CLASSIFICATION OF C*-ALGEBRAS,
FLOW EQUIVALENCE OF SHIFT SPACES, AND
GRAPH AND LEAVITT PATH ALGEBRAS


MAY 11-15, 2015
University of Louisiana at Lafayette

Principal speaker: SØREN EILERS

Plenary speakers:
PERE ARA, MIKE BOYLE, TOKE MEIER CARLSEN,
LISA ORLOFF CLARK, RALF MEYER, SARAH REZNIKOFF





This conference will center around recent advances in the classification of nonsimple C*-algebras, and their applications to symbolic dynamical systems, graph C*-algebras, and Leavitt path algebras (the algebraic siblings of graph C*-algebras). This is a rich subject, displaying a beautiful interplay between operator algebras, K-theory, ring theory, symbolic dynamics, and graph theory.

The principal speaker (Søren Eilers) will give five lectures on the following topics (tentative):

  1. Graph and Leavitt path algebras:
    2. Graphs (3044 examples), Graph C*-algebras, LPAs, Isomorphism and Morita equivalence, The classification problems, Abrams-Tomforde conjectures, (Gauge invariant) ideals, The primitive ideal space.

  2. Shifts and flow equivalence:
    3. General shift spaces, SFTs as shift spaces arising from graphs (3044 examples), Conjugacy and flow equivalence, Williams' theorem, splitting and amalgamation, Franks' theorem, the Bowen-Franks invariant, Boyle-Huang classification.

  3. Classification of gauge simple graph C*-algebras:
    4. Gauge simple trichotomy, The tempered primitive ideal space, Flow equivalence implies Morita equivalence (for finite essential graphs), K-theory, Rørdam's theorem and the Cuntz splice, Elliott and Kirchberg/Phillips classification, Matsumoto/Matui.

  4. Classification of general graph C*-algebras:
    5. Asymmetry: sinks vs. sources, Move equivalence for unital graph C*-algebras, Geometric classification results, Finite graphs (3044 examples), Condition K, External classification, The Bentmann/Meyer invariant.

  5. Applications, speculations and further questions:
    6. Classification of Leavitt path algebras, Invariance of Cuntz splice, Other open classification questions, Closure and lifting properties, Applications to quantum lens spaces.

These lectures will be accessible to graduate students and mathematicians with only a basic background on C*-algebra theory. Open problems and new research opportunities for beginning researchers will also be discussed.

The lectures by the plenary speakers will revolve around the topics of the conference. Participants are encouraged to give contributed talks. (Please go to Registration.)

This conference is generously supported by the NSF. We are committed to the strengthening and enrichment of the mathematics personnel base, and to the development of the local region. Students, junior mathematicians, mathematicians from underrepresented groups, and researchers from the local region, are encouraged to apply for support. (Please go to Registration.)

Please send any questions to mathconference@louisiana.edu or to any of the organizers.

Organizers: Gary Birkenmeier (UL - Lafayette), Daniel Davis (UL - Lafayette), P. W. Ng (UL - Lafayette), Leonel Robert (UL - Lafayette), Mark Tomforde (Houston)