with polynomials in noncommutative variables.
It leads, for example, in combination with results about the operatorvalued
free additive convolution to an effective algorithm for the calculation
of the distribution of any selfadjoint polynomial in free random variables
(joint work with S. Belinschi and R. Speicher). In my talk, I will present
some facts about the linearization trick and I will discuss some of
its applications.

John
McKay
Concordia University 
Some remarks on groups and cumulants
I describe how an interest in representations of certain finite
simple groups led to free cumulants and ultimately the work with Roland
Friedrich of which has spoke on Wednesday.
There are many open problems:
Are sporadic simples sporadic?
Does M have an action on the free loop space of the 24dimensional manifold?
How general is moonshine?
Book: Mark Ronan, Symmetry and the Monster

Olver,
Sheehan
University of Sydney 
Numerical Computation of Convolutions in Free Probability
We construct a numerical toolbox for computing the additive,
multiplicative and compressive convolution operations from free probability.
In the univalent case, the method exploits the fact that the output
measure is, under broad conditions, either smooth and exponentially
decaying (i.e. Schwartz) or an analytic function times a semicircle.
High accuracy is obtain by representing the output measure using a basis
that incorporate its regularity, and imposing that the inverse of the
Cauchy transform takes the correct values at specified points in the
complex plane. The approach is further extended to the multiple interval
case, by taking into account the multivalued nature of the inverse of
the Cauchy transform.

Peterson,
Jesse
Vanderbilt University 
Rigidity for characters on lattices and commensurators
A character on a discrete group is a conjugation invariant
function of positive type which take value 1 at the identity. The study
of characters on infinite groups was initiated by Thoma in 1964 where
he classified extreme characters on the group of finite permutations
of the natural numbers. Recently, Bekka has shown that characters on
the groups PSL_n(Z), for n > 2 have a remarkable rigidity property,
they correspond either to finite dimension representations, or else
the left regular representation. For the case n = 2, this was generalized
to other rings of integers by the speaker and Thom. In this talk we
will describe a similar rigidity property for characters on many irreducible
lattices in higher rank semisimple groups. This is related to rigidity
results of Margulis, and BaderShalom, and confirms a conjecture of
Connes for such groups. This is joint work with Darren Creutz.

Popa,
Mihai
Queen's University 
Hardy classes on some noncommutative unit balls
The talk will present some results, joint work with V. Vinnikov,
in the study of the Hardy space H2 of locally bounded noncommutative
functions on the noncommutative unit ball of a variety of finite dimensional
operator spaces. The results are part of a larger work on noncommutative
symmetric domains. Our methods combine the general theory of noncommutative
functions with asymptotic freeness results of D.V. Voiculescu and formulas
for integration over unitary groups of B. Collins and P. Sniady.

Redelmeier,
Daniel
Texas A&M University 
The Amalgamated Free Product of Semifinite Hyperfinite von Neumann
Algebras over Type I atomic Subalgebras
The amalgamated free product for von Neumann algebras is
a construction which has seen considerable use over the years. Here
we examine the amalgamated free product of first finite then semifinite
hyperfinite von Neumann algebras over type I atomic subalgebras. Generalising
the concept of standard embeddings to what we call substandard embeddings
we are able to show these are composed of direct sums interpolated free
group factors and hyperfinite algebras in the finite case, and those
with the addition of B(H) tensored with interpolated free group factors
in the semifinite case (as well as allowing semifiniteness in the hyperfinite
part). Further we show that these classes are closed under this type
of amalgamated free product. We also adapt the concept of free dimension
so that these products continue to satisfy the equation $fdim(A*_{D}B)=fdim(A)+fdim(B)fdim(D)$.

Skoufranis,
Paul
University of California, Los Angeles 
Distributions of Polynomials of Free Semicircular Variables
One central concept in the study of free probability is to
describe the spectral distributions of noncommutative polynomials of
freely independent random variables. In this talk we will briefly outline
the recent results that if $\mu$ is the spectral distribution
of a selfadjoint (matricial) polynomial in freely independent semicircular
variables then $\mu$ is nonatomic and the Cauchy
transform of $\mu$ is algebraic. The fact that $\mu$ is nonatomic follows
from the extension of the strong Atiyah conjecture to certain tracial
*algebras and the fact that the Cauchy transform of $\mu$ is algebraic
follows from demonstrating (using a specific Schwinger?Dyson equation)
that a specific formal power series in noncommuting variables is algebraic.
This is joint work with D. Shlyakhtenko.

Sunder,
V.S.
The Institute of Mathematical Sciences 
Minimax theorems of Ky Fan and Wielandt
Let $\alpha_1 \leq \cdots \leq \alpha_n$ be an increasing
rearrangement of the eigenvalues of a selfadjoint matrix in $M_n(\mathbb{C})$.
The classical minimax theorem of Ky Fan is an extremal characterisation
of $\sum_{i=1}^k \alpha_i$ for each $1 \leq k \leq n$. The classical
minimax theorem of Wielandt is an extremal characterisation of $\sum_{j=1}^k
\alpha_{i_j}$ for any subset $\{i_1, \cdots, i_k\} \subset \{1, \cdots,
n\}$.
In joint work with Madhushree Basu, we have obtained `continuous versions'
of Ky Fan's theorem as well as of Wielandt's theorem but only for $k=2$.
Our attempts to prove this for all $k$ seem to be blocked by our proof
depending on a result on `a standard form for two projections in a von
Neumann algebra' which has no satisfactory analogue for more than two
projections. An attempt will be made to describe our results and this
hurdle as well as the reasons for our interest in Wielandt's theorem.

Thorbjørnsen,
Steen
University of Aarhus 
On the free Gamma distributions
In free probability theory the role of the Gaussian distribution
is played by the semicircle distribution, and the square of a semicircular
distributed random variable has the MarchenkoPastur distribution. However,
the MarchenkoPastur distribution is also the free analog of the Poisson
distribution, so the free analog of the chisquare distribution is instead
thought of as the image of the classical chisquare distribution by
the BercoviciPata bijection between the classes of infinitely divisible
probability measures in classical and free probability. More generally
the free gamma distributions are defined similarly in terms of the mentioned
bijection. It follows from general properties of the BercoviciPata
bijection that the free Gamma distributions are nonstable, selfdecomposable
distributions (with respect to free convolution) with moments of any
order, but further detailed properties remained until recently unrevealed.
In the talk I will report on a recent detailed study of the free Gamma
distributions based on the method of Stieltjes inversion. In particular
I will address the following features: Absolute continuity, tail behavior
and unimodality.
The talk is on joint work with Uffe Haagerup.

Ueda,
Yoshimichi
Kyushu University 
Orbital free entropy and its dimension counterpart
A couple of years ago, Hiai, Miyamoto and I introduced the
orbital free entropy $\chi_\mathrm{orb}$ and its dimension counterpart
$\delta_{0,\mathrm{orb}}$. The quantities originate in two things 
the socalled change of variable formula by matrix diagonalization on
the matrix Euclidean space on one hand and the free entropy adapted
to projections studied by Hiai and myself following Voiculescu's proposal
on the other hand. We will start with those origins, then report the
current status of the study of those quantities, and finally conclude
a few questions.

Vergnioux,
Roland
Université de Caen BasseNormandie 
On the adjoint representation of orthogonal free quantum groups
I will review some operatoralgebraic properties of free
quantum groups and present a new result about the adjoint representation
of orthogonal free quantum groups, with application to strong solidity.
This is joint work with Pierre Fima.

Vinnikov,
Victor
Ben Gurion University 
Realization and interpolation for noncommutative functions
I will discuss concepts, conjectures, and preliminary results
generalizing the classical results on contractive analytic functions
(or analytic functions with positive imaginary part) on the unit disc
(or the upper halfplane) to the setting of noncommutative functions,
that is functions defined on appropriate matrices of all sizes over
a given vector space ${\mathcal V}$, which satisfy certain compatibility
conditions as we vary the size of matrices  they respect direct sums
and similarities. The space ${\mathcal V}$ here is an operator space
(or an operator system), so that we can define the noncommutative unit
disc (or the noncommutative upper halfplane). In case ${\mathcal V}$
is finite dimensional, we recover essentially the results of BallGroenewaldMalakorn
on the $d$variable noncommutative Schur class whose elements are viewed
as formal power series in $d$ noncommuting indeterminates.
This is a joint work in progress with Joe Ball, Serban Belinschi,
and Mihai Popa.

Weber,
Moritz Saarland University

Partitions and Quantum Groups
In 2009, Banica and Speicher initiated the systematic study
of the so called easy quantum groups. These are compact matrix quantum
groups with a very intrinsic combinatorial structure, given by partitions.
The classification of these objects has recently been completed in joint
work with Sven Raum, and I will report on that. Furthermore, the fusion
rules (i. e. the representation theory) of easy quantum groups can be
expressed in terms of partitions (joint work with Amaury Freslon). This
gives a unified approach to the fusion rules of Wang's quantum permutation
group S_n^+, the free orthogonal quantum group O_n^+, and many others.

Williams,
John
Texas A&M University 
Analytic Function Theory for OperatorValued Free Probability
In this talk, we discuss the properties of analytic maps from
the noncommutative upperhalf plane to the noncommutative lowerhalf
plane. In particular, we prove a characterization of the noncommutative
Cauchy transforms that is analogous to the scalarvalued result. We
will also discuss the immediate consequences of this work.

Yoshida,
Hiroaki
Ochanomizu University

Applications of the time derivative of the $L^2$Wasserstein distance
and the free entropy dissipation.
For compactly supported probability measures on the real,
we consider the timeevolution by the free FokkerPlanck equation. We
shall see the timederivative formula of the square of the $L^2$Wasserstein
distance by using the optimal transport map and the dissipation formulas
of the free relative entropy. Then using these formulas we will show
that the free analogue of HWI, the logarithmic Sobolev, and the transportation
cost inequalities can be derived more directly for a strongly convex
potential function.We shall also show the time derivative formula of
the relative free entropy for the semicircular perturbations, which
gives another integral representation of the relative free entropy in
univariate case.

Zhong,
Ping
Indiana University, Bloomington 
Free convolution with a free multiplicative analogue of the normal
distribution
We obtain a formula for the density of the free convolution
of an arbitrary probability measure on the unit circle
of $\mathbb{C}$ with the free multiplicative analogues of the normal
distribution on the unit circle. This description relies on a characterization
of the image of the unit disc under the subordination function, which
also allows us to prove some regularity properties of the measures obtained
in this way. We also obtain analogue results for probability measures
on $\mathbb{R}^+$.

Participants as of July 4, 2013
Full Name 
University/Affiliation 
Andrews, Rob 
no affiliation 
Avsec, Stephen 
University of Ottawa 
Barmherzig, David 
University of Toronto 
Basu, Madhushree 
Institute of Mathematical Sciences 
Belinschi, Serban 
Queen's University 
Bercovici, Hari 
Indiana University 
Blitvic, Natasha 
Vanderbilt Univ 
Bozejko, Marek 
University of Wroclaw 
Brannan, Michael 
University of Illinois at UrbanaChampaign 
Bryc, Wlodzimierz 
University of Cincinnati 
CabanalDuvillard, Thierry 
Université René Descartes, 
Cebron, Guillaume 
Université Pierre et Marie Curie (Paris 6) 
Cheng, Oliver 
Brown University 
Cipriani, Fabio* 
Politecnico di Milano 
Collins, Benoît 
University of Ottawa 
Dabrowski, Yoann 
Université Lyon 1 
Dewji, Rian 
University of Cambridge 
Dykema, Ken 
Texas A&M University 
Elliott, George 
University of Toronto 
Farah, Ilijas 
York University 
Friedrich, Roland 
HumboldtUniversität zu Berlin 
Gerhold, Malte 
Universität Greifswald 
Götze, Friedrich 
Bielefeld University 
Grabarnik, Genady 
St John's University 
Green, Philip* 
University of Washington 
Grela, Jacek 
Jagiellonian University 
Gu, Yinzheng 
Queen's University 
Haagerup, Uffe 
University of Copenhagen 
Halevy, Itamar 
no affiliation 
Hartglass, Michael 
University of California, Berkeley 
Hasebe, Takahiro 
University of FrancheComte 
Hayes, Benjamin 
University of California, Los Angeles 
Helton, J. William 
University of California, San Diego 
Hu, Yi 
Colorado State University 
Huang, HaoWei 
Indiana University, Bloominton 
Huang, Xuancheng 
University of Toronto 
Jain, Madhu 
Indian Institute of Technology, Roorkee 
Jeong, Ja A 
Seoul National University 
Jones, Vaughan* 
Vanderbilt University 
Jurczynski, Mateusz 
Lancaster University 
Kappil, Sumesh 
Indian Statistical Institute 
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