Dr. Matthias Neufang

Deputy Director, Fields Institute for Research in Mathematical Science
Associate Professor, School of Mathematics and Statistics, Carleton University

Where I am mentally

My research interests lie within functional analysis and harmonic analysis, whose interaction naturally takes place in the framework of Banach and operator algebras. One of my central objectives is to investigate the link between two important branches of modern analysis, one classical, the other pretty young, but mature enough for important applications: abstract harmonic analysis and Banach algebra theory on the one hand, and the theory of operator spaces and completely bounded maps, on the other hand. The bridge which makes this fruitful interplay possible is provided by representation theory - and this is indeed the place where I spend quite some time walking... A particular highlight where such a walk can lead, is the recent theory of locally compact quantum groups, a beautiful blend of operator algebras and abstract harmonic analysis.

For those interested in a monograph on operator spaces and completely bounded maps written by my former supervisor Prof. Gerd Wittstock and his research group (Benedikt Betz, Hans-Jörg Fischer, Anselm Lambert, Kim Louis, Matthias Neufang, and Ina Zimmermann):

Operator Space Dictionary

dito in German

Some stages from my education

- Licence de Lettres Modernes (Bachelor in French Literature and Linguistics), Université de Lille III (France), 1997
- Maîtrise de Mathématiques (Master's Degree in Mathematics), Université de Lille I (France), 1997
- Dr. rer.nat. (Ph.D. in Mathematics), Universität des Saarlandes, Saarbrücken (Germany), 2000
- Postdoc of the Pacific Institute for the Mathematical Sciences (PIMS), University of Alberta, Edmonton (Canada), 2001-2002

Some of my mathematical work

- Amplification of completely bounded operators and Tomiyama's slice maps
- Operator space structure and amenability for Figà-Talamanca-Herz algebras (with A. Lambert and V. Runde)
- Solution to a conjecture by Hofmeier-Wittstock
- On a conjecture by Ghahramani-Lau and related problems concerning topological centres
- On the topological centre of the algebra LUC(G)* for general topological groups (with S. Ferri)
- The Choquet-Deny equation in a Banach space (with W. Jaworski)
- Harmonic operators: the dual perspective (with V. Runde)
- Completely isometric representations of M_cbA(G) and UCB(G^)* (with Z.-J. Ruan and N. Spronk)
- Column and row operator spaces over QSL_p-spaces and their use in abstract harmonic analysis (with V. Runde)
- A representation theorem for locally compact quantum groups (with M. Junge and Z.-J. Ruan)
- On topological centre problems and SIN quantum groups (with Z. Hu and Z.-J. Ruan)
- On Mazur's property and property (X)
- A unified approach to the topological centre problem for certain Banach algebras arising in abstract harmonic analysis

My teaching at the University of Alberta

Fall 2001:

Calculus I (MATH 100)

My teaching at Carleton University

Fall 2002:

Multivariable Calculus for Engineering Students (MATH 2004), Section C

Winter 2003:

Advanced Calculus (MATH 3002)

Mathematical Methods I (MATH 3705), Section C

Fall 2003:

Functions of a Complex Variable (MATH 3007)

Introduction to General Topology (MATH 4205/5205)

Winter 2004:

Advanced Calculus (MATH 3002, formerly 70.302*)

Mathematical Methods I (MATH 3705, formerly 69.375*), Section A

Fall 2004:

Functions of a Complex Variable (MATH 3007)

Winter 2005:

Seminar: Fourier Analysis (MATH 4907F/5900X)

Fall 2005 and Winter 2006:

Calculus (MATH 1002)

Fall 2006 and Winter 2007:

Calculus (MATH 1002)

Fall 2007:

Banach Algebras (MATH 5003)

Winter 2008:

Fourier Analysis (MATH 4907/5900)

My (not only mathematical) friends and former PIMS sponsors

Prof. Anthony To-Ming Lau
Prof. Volker Runde