
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES 
JanuaryJune
2014
Thematic Program on Abstract Harmonic Analysis,
Banach and Operator Algebras
February 1020: Group
Structure, Group Actions and Ergodic Theory
Organizer: George Willis (Newcastle,
Australia)


Theme
Periods Activities
Group Photos (click for enlarged version)
I. Week of February
1014
Time

Monday
February 10

Tuesday
February 11

Wednesday
February 12

Thursday
February 13

Friday
February 14

10:0011:00

PierreEmmanuel Caprace
Lecture 1

Lewis Bowen
Lecture 1

Lewis Bowen
Lecture 2

Lewis Bowen
Lecture 4

PierreEmmanuel Caprace
Lecture 4

11:1012:10


PierreEmmanuel Caprace
Lecture 2


PierreEmmanuel Caprace
Lecture 3


2:003:00

George Willis
Lecture 1
Notes

George Willis
Lecture 2
Notes

Lewis Bowen
Lecture 3

George Willis
Lecture 3
Notes

George Willis
Lecture 4
Notes

3:304:30




Helge Glöckner
Expansive automorphisms of totally disconnected,
locally compact groups


Speakers 
PierreEmmanuel Caprace, Université
catholique de Louvain
Totally disconnected, locally
compact groups (local structure)
George Willis, University of Newcastle
Totally disconnected, locally compact groups (the scale and minimising
subgroups)
Lewis Bowen, Texas A & M University
Sofic groups
Helge Glöckner, University of Paderborn (Germany)
Expansive automorphisms of totally disconnected, locally compact
groups (slides)
An automorphism f of a totally disconnected, locally
compact group G is called expansive if there exists an identity
neighborhood V in G for which the sets f^n(V) (for n ranging through
the set of integers) intersect in the trivial group {1}. For example,
every contractive automorphism (i.e., f^n(x) converges to 1 as
n tends to infinity, for each x in G) is expansive. The structure
of expansive automorphisms of profinite groups was elucidated
by G.A. Willis (who called them "automorphisms of finite
depth"). In the talk, I'll explain recent results concerning
expansive automorphisms for general, not necessarily compact groups,
obtained in joint work with C.R.E. Raja (see arXiv:1312.5875).

II. Week of February 1820
Minicourses Lectures 
Uri Bader Technion
Algebraic Representations of Ergodic Actions and SuperRigidity
Tsachik Gelander, Hebrew University
Invariant random subgroups and L(2) Betti numbers 
Visitor Seminar 
Phillip Wesolek, University of Illinois
Constructible totally disconnected locally compact second countable
groups and applications (slides)
The class of constructible totally disconnected locally
compact second countable (t.d.l.c.s.c.) groups is the collection
of t.d.l.c.s.c. groups built from profinite and discrete groups
via group extension and countable increasing union. These groups
appear often in the study of t.d.l.c.s.c. groups. We show this
class satisfies surprisingly robust closure properties. We go
on to give an application to the study of ${p}$adic Lie groups.
In particular, we show every ${p}$adic Lie group decomposes into
constructible and topologically simple groups via group extensions.
This result is analogous to the solvable by semisimple decomposition
for connected Lie groups. Time permitting, we discuss a second
application to a question of S. Gao's on surjectively universal
t.d.l.c.s.c. groups.
Raddhi Shah, Jawaharlal Nehru University
Distal Groups and Shifted Convolution Property
A locally compact group is said to be distal if under
the conjugacy action of the group on itself, the orbit of every
nontrivial element stays away from the identity. We study properties
of distal groups and characterise (pointwise) distal groups in
terms of behaviour of convolution powers of probability measures.
(Most of the results are obtained jointly with C.R.E. Raja).
Bachir Bekka, Institut de Recherche mathématique de
Rennes
Character Rigidity of Countable Groups 
Time

Tuesday
February 18

Wednesday
February 19

Thursday
February 20

Friday
February 21

10:0011:00

Uri Bader
Lecture 1

Uri Bader
Lecture 2

Tsachik Gelander
Lecture 4


11:1012:10

Tsachik Gelander
Lecture 1


Uri Bader
Lecture 4


2:003:00

Tsachik Gelander
Lecture 2

Tsachik Gelander
Lecture 3

Visitor Seminar
Raddhi Shah


3:304:30

Visitor Seminar
Phillip Wesolek

Uri Bader
Lecture 3



4:405:40

Visitor Seminar
Uri Bader

Visitor Seminar
Bachir Bekka




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