picture of me Dr. Claus Köstler
Visiting Assistant Professor

Department of Mathematics, Computer Science and Statistics
St. Lawrence University
23 Romoda Drive, Canton, New York, 13617, USA

E-mail:  
Phone: +1 (315) 229-5976
Fax: +1 (315) 229-7413
Office: 210-1 Valentine Hall



Research

Research interests: Operator Algebras, Noncommutative Probability, Quantum Dynamics

My research lies in the areas of noncommutative probability and quantum dynamics. It combines techniques from functional analysis, probability theory, as well as dynamical systems and ergodic theory. It is guided from a probabilistic point of view onto operator algebras and, vice versa, an operator algebraic approach to probability theory.

Central for my research are suitable operator algebraic concepts of:
  • noncommutative independence and distributional symmetries;
  • Brownian motion and Levy processes;
  • Bernoulli shifts in discrete and continuous time;
  • white noise as a dynamical system in continuous time.
    • My work contributes to the foundation and development of these theories, as well as to the construction of new examples for them. This establishes contacts with fascinating areas of research, among which are:
  • Arveson's classification program of E_0-semigroups and continuous tensor products of Hilbert spaces;
  • Jones' subfactor theory;
  • Pisier- Xu's work on non-commutative martingales and their inequalities;
  • Tsirelson-Vershik's approach to continuous products of probability spaces and stochastic flows;
  • Voiculescu's free probability theory.

    • Recent Preprints

    Preprints may be downloaded by clicking the icon.
  • A noncommutative de Finetti theorem: Invariance under quantum permutations is equivalent to freeness with amalgamation. (With R. Speicher). To appear in Commun. Math. Phys. .pdf file (Preprint Version 2008)
  • Noncommutative independence from the braid group $B_\infty$. (With R. Gohm.) To appear in Commun. Math. Phys. .pdf file (Preprint Version February 2009)
  • On Lehner's `free' noncommutative analogue of de Finetti's theorem. To appear in Proc. Amer. Math. Soc. .pdf file (Preprint Version 2008)
  • A noncommutative extended de Finetti theorem. Preprint 2008. .pdf file
  • On the structure of noncommutative white noises. (With R. Speicher) Trans. Amer. Math. Soc. 359 (2007), no. 9, 4325--4338. .pdf file (Preprint Version 2007)
  • Noncommutative continuous Bernoulli shifts. (With J. Hellmich, and B. Kümmerer.) Preprint 2006. .pdf file

    • 2008 - 2009 Teaching at St. Lawrence University (Canton, New York, U.S.A.)

    Spring 2009
    		MATH 205 A: Multivariable Calculus
    MATH 217 A: Linear Algebra
    MATH 348 A: Fourier Series
    Fall 2008
    		MATH 135 A & B: Calculus I
    MATH 217 A: Linear Algebra

    2007 - 2008 Teaching at UIUC (Urbana, Illinois, U.S.A.)

    Spring 2008
    		MATH 124: Finite Mathematics
    MATH 231: Calculus II
    Fall 2007
    		MATH 255: Introductory Matrix Theory
    MATH 386: Introduction to Differential Equations Plus

    2005 - 2007 Teaching at Carleton University (Ottawa, Ontario, Canada)

    Winter Term 2007
    		MATH 2404 A: Ordinary Differential Equations I
    MATH 3101 B: Algebraic Structures with Computer Applications
    Fall Term 2006
    		MATH 2004 A: Multivariable Calculus for Engineers
    MATH 2004 C: Multivariable Calculus for Engineers
    Winter Term 2006
    		MATH 2004 D: Multivariable Calculus for Engineers
    MATH 2404 A: Ordinary Differential Equations I
    Fall Term 2005
    		MATH 2004 B: Multivariable Calculus for Engineers
    MATH 2454 A: Ordinary Differential Equations
    Last Modified: 20-Jan-2009