Stuart White

Hello and welcome to my mathematical website. I'm a lecturer in the maths department of the University of Glasgow.

If you're interested, the photo on the right is of the jump between the horns of the Svolvaer Goat located well inside the arctic circle on the Lofoten islands in Norway. Some more photos can be found here.

My research examines operator algebras and their structural properties. Operator algebras is a branch of functional analysis with many applications in other areas of mathematics including quantum theory, mathematical physics, geometry and topology, ergodic theory, group representations and harmonic analysis, recently even number theory. Operator algebras provide non-commutative or quantum analogues of mathematical objects. Every abelian C*-algebra is of the form C₀(X) for a locally compact Hausdorff space X, leading to the view point that the study of C*-algebras corresponds to the study of non-commutative locally compact spaces. In a similar way, von Neumann algebras correspond to measure spaces and so provide an environment for non-commutative measure theory and non-commutative probability.

My recent research has focused on:

• Perturbation questions. Suppose we have two C*-algebras A and B acting on the same Hilbert space. Kadison and Kastler measured the distance between A and B by using the Hausdorff metric on their unit balls and asked whether sufficiently close operator algebras must be isomorphic. Various authors (including Christensen, Phillips, Raeburn) worked on this problem and positive results where established when one algebra is an injective von Neumann algebra, or when one algebra is a C*-algebra lying in various classes (AF, or continuous trace etc). I have recently revisited this problem with Christensen, Sinclair and Smith and we are able to give a positive answer when one algebra is separable nuclear. I intend to investigate perturbation questions outside the amenable setting in the near future.
• Structral properties of subalgebras of finite von Neumann algebras. Over the last few years I've examined questions regarding inclusions of a von Neumann subalgebra $B$ inside a larger von Neumann algebra M. In most cases I'm interested in M will be a finite von Neumann algebra and often a II₁ factor. Recent work has examined the location of the normalising elements of B in M, namely those unitaries u which have uBu*=B and how these objects behave under taking tensor products. To obtain satisfactory results it is often necessary to consider the more general class of groupoid normalisers, which are partial isometries v in M such that vBv* and v*Bv are both subalgebras of B. I've also examined questions regarding maximal injective subalgebras and how these behave under tensor products.

Click here for my published papers via mathscinet and here to view all my publications that are on the arXiv. Click through links take you to the official published version of the paper if available and the arXiv otherwise.

• Tauer masas in the hyperfinite II_1 factor, Q. J. Math. 57 (3) 2006, 377--393.
• A continuous path of singular masas in the hyperfinite II_1 factor, with Allan Sinclair, J. Lond. Math. Soc. (2) 75 (1) 2007, 243--254.
• Covering polygonal annuli by strips, with Laura Wisewell, Discrete Comput. Geom. 37 (4) 2007, 577--585.
• Semi-regular masas of transfinite length, with Alan Wiggins. Internat. J. Math. 18 (9) 2007, 995--1007.
• Strong Singularity of Singular masas in II_1 factors, with Allan Sinclair, Roger Smith and Alan Wiggins. Illinois J. Math. 57 (4) 2007: 1077--1084.
• Values of the Pukanszky Invariant in McDuff Factors. J. Funct. Anal., 254 2008, 612--631.
• Generators of II_1 Factors, with Ken Dykema, Allan Sinclair and Roger Smith. Oper. Matrices, 2 2008, 555-582.

Click here to view all my publications that are on the arXiv. Alternatively the paper titles give click through links to the most recent versions.

• Normalisers of Irreducible Subfactors, with Roger Smith and Alan Wiggins. J. Anal. Math. Appl., to appear.
• Conditions implying the uniqueness of the weak*-topology on certain group algebras, with Matt Daws and Hung Le Pham. Houston J. Math., to appear.
• Groupoid normalizers and tensor products, with Junsheng Fang, Roger Smith and Alan Wiggins.
• The radial masa in a free group factor is maximal injective, with Jan Cameron, Junsheng Fang, and Mohan Ravichandran.
• Preduals of semigroup algebras, with Matt Daws and Hung Le Pham.
• Perturbations of C*-algebraic invariants, with Erik Christensen, Allan Sinclair and Roger Smith.

Slides from some of the talks I've given will appear here. Since I mainly use the blackboard, there won't be very many!

• Perturbations of nuclear C* algebrasTalk given at CIRM in June 2009.
• Perturbations of nuclear C* algebrasTalk given in Lancaster in May 2009.
• Perturbations of nuclear C* algebrasTalk given in Trinity College Dublin, March 2009.
• Perturbations of nuclear C* algebras Talk given at the Texas A&M Linear analysis seminar (the middle section used the board and is missing) in February 2009.
• Perturbations of nuclear C* algebras Talk given in the Vanderbilt subfactor seminar in January 2009.
• Perturbations of C* algebraic invariants Talk given in the concentration week on classification, dynamics and operator algebras at Texas A&M in July 2008.
  Update: Since this talk was given, we now have a positive answer to the 'annoyance' on the last slide. Namely any algebra sufficiently close (via a universal constant) to an AT algebra is again AT.

This year I taught Introductory Analysis (Level 3 Honours) and 3P Real and Complex Variables (Level 3 Non-Honours). Information and course materials can be found on moodle.

Revision lectures for introductory analysis will take place in March or April. Further information will be announced in due course.

Office Hours: I'm always happy to see students taking my courses. Please drop by my office (308) or email me to arrange a convenient appointment. I will not be running formal office hours from Jan-June 2009.

As your advisor of studies you have the right to see me to discuss anything which affects your studies. Please do not ever feel shy or embarrassed about approaching me if there is anything that is affecting your studies that you wish to discuss.

My office is 308 in the maths building and I can be contacted at s.white@maths.gla.ac.uk to arrange an appointment. Alternatively simply drop by the office. If I am in and available I will be able to see you.In addition I wish to see all students in levels one and two three times a year: in October-November, in February and in May-June. These appointments are arranged through moodle at this page.