SCIENTIFIC PROGRAMS AND ACTIVITIES

September 23, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

January-June 2014
Thematic Program on Abstract Harmonic Analysis, Banach and Operator Algebras

February 10-20: 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 10-14

Time
Monday
February 10
Tuesday
February 11
Wednesday
February 12
Thursday
February 13
Friday
February 14
10:00-11:00
Pierre-Emmanuel Caprace
Lecture 1
Lewis Bowen
Lecture 1
Lewis Bowen
Lecture 2
Lewis Bowen
Lecture 4
Pierre-Emmanuel Caprace
Lecture 4
11:10-12:10
Pierre-Emmanuel Caprace
Lecture 2
Pierre-Emmanuel Caprace
Lecture 3
2:00-3:00
George Willis
Lecture 1
Notes
George Willis
Lecture 2
Notes
Lewis Bowen
Lecture 3
George Willis
Lecture 3
Notes
George Willis
Lecture 4
Notes
3:30-4:30
     
Helge Glöckner
Expansive automorphisms of totally disconnected,
locally compact groups
 

Speakers

Pierre-Emmanuel 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 pro-finite 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 18-20
Mini-courses Lectures
Uri Bader Technion
Algebraic Representations of Ergodic Actions and Super-Rigidity

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 semi-simple 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 non-trivial 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
10:00-11:00
Uri Bader
Lecture 1
Uri Bader
Lecture 2
Tsachik Gelander
Lecture 4
 
11:10-12:10
Tsachik Gelander
Lecture 1
11:10-12:00
N. C. Phillips
Uri Bader
Lecture 4
11:10-12:00
N. C. Phillips
2:00-3:00
Tsachik Gelander
Lecture 2
Tsachik Gelander
Lecture 3
Visitor Seminar
Raddhi Shah
 
3:30-4:30
Visitor Seminar
Phillip Wesolek
Uri Bader
Lecture 3
   
4:40-5:40
Visitor Seminar
Uri Bader
Visitor Seminar
Bachir Bekka
   

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