THEMATIC PROGRAMS

September 20, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th ANNIVERSARY YEAR

Focus Program on Noncommutative Geometry and Quantum Groups

MINICOURSES AND ACTIVITIES

June 17-21,2013
Theme Week on Noncommutative Geometry and Index Theory, Geometry and Mathematical Physics

Location:
Bahen Building, Room 1170 (map)

Organized by Jonathan Rosenberg (Maryland)

Activities during this period will be devoted to connections between noncommutative geometry and index theory, geometry, and mathematical physics.

Preliminary Schedule:
Monday, June 17
9:30 - 10:30
Short course: Paul Baum (Pennsylvania State University)
The Dirac Operator
10:30 - 11:00
Break
11:00 - 12:00
Seminar Session: Masoud Khalkhali (University of Western Ontario)
Scalar curvature and local spectral invariants in noncommutative geometry, I
2:00 - 3:00
Short course: Nigel Higson (Pennsylvania State University)
Crash Course on Group C*-Algebras
3:00 - 3:30
Tea Break
3:30 - 4:30
Seminar Session: Farzad Fathizadeh (University of Western Ontario)
Scalar curvature and local spectral invariants in noncommutative geometry, II
Tuesday, June 18
9:30 - 10:30
Short course: Paul Baum (Pennsylvania State University)
Atiyah-Singer Revisited
10:30 - 11:00
Break
11:00 - 12:00
Seminar Session: Masoud Khalkhali (University of Western Ontario)
Scalar curvature and local spectral invariants in noncommutative geometry, III
2:00 - 3:00
Short course: Nigel Higson (Pennsylvania State University)
Compact Representations
3:00 - 3:30
Tea Break
3:30 - 4:30
Seminar Session: Piotr M. Hajac (Polish Academy of Sciences/Warsaw University)
Tautological line bundle over the triple-pullback quantum complex projective plane
Wednesday, June 19
9:30 - 10:30
Short course: Paul Baum (Pennsylvania State University)
What is K-homology?
10:30 - 11:00
Break
11:00 - 12:00
Seminar Session: Farzad Fathizadeh (University of Western Ontario)
Scalar curvature and local spectral invariants in noncommutative geometry, IV
2:00 - 3:00
Short course: Nigel Higson (Pennsylvania State University)
Parabolic Induction
3:00 - 3:30
Tea Break
3:30 - 4:30

Seminar Session: Andrzej Sitarz (Jagiellonian University, Kraków)
Minimal operators on noncommutative tori

Thursday, June 20
9:30 - 10:30
Short course: Paul Baum (Pennsylvania State University)
Beyond Ellipticity
10:30 - 11:00
Break
11:00 - 12:00
Nicolas Franco (Jagiellonian University, Kraków)
Lorentzian generalization of noncommutative geometry: introducing a notion of causality

2:00 - 3:00
Short course: Nigel Higson (Pennsylvania State University)
Parabolic Induction and Hilbert Modules
3:00 - 3:30
Tea Break
3:30 - 4:30
Seminar Session: Debashish Goswami (Indian Statistical Institute)
Quantum Isometry Groups
4:45 - 5:15
Seminar Session: Farzad Fathizadeh (University of Western Ontario)
Scalar curvature and local spectral invariants in noncommutative geometry, V
Friday, June 21
9:30 - 10:30
Short course: Paul Baum (Pennsylvania State University)
The Riemann-Roch theorem
10:30 - 11:00
Break
11:00 - 12:00
Seminar Session: Ryszard Nest (University of Copenhagen)
Index and determinant of n-tuples of commuting operators

2:00 - 3:00
Short course: Nigel Higson (Pennsylvania State University)
Deformations of Groups and Representations
3:00 - 3:30
Tea Break
3:30 - 4:30
Seminar Session: Jonathan Rosenberg (University of Maryland)
Twistings of KR theory and noncommutative geometry


Nigel Higson, Pennsylvania State University
Noncommutative geometry and representation theory

Lecture 1 Crash Course on Group C*-Algebras
Lecture 2 Compact Representations
Lecture 3 Parabolic Induction
Lecture 4 Parabolic Induction and Hilbert Modules
Lecture 5 Deformations of Groups and Representations

Paul Baum, Pennsylvania State University
Minicourse on Index Theory
Lecture Notes available here

Lecture 1 The Dirac Operator
Lecture 2 Atiyah-Singer Revisited
Lecture 3 What is K-homology?
Lecture 4 Beyond Ellipticity (Index theory for non-elliptic Fredholm differential operators)
Lecture 5 The Riemann-Roch theorem