»Center of Excellence in Computation, Algebra, and Topology

The mission of the Center of Excellence in Computation, Algebra and Topology (CECAT) is to provide a forum for world class interdisciplinary research where computation meets algebra, topology and related mathematical fields. The CECAT has a track record of supporting its mission by hosting workshops that attract national and international visitors, attracting national and international visitors for research collaboration, developing affiliations with research groups at fellow institutions, seeking external funding and developing online mathematical resources. In addition, the Center will seek to support post-doctoral fellows and graduate students in affiliation with Chapman's graduate programs in Computational Sciences.

Separation Axioms Mug and Torus Morph Distributive Lattice

Separation Axioms

Distributive Lattice

  • Members
  • Workshops
  • Director

    Drew Moshier Drew Moshier, Professor of Mathematics and Computer Science, has been at Chapman University since 1994.  His research interests include real number computation, bitopolopgical spaces and their applications in logic and information theory, and computational linguistics.

    Full-Time Faculty

    Michael Fahy Michael Fahy, Professor of Mathematics and Computer Science, is interested in computational methods for generalizing the Ore condition to explore the structure of localizations of non-commutative rings.
    Peter Jipsen Peter Jipsen, Associate Professor of Mathematics, is an expert on algebraic logic and ordered algebraic structures. He is particularly interested in residuated lattices, including Linear logic algebras, Basic Logic algebras, MV-algebras, lattice-ordered groups and relation algebras, as well as lattices and semilattices with operators in general.

    External Members

    Rick Ball Rick Ball, Professor of Mathematics, University of Denver
    Bernhard Banaschewski  Bernhard Banaschewski, Emeritus Professor of Mathematics, McMaster University, Canada. List of publications.
    Frederick K. Dashiell, Jr. Frederick K. Dashiell, Jr., Ph. D. in Mathematics, Visiting Scholar at UCLA. Dr. Dashiell investigates areas in pointfree topology, lattice theory, topological questions related to computer science, rings of continuous functions, descriptive set theory, and Banach space theory. The interplay between algebra and topology remains a long time theme in his research.
    Achim Jung Achim Jung, Professor of Theoretical Computer Science, University of Birmingham, UK. His research interests include domain theory, denotational semantics of programming languages, lambda calculus, topology, cryptography, and Computer Science education.
    Ales Pultr Aleš Pultr, Professor of Mathematics, Charles University, Prague, Czech Republic.
    Joanne Walters-Wayland Joanne Walters-Wayland, Ph. D. in Mathematics. Research interests include frames (locales), σ-frames, Lindelöf frames and other aspect of point-free topology.

    In Memory of a Founding Member

    Melvin Henriksen Melvin Henriksen, Professor of Mathematics at Harvey Mudd College 1969-2009. Memorial conference:
    Mel Henriksen Special Issue of Topology and its Applications.
    List of publications.
  • 4th Annual Workshop in Pointfree Topology and Analysis

    January 9 - January 18, 2012

    Held at Chapman University, Von Neumann Hall (545 W. Palm Ave, Orange, CA 92866)

    PDF version of Programme

    Monday 9th: 12pm-2pm Bernhard Banaschewski (McMaster University, Canada)
    "Pseudocompactness in Frames"
    2.30pm-3.30pm Drew Moshier (Chapman University)
    "D-frames"
    Tuesday 10th: 10am-12pm Drew Moshier
    "D-frames"
    12.30pm-2.30pm Bernhard Banaschewski
    "Pseudocompactness in Frames"
    Wednesday 11th: No scheduled talks
    Thursday 12th: 11am-1pm Drew Moshier
    "D-frames"
    1.30pm-3.30pm Bernhard Banaschewski
    Friday 13th: 10.30am-noon Bernhard Banaschewski
    "The rings of continuous functions on sigma frames"
    12.30pm-2pm Drew Moshier
    "A relational category of formal contexts"
    Saturday 14th: 10.30am-noon Bernhard Banaschewski
    "The rings of continuous functions on sigma frames"
    12.30-2pm Rick Ball (University of Denver, joint work with Tony Hager)
    "Truncated and diminished l-groups"
    2.30pm-4pm Garth Dales (University of Lancaster, UK)
    "The hyper-Stonean cover of a compact space"
    Sunday 15th: 10.30am-noon Bernhard Banaschewski
    "The rings of continuous functions on sigma frames"
    12.30-2pm Rick Ball (joint work with Tony Hager)
    "Truncated and diminished l-groups"
    4pm Cello Concert followed by informal reception
    Monday 16th: 10am Coffee at Cafe Lucas
    11am-1pm Rick Ball (joint work with Tony Hager)
    "Truncated and diminished l-groups"
    1.30pm-3pm Peter Jipsen (Chapman University)
    "On the duality between lattices and topological contexts"
    Tuesday 17th: 10am-12pm Bernhard Banaschewski
    "TBD"
    12:30pm-2pm Peter Jipsen
    "On the duality between lattices and topological contexts"
    Wednesday 18th: No scheduled talks
    Thursday 19th: 11am-2.30pm Open session
    "D-frames"

     

     

    3rd Annual Workshop in Pointfree Topology

    January 10 - January 19, 2011

    Held at Chapman University, Von Neumann Hall (545 W. Palm Ave, Orange, CA 92866)

     

    Monday 10th: 12pm-2pm Bernhard Banaschewski
    "Essential completions - update"
    3pm-5pm Olaf Klinke
    "Pointfree bitopological compactification"
     
    Tuesday 11th: 10am-12pm Bernhard Banaschewski
    "Essential completions - update"
    2pm-4pm Open session
     
    Wednesday 12th: 12pm-2pm Bernhard Banaschewski
    "Essential completions - update"
    3pm-5pm Andrew Moshier
    "Another Duality for Commutative C* Algebras"
     
    Thursday 13th: No scheduled talks
     
    Friday 14th: 11am-1pm Bernhard Banaschewski
    "Extended real-valued functions"
    2pm-4pm Open session
    5pm - 7pm Drinks and snacks at Von Neumann Hall
     
    Saturday 15th: 10am Coffee at Café Lucas
    11am-1pm Bernhard Banaschewski
    "Extended real-valued functions"
    2pm-4pm Andrew Moshier
    "Integration in Logical Form"
     
    Sunday 16th: 10am-12pm Rick Ball
    "Integration ideas in a pointfree context"
    1pm-3pm Open session
     
    Monday 17th: 12pm-2pm Bernhard Banaschewski
    "Extended real-valued functions"
    3pm-5pm Open session
     
    Tuesday 18th: 10am-12pm Bernhard Banaschewski
    "To be announced"
    2pm-4pm Open session
     
    Wednesday 19th: 12pm-2pm Bernhard Banaschewski
    "To be announced"
    3pm-5pm Open session

     

     

    2nd Workshop on Contemporary Topology

    Held at Chapman University, Von Neumann Hall (545 W. Palm Ave, Orange, CA 92866)

    January 4 - 15, 2010

    Speaker: Prof. Bernhard Banaschewski, McMaster University
    Title: Essential completions in categories of Archimedean l-groups with order unit

    Speaker: Prof. Bernhard Banaschewski, McMaster University
    Title: On the ccc characterization of the function rings in pointfree topology.

    Speakers: Prof. Rick Ball, University of Denver, and Dr. Joanne Walters-Wayland, OCCTAL
    Title: The K-Briar Patch

    Speaker: Dr. Peter Jipsen, Chapman University
    Title: Some open problems regarding lattice-ordered pregroups

    Speaker: Prof. M. Andrew Moshier, Chapman University
    Title: Locales and Quantales Concretely

     

     

    1st Workshop on Contemporary Topology

    WORKSHOP ON POINT-FREE TOPOLOGY in honor of Bernhard Banaschewski's visit to Chapman University.

    Feb 17 - 20, 2009

    Organized by Prof. Andrew Moshier

    Feb 17

    11:00 - 1:00 B. Banaschewski, Essential Completion in Point-free Topology, Part I.

    4:00 - 5:00 M. A. Moshier, Skew frames and Point-free Bitopology.

    Feb 18

    11:00 - 1:00 B. Banaschewski, Essential Completion in Point-free Topology, Part II.

    Feb 19

    10:00 - 11:15 F. Dashiell, Kuratowski Reduction in $\sigma$-frames.

    4:00 - 5:00 B. Banaschewski, Point-free Topology and the Representation of Lattice-ordered Rings.

    Feb 20

    11:00 - 1:00 B. Banaschewski, Essential Completion in Point-free Topology, Part III.