picture of me Dr. Claus Köstler
Visiting Assistant Professor

Department of Mathematics
University of Illinois at Urbana-Champaign
1409 West Green Street, Urbana, Illinois, 61801, USA

E-mail:  
Phone: +1 (217) 333-7782
Fax: +1 (217) 333-9576
Office: B13 Coble Hall



Research

Research interests: Operator Algebras, Noncommutative Probability, Quantum Dynamics

My research lies in the areas of non-commutative probability theory 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.
    • A more detailed research statement is here.

    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). Preprint 2008. .pdf file
  • Noncommutative independence from the braid group $B_\infty$. (With R. Gohm.) Preprint 2008. .pdf file
  • On Lehner's `free' noncommutative analogue of de Finetti's theorem. Preprint 2008. .pdf file
  • 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

    • Teaching

    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: 14-Jan-2008
    Department of Mathematics
    College of Liberal Arts and Sciences
    University of Illinois at Urbana-Champaign
    273 Altgeld Hall, MC-382
    1409 W. Green Street, Urbana, IL 61801 USA
    Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576