## SCIENTIFIC PROGRAMS AND ACTIVITIES

March  7, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

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

 Lead Organizers Anthony To-Ming Lau (Alberta) Matthias Neufang (Carleton and Lille 1) Organizing Committee H. Garth Dales (Lancaster) George Elliott (Toronto) Thierry Giordano (Ottawa) Eberhard Kaniuth (Paderborn) David Kerr (Texas A&M) Zhong-Jin Ruan (UIUC) Andrew Toms (Purdue) George Willis (Newcastle, Australia)
 Registration for Program activity Elliott Distinguished Visitor Lectures and von Neumann Lecture Series Toronto Confirmed participants Accommodation in Toronto

To be informed of Program updates please subscribe to the Fields maillist.

Program Outline
The six-month Thematic Program will begin with a month-long Winter School on Basics in Abstract Harmonic Analysis, Banach and Operator Algebras followed by four concentration periods, devoted to one of the Program themes.

Phillips Course
Professor N. C. Phillips (Oregon)
(Dean's Distingished Visiting Professor) will give a full-term graduate course (January 6-April 4, 2014, Monday, Wednesday and Friday at 11:10 a.m.), Crossed products of C*-algebras and Banach algebras.
Note: Registration for this course is through the University of Toronto Mathematics Department.
Location: Room 230

Special Lectures

Coxeter Lecture Series
Sorin Popa (University of California, Los Angeles)

# Theme Concentration Periods

January 6-17: Winter School

Organizer: Zhiguo Hu

February 10-20: Group Structure, Group Actions and Ergodic Theory

Organizer: George Willis

Schedule for Mini-courses on Group Structure, Group Actions and Ergodic Theory
I. Week of February 10-14 activities

II. Week of February 18-20 activities

March:
C*-Algebras and Dynamical Systems

Organizer: George Elliott

Elliott Distinguished Visitor Lectures
February 25 - March 27

Every Tuesday and Thursday from 11:10 a.m. to 12:30 p.m. in Room 230, March 27 in the Stewart Library

Speaker: Eberhard Kirchberg, Humboldt-Universität zu Berlin
 Content of Lectures 1 Towards ideal-system equivariant classification (Lecture Notes) Basic definitions and terminology, statement of the main results: Embedding Theorem, Theorem on realization of ${\mathrm{KK}(\mathcal{C}; \cdot,\cdot)}$) by C*-morphisms, On applications. 2 An ideal system equivariant Embedding Theorem (I) A generalized Weyl-von-Neumann Theorem in the spirit of Voiculescu and Kasparov, Actions of topological spaces on C*-algebras versus matrix operator convex cones $\mathcal{C}$, related "universal" Hilbert bi-modules, Cone ${\mathcal{C}}$-dependent Ext-groups $\mathrm{Ext}(\mathcal{C};\, A,B)$, Related semi-groups. 3 Ideal system equivariant Embedding Theorem (II) C*-systems and its use for embedding results, the example of embeddings into $\mathcal{O}_2$, criteria for existence of ideal equivariant liftings, i.e. characterization of invertible elements in the extension semigroup. 4 Ideal system equivariant Embedding Theorem (III) Proof of a special case by construction of a suitable C*-system, Outline of the idea for the proof of the general case by study of asymptotic embeddings, using continuous versions of Rørdam semi-groups. 5 Some properties of strongly purely infinite algebras Operations on the class of s.p.i. algebras, coronas and asymptotic algebras of strongly purely infinite algebras, tensorial absorption of $\mathcal{O}_\infty$, 1-step innerness of residually nuclear c.p. maps. 6 Rørdam groups R($\mathcal{C};\, A,B)$ (I) Definition and properties of the natural group epimorphism from the $\mathcal{C}$-dependent Rørdam group R($\mathcal{C};\, A,B)$ onto Ext($\mathcal{SC}; A; SB$), reduction of the isomorphism problem to the question on homotopy invariance of R($\mathcal{C};\, A,B)$, Some cases of automatic homotopy invariance: the "absorbing" zero element. 7 Rørdam groups (II) Homotopy invariance of R($\mathcal{C};\, A,B)$, existence of C*-morphisms $\varphi:A \rightarrow B$ that represent the elements of R($\mathcal{C};\, A,B)$, proof of the Embedding Theorem in full generality. 8 Cone-related KK-groups KK($\mathcal{C};\, A,B)$) (I) Definition and basic properties of $\mathcal{C}$-related ($\mathbb{Z_2}$-graded) Kasparov groups KK($\mathcal{C};\, A,B$) for graded m.o.c. cones $\mathcal{C}$, the isomorphisms Ext($\mathcal{C};\, A,B$) $\cong$ KK($\mathcal{C_{(1)}};\, A,B_{(1)}$) and Ext($\mathcal{SC};\, A,SB$) $\cong$ KK($\mathcal{C};\, A,B$) in trivially graded case. Homotopy invariance of Ext($\mathcal{SC};\, A,SB$). The isomorphism Ext($\mathcal{SC};\, A,SB$) $\cong$ R($\mathcal{C};\, A,B$). 9 Cone-related KK-groups KK($\mathcal{C};\, A,B$) (II) The $KK_{X}(A;B)$ := KK($\mathcal{C_{X}};\, A,B$) classification for X $\cong$ Prim(A) $\cong$ Prim(B), where A, B are stable amenable separable C*-algebras.Structure of the algebras with ideal-system preserving zero-homotopy. 10 Some conclusions of the classi cation results and open questions Constructions of examples of algebras with given second countable locally compact sober $T_0$ spaces (not necessarily Hausdorff). Minimal requirement for a weak version of a universal coefficent theorem for ideal-equivariant classi cation, indications of possible equivariant versions for actions of compact groups (up to 2-cocycle equivalence).

March 19-26 at 2:00 p.m.
Mini-session on "Multi-norms"

March 20 & 21, H.G.Dales
Multi-norms 1, 2

Multi-norms and Banach lattices

March 25, Niels Laustsen
Ideals of operators on Banach spaces

March 26-28 at 3:30 p.m.
von Neumann Lecture Series
*Note: location of talks varies*
• March 26: Sidney Smith Hall, Room 1069 (Address: 100 St. George Street)
• March 27: Galbraith Building, Room 220 (Address: 35 St. George Street)
• March 28: Galbraith Building, Room 220 (Address: 35 St. George Street)
• Uffe Haagerup, University of Copenhagen
Approximation Properties for Groups and von Neumann Algebras

March-April:
Banach and Operator Algebras over Groups

Organizer: Garth Dales

 SCHEDULE OF INTRODUCTORY LECTURES Location: Room 230, Fields Institute March 27, Thursday 10:00 a.m. Nico Spronk Fourier and Fourier-Stieltjes Algebras, and their Operator Space Structure, Lecture 1 2:00 p.m. Eberhard Kaniuth Spectral Synthesis, Ideals and Homomorphisms, lecture 1 March 28, Friday 10:00 a.m. Nico Spronk Fourier and Fourier-Stieltjes Algebras, and their Operator Space Structure, Lecture 2 2:00 p.m. Eberhard Kaniuth Spectral Synthesis, Ideals and Homomorphisms, Lecture 2 March 31, Monday 10:00 a.m. Nico Spronk Fourier and Fourier-Stieltjes Algebras, and their Operator Space Structure, Lecture 3 12:00 p.m. Ivan Todorov Herz-Schur Multipliers and Related Group Properties, Lecture 1 April 1, Tuesday 10:00 a.m. Narutaka Ozawa Approximation Properties for Group C*-Algebras, Lecture 1 11:00 a.m. Ivan Todorov Herz-Schur Multipliers and Related Group Properties, Lecture 2 2:00 p.m. Nico Spronk Fourier and Fourier-Stieltjes Algebras, and their Operator Space Structure, Lecture 4 April 2, Wednesday 10:00 a.m. Narutaka Ozawa Approximation Properties for Group C*-Algebras, Lecture 1 12:00 p.m. Ivan Todorov Herz-Schur Multipliers and Related Group Properties, Lecture 3 2:00 p.m. Eberhard Kaniuth Spectral Synthesis, Ideals and Homomorphisms, Lecture 3 April 3, Thursday 10:00 a.m. Narutaka Ozawa Approximation Properties for Group C*-Algebras, Lecture 3 11:00 a.m. Ivan Todorov Herz-Schur Multipliers and Related Group Properties, Lecture 4 2:00 p.m. Eberhard Kaniuth Spectral Synthesis, Ideals and Homomorphisms, Lecture 4 3:30 p.m. Ali Ulger Weak-* closed ideals of A(G) and spectral synthesis April 4, Friday 10:00 a.m. Narutaka Ozawa Approximation Properties for Group C*-Algebras, Lecture 4

 SCHEDULE FOR SPECIALIZED LECTURES April 7, Monday 11:30 a.m. Lyudmila Turowska Synthesis in harmonic analysis and operator theory, Lecture 1 2:00 p.m. Charles Read Operator algebras and contractive approximate identities, Lecture 1 3:30 p.m. Lyudmila Turowska Synthesis in harmonic analysis and operator theory, Lecture 2 April 8, Tuesday Location: Morning talks, Bahen Centre, BA 1230 Afternoon Talks, Bahen Centre, BA 1210 11:30 a.m. Nico Spronk On subalgebras of Fourier-Stieltjes algebras 2:00 p.m. Charles Read Operator algebras and contractive approximate identities, Lecture 2 3:30 p.m. Monica Illie Completely bounded homomorphisms of the Fourier algebras April 9, Wednesday Location: Bahen Building 1130 2:00 p.m. Charles Read Operator algebras and contractive approximate identities, Lecture 3 3:30 p.m. Cho-Ho Chu Automatic continuity in non-associative Banach algebras April 10, Thursday 10:00 a.m. To-Ming Lau Complemented subspaces of the group von Neumann algebras 11:30 a.m. Ed Granirer Some geometric properties of Banach algebras related to the Fourier algebra 2:00 p.m. David Blecher Aspects of positivity in operator algebras 3:30 p.m. Matthew Mazowita Topological centres and weighted convolution algebras April 11, Friday 10:00 a.m. Zhong-Jin Ruan Some local properties of group and quantum group C*-algebras 11:30 a.m. Zhiguo Hu Convolution algebras associated with locally compact groups 2:00 p.m. Yong Zhang Weak amenability of weighted group algebras April 14, Monday 10:00 a.m. Matthias Neufang Lecture 1 11:30 a.m. Garth Dales Approximate identities in Banach function algebras and BSE norms 2:00 p.m. Yemon Choi Weak amenability of Fourier algebras: old and new results 3:30 p.m. Mahya Ghandehari Weak amenability of the Fourier algebra of the Heisenberg group April 15, Tuesday 10:00 a.m. Volker Runde Connes-amenability of Fourier-Stieltjes algebras 11:30 a.m. Hung Le Pham Contractive homomorphisms from the Fourier algebras 2:00 p.m. Matthias Neufang Lecture 2 April 16, Wednesday 10:00 a.m. Keith Taylor Generalized Wavelet Transforms

May:
Operator Spaces, Locally Compact Quantum Groups and Amenability

Organizer: Volker Runde

Mini-courses (one lecture in the morning and one in the afternoon on each day).

May 13 & 14
David Blecher
, University of Houston
Operator spaces

May 20 & 22
Matt Daws, University of Leeds
Locally Compact Quantum Groups

May 12 & 13
Volker Runde
Amenability of Banach algebras

May 15 & 16
Michael White, University of Newcastle
Cohomology of Banach and topological algebras

May 20 & 21
Zinaida Lykova, University of Newcastle-upon-Tyne
Higher-dimensional amenability

May 22 & 23
Quantization of topological homology

May 26-30, 2014
Workshop

June:
C*-Algebras and Dynamical Systems (continued)

Organizer: George Elliott

June 2-13, 2014
Mini-courses
(one lecture in the morning and one in the afternoon each day)

Preliminary Schedule

June 2, 4, 6
David Kerr, Texas A&M University
Dynamical systems and C*-algebras

June 3, 5, 6
Thierry Giordano, University of Ottawa
Dynamical systems and C*-algebras

June 2, 3, 4, 5, 9, 10, 11, 12
Andrew Toms, Purdue University
Finite Toms-Winter C*-algebras

June 9, 10, 11, 12, 13
N. C. Phillips, University of Oregon
The proof of the classification theorem for UCT Kirchberg algebras

June 13
Eberhard Kirchberg, Humboldt-Universität zu Berlin
The proof of the classification theorem for UCT Kirchberg algebras

June 16-20, 2014
Workshop

Affiliated Activity
June 23-27, 2014
42nd Canadian Annual Symposium on Operator Algebras and Their
Applications (COSy),

Postdoctoral Fellows and Program Visitors

The Thematic Program on Abstract Harmonic Analysis, Banach and Operator Algebras is pleased to welcome the following Postdoctoral Fellows to the Program:
 Fields Postdoctoral Fellows Mahmood Alaghmandan (PhD, University of Saskatchewan, 2013) Mahya Ghandehari (PhD, University of Waterloo, 2010) Matthew Mazowita (PhD, University of Alberta, 2013) Luis Santiago Moreno (PhD, University of Toronto, 2008) Karen Strung (PhD, Fachbereich Mathematik und Informatik der Universität Münster)-Starting Feb. 1, 2014 Hannes Thiel, (PhD, University of Copenhagen, 2012) Fields-Ontario Postdoctoral Fellow Sutanu Roy (PhD, University of Goettingen, 2013)

Visitor and Young Researchers' Seminars

TBA

Taking the Institute's Courses for Credit
As graduate students at any of the Institute's University Partners, you may discuss the possibility of obtaining a credit for one or more courses in this lecture series with your home university graduate officer and the course instructor. Students wishing credit may need to arrange for additional individual instruction to make up for the extra hours. Assigned reading and related projects may be arranged for the benefit of students requiring these courses for credit.