» 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

Separation Axioms

Mug and Torus Morph

Distributive Lattice

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. 
    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.
  • CECAT Workshops and Conferences

    CECAT: Center of Excellence in Computation, Algebra, and Topology

     


     

    11th Annual CECAT Workshop in Pointfree Mathematics

    February 5 - 9, 2019

    Held at Chapman University, Keck Center for Science and Engineering (Orange, California)

    Organizers: M. Andrew Moshier and Joanne Walters-Wayland

    Tuesday, February 5th

    1:00 - 2:00pm: M. Andrew Moshier, Chapman University, Weakening relations

    Thursday, February 7th

    10:30 - 11:30am: Peter Jipsen, Chapman University, Involutive residuated lattices and relation algebras

    11:30 - 12:30pm: Sara Vannucci, University of Salerno, Semiring and Semimodule Issues in Residuated Lattices

    1:00 - 2:15pm: Rick Ball, University of Denver, Pointfree Integration

    2:15 - 3:15pm: Anna Laura Suarez, University of Birmingham, D-frames and frame coproducts

    3:30 - 4:30pm: Alexander Kurz, Chapman University, On the duality theory of weakening relations

    Friday, February 8th

    10:30 - 11:30am: Ales Pultr, Charles University, Strong Hausdorff properties of frames

    11:30 - 12:30pm: Diego Valota, University of Milan, Computing Spectra via Dualities in the MTL hierarchy

    2:00 - 3:00pm: Olim Tuyt, University of Bern, Algebraic finite model property of a modal Gödel logic

    3:00 - 4:15pm: Rick Ball, University of Denver, Pointfree Integration, continued

    Saturday, February 9th

    1:00 - 5:00pm: Discussion session

     


     

    4th SYSMICS Workshop on Duality in Algebra and Logic

    September 14 - 17, 2018

    Held at Chapman University, Keck Center for Science and Engineering (Orange, California)

    4th SYSMICS website

    Organizers: Peter Jipsen, Alexander Kurz and M. Andrew Moshier

     


     

    Colloquium talk

    Monday, February 5th, 2018

    4:00 - 5:00pm: Ales Pultr, Charles University, Prague, Point-free topology and some of its merits

     


     

    9th Annual CECAT Workshop in Pointfree Mathematics

    February 6 - 11, 2017

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

    Organizers: M. Andrew Moshier and Joanne Walters-Wayland

     


     

    Special Session on Algebraic Logic

    at the American Mathematical Society Fall Western Sectional Meeting

    Special session website

    October 8 - 9, 2016

    Held at the University of Denver, Colorado

    Session Organizers: Nick Galatos (University of Denver) and Peter Jipsen (Chapman University)

     


     

    8th Annual CECAT Workshop in Pointfree Mathematics

    February 6, 2016

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

    Organizers: M. Andrew Moshier and Joanne Walters-Wayland

    Saturday, February 6

    10:00 - 10:50am: M. Andrew Moshier, Chapman University, Contexts that determine locales

    11:00 - 11:50am: Ales Pultr, Charles University, Prague, An aspect of scatteredness in frames

    12:00 - 12:50pm: Papiya Bhattacharjee, Pennsylvania State University, Erie, Complemented frames

    2:00 - 2:50pm: Peter Jipsen, Chapman University, Duality for (residuated) lattices and correspondence theory

    3:00 - 3:50pm: Joanne Walters-Wayland, CECAT, Smallest dense C and C*-quotients

     


     

    7th Annual CECAT Workshop in Pointfree Mathematics

    February 6 - 12, 2015

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

    PDF version of Program

    Conference Organizers: M. Andrew Moshier and Joanne Walters-Wayland

    Friday, February 6th

    12:30 - 2:00pm: M. Andrew Moshier, Chapman University, A Coherence Theorem for Cartesian Bicategories, and applications

    2:30 - 4:00pm: Open Session

    Saturday, February 7th

    12:30 - 2:00pm: Ales Pultr, Charles University, Tightness relative to some (co)reflections

    2:30 - 4:00pm: Peter Jipsen, Chapman University, Algebraic models for Concurrent Programs and Bunched Implication Algebra

    Monday, February 9th 11:30am: Coffee at Luccas

    1:00 - 4:00pm: Open Session

    Tuesday, February 10th

    10:30 - 12:00pm: Joanne Walters-Wayland, CECAT, I:Domain frames and II: Pointfree Disconnectivity

    Dinner at Joanne’s house

    Wednesday, February 11th 11:30am: Coffee at Luccas

    1:00 - 4:00pm: Open Session

    Thursday, February 12th 11:30am: Coffee at Luccas

    1:00 - 4:00pm: Open Session

     


     

    6th Annual CECAT Workshop in Pointfree Mathematics

    January 23 - 28, 2014

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

    PDF version of Program

    Organizers: M. Andrew Moshier and Joanne Walters-Wayland

    Thursday, January 23rd

    10:00 - 11:30am Bernhard Banaschewski, McMaster University, Further thoughts on Pointfree Function Rings

    12:30 - 1:30pm: Fred Dashiell, CECAT, A Geometric description of the second dual of C(K)

    6:00pm: Dinner - Mexican/OC Mining Co

    Friday, January 24th: 10:00am Coffee at Luccas

    11:30 - 12:30pm: Bernhard Banaschewski, McMaster University, Further thoughts on Pointfree Function Rings cont.

    1:00 - 2:00pm: Peter Jipsen, Chapman University, Planar (semi) modular lattices

    Saturday, January 25th

    11:30 - 1:00pm: Mark Sioen, Vrije Universiteit Brussel, Some remarks (and more questions) about the topology of uniform convergence on preferred sublocales

    1:00 - 2:00pm: Open session

    Monday, January 27th

    12:00 - 1:30pm: Bernhard Banaschewski, McMaster University, Archimeadean Kernels and Function Rings

    2:00 - 3:30pm: M. Andrew Moshier, Chapman University, Gelfand Naimark Duality for Ordered Spaces

    Tuesday, January 28th

    10:00 - 11:30pm: Bernhard Banaschewski, McMaster University, Realcompact Alexandroff Frames

    12:30 - 1:30pm: Open session

     


     

    BLAST 2013

    August 5 - 9, 2013

    Held at Chapman University, Irvine Lecture Hall, Science Center, Orange, CA 92866

    Conference website

    Conference schedule | Speakers and titles | Booklet of abstracts (PDF) | Participants

    Conference Organizers: Fred Dashiell, Peter Jipsen, M. Andrew Moshier, Joanne Walters-Wayland

     


     

    5th Annual CECAT Workshop in Pointfree Mathematics

    January 16 - January 23, 2013

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

    PDF version of Program

    Organizers: M. Andrew Moshier and Joanne Walters-Wayland

    Wednesday, January 16th: 12:00 - 2:00pm: Open session

    Thursday, January 17th

    12:30 - 2:00pm: Bernhard Banaschewski, McMaster University, Regular rings and the Prime Ideal Theorem

    Friday, January 18th: 10:30am Coffee at Luccas

    12:00 - 1:30pm: Bernhard Banaschewski, McMaster University, On the minimal spectrum of a compact normal frame

    Monday, January 21st

    12:00 - 1:30pm: Bernhard Banaschewski, McMaster University, An example of a pointless countably compact completely regular frame

    2:00 - 3:30pm: Peter Jipsen, Chapman University, Implementing decision procedures for (generalized) Basic Logic

    Tuesday, January 22nd

    11:00 - 12:30pm: Ales Pultr, Charles University, Techniques on taking quotients in frames, lattices, quantales etc

    1:00 - 2:00pm: Joanne Walters-Wayland, CECAT, Some comments on Coz and quotients

    Wednesday, January 23rd

    12:00 - 1:30pm: Ales Pultr, Charles University, Techniques on taking quotients in frames, lattices, quantales etc

    6:30pm: Dinner at Joanne's

    Thursday, January 24th

    11:00 - 12:30pm: Bernhard Banaschewski, McMaster University, Aspects of Strong 0-dimensionality

    1:00 - 2:30pm: M. Andrew Moshier, Chapman University, An overview of Co-algebras on Compact Regular Spaces

    Friday, January 25th

    12:00 - 1:30pm: Bernhard Banaschewski, McMaster University, Aspects of Strong 0-dimensionality

    Saturday, January 26th: 7:00pm Cello Concert in Von Neumann hall

     


     

    4th Annual CECAT 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)

    Organizers: M. Andrew Moshier and Joanne Walters-Wayland

    PDF version of Program

    Monday, January 9th

    12:00 - 2:00pm: Bernhard Banaschewski, McMaster University, Pseudocompactness in Frames

    2:30 - 3:30pm: M. Andrew Moshier, Chapman University, D-frames

    Tuesday, January 10th

    10:00 - 12:00pm: M. Andrew Moshier, Chapman University, D-frames

    12:30 - 2:30pm: Bernhard Banaschewski, McMaster University, Pseudocompactness in Frames

    Thursday, January 12th

    11:00 - 1:00pm: M. Andrew Moshier, Chapman University, D-frames

    1:30 - 3:30pm: Bernhard Banaschewski, McMaster University,

    Friday, January 13th

    10:30 - 12:00: Bernhard Banaschewski, McMaster University, The rings of continuous functions on sigma frames

    12:30 - 2:00pm: M. Andrew Moshier, Chapman University, A relational category of formal contexts

    Saturday, January 14th

    10:30 - 12:00: Bernhard Banaschewski, McMaster University, The rings of continuous functions on sigma frames

    12:30 - 2:00pm: Rick Ball, University of Denver, joint work with Tony Hager, Wesleyan University, Truncated and diminished l-groups

    2:30 - 4:00pm: Garth Dales, University of Lancaster, The hyper-Stonean cover of a compact space

    Sunday, January 15th

    10:30 - 12:00pm: Bernhard Banaschewski, McMaster University, The rings of continuous functions on sigma frames

    12:30 - 2:00pm: Rick Ball, University of Denver, joint work with Tony Hager, Wesleyan University, Truncated and diminished l-groups

    4:00pm: Cello Concert followed by informal reception

    Monday, January 16th: 10am Coffee at Cafe Lucas

    11:00 - 1:00pm: Rick Ball, University of Denver, joint work with Tony Hager, Wesleyan University, Truncated and diminished l-groups

    1:30 - 3:00pm: Peter Jipsen, Chapman University, On the duality between lattices and topological contexts

    Tuesday, January 17th

    10:00 - 12:00pm: Bernhard Banaschewski, McMaster University

    12:30 - 2:00pm: Peter Jipsen, Chapman University, On the duality between lattices and topological contexts

    Thursday, January 19th

    11:00 - 2:30pm: Open session on D-frames

     


     

    3rd Annual CECAT Workshop in Pointfree Topology

    January 10 - 19, 2011

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

    Organizers: M. Andrew Moshier and Joanne Walters-Wayland

    Monday, January 10th

    12:00 - 2:00pm: Bernhard Banaschewski, McMaster University, Essential completions - update

    3:00 - 5:00pm: Olaf Klinke, University of Birmingham, Pointfree bitopological compactification

    Tuesday, January 11th

    10:00 - 12:00pm: Bernhard Banaschewski, McMaster University, Essential completions - update

    2:00 - 4:00pm: Open session

    Wednesday, January 12th

    12:00 - 2:00pm: Bernhard Banaschewski, McMaster University, Essential completions - update

    3:00 - 5:00pm: M. Andrew Moshier, Chapman University, Another Duality for Commutative C* Algebras

    Friday, January 14th

    11:00 - 1:00pm: Bernhard Banaschewski, McMaster University, Extended real-valued functions

    2:00 - 4:00pm: Open session

    Saturday, January 15th: 10am Coffee at Café Lucas

    11:00 - 1:00pm: Bernhard Banaschewski, McMaster University, Extended real-valued functions

    2:00 - 4:00pm: M. Andrew Moshier, Chapman University, Integration in Logical Form

    Sunday, January 16th

    10:00 - 12:00pm: Rick Ball, University of Denver, Integration ideas in a pointfree context

    1:00 - 3:00pm: Open session

    Monday, January 17th

    12:00 - 2:00pm: Bernhard Banaschewski, McMaster University, Extended real-valued functions

    3:00 - 5:00pm: Open session

    Tuesday, January 18th

    10:00 - 12:00pm: Bernhard Banaschewski, McMaster University

    2:00 - 4:00pm: Open session

    Wednesday, January 19th

    12:00 - 2:00pm: Bernhard Banaschewski, McMaster University

    3:00 - 5:00pm: Open session

     


     

    2nd CECAT Workshop on Contemporary Topology

    January 4 - 15, 2010

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

    Organizer: M. Andrew Moshier

    Bernhard Banaschewski, McMaster University, Essential completions in categories of Archimedean l-groups with order unit

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

    Rick Ball, University of Denver and Joanne Walters-Wayland, OCCTAL, The K-Briar Patch

    Peter Jipsen, Chapman University, Some open problems regarding lattice-ordered pregroups

    M. Andrew Moshier, Chapman University, Locales and Quantales Concretely

     


     

    1st CECAT Workshop on Contemporary Topology

    Workshop on Pointfree Topology in honor of Bernhard Banaschewski's visit to Chapman University.

    February 17 - 20, 2009

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

    Organizer: M. Andrew Moshier

    Tuesday, February 17

    11:00 - 1:00pm: Bernhard Banaschewski, McMaster University, Essential Completion in Point-free Topology, Part I

    4:00 - 5:00pm: M. Andrew Moshier, Chapman University, Skew frames and Point-free Bitopology

    Wednesday, February 18

    11:00 - 1:00pm: Bernhard Banaschewski, McMaster University, Essential Completion in Point-free Topology, Part II

    Thursday, February 19

    10:00 - 11:15am: Fred Dashiell, CECAT, Kuratowski Reduction in σ-frames

    4:00 - 5:00pm: Bernhard Banaschewski, McMaster University, Point-free Topology and the Representation of Lattice-ordered Rings

    Friday, February 20

    11:00 - 1:00pm: Bernhard Banaschewski, McMaster University, Essential Completion in Point-free Topology, Part III