From: BrendaSueCook (brenda@math.missouri.edu)
Date: Fri Mar 16 2007 - 15:25:58 CDT
Colloquium
Department of Mathematics
Finn F. Knudsen
Department of Mathematical Sciences,
Norwegian University of Science and Technology
currently visting the University of Michigan at Ann Arbor
On the Theory of Aarnes
In this talk I will try to show you some aspects of the theory of
Aarnes. The theory of bounded linear functionals on C*-algebras is very
well explored. Aarnes theory genuinely extends this theory in the case
of commutative C*-algebras, settling a long standing conjecture in the
field. Here is a list of topics I will try to say something about. In my
opinion the nicest thing about this theory is its proofs, so even though
proofs are not recommended in a colloquium talk, I intend to present a
couple.
- Some historical remarks.
- Topological measures and Aarnes’ representation theorem for
quasi-linear functionals.
- One to oneness of the restriction of topological measures to solid sets.
- Ontoness of the restriction of topological measures to certain
functions on solid sets on simple spaces (i.e., spaces of Aarnes genus
equal to zero).
- Examples of simple spaces via the Mayer-Vietoris sequence.
- Examples of simple (multiplicative) non-Borel topological measures.
- Topological measures on general spaces (i.e., spaces of Aarnes genus
greater than zero).
- Applications to probability and to symplectic intersection theory.
Thursday, March 22
3:30 p.m.
114 General Classroom Building
Refreshments will be served at 3:00 p.m. in Room 326 Mathematical
Sciences (Math Lounge).
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