» 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

Distributive Lattice

Distributive Lattice

Members

Drew Moshier

Director

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.

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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.

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Peter Jipsen

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.

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Alexander Kurz

Professor of Computer Science, studies models of computation using techniques from logic, algebra, topology, category theory and other areas of mathematics. He is known for his work on modal logic and coalgebras. More recently he has been pursuing foundations of quantitative logics for the specification and verification of heterogeneous systems as well as relational and compositional techniques supporting scalable solutions for blockchain-based technologies. He is also interested in applications of these mathematical techniques outside of computer science, in particular in economics and the political and social sciences.

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Oghenetega Ighedo

Associate Professor of Mathematics

Jonathan Weinberger

Assistant Professor, Fowler School of Engineering, works in theoretical computer science and mathematical logic. His work employs category theory and (homotopy) type theory. These are foundational theories to capture and unify a range of concepts and constructions in computer science (e.g. programming languages, software erification, computability theory) and mathematics (e.g. algebra, topology, geometry). He is also interested in computer proof assistants and formalized mathematics, as well as the foundations of machine learning.

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Rick Ball

Professor of Mathematics, University of Denver

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Guram Bezhanishvili

Professor of Mathematics, New Mexico State University

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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

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.

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Aleš Pultr

Professor of Mathematics, Charles University, Prague, Czech Republic.

Joanne Walters-Wayland

Ph. D. in Mathematics. Research interests include frames (locales), σ-frames, Lindelöf frames and other aspect of point-free topology.

Melvin Henriksen

Founding Member

Professor of Mathematics at Harvey Mudd College 1969-2009.

Memorial Conference

Bernhard Banaschewski

Professor of Mathematics, McMaster University, Canada, 1955-2022

math.mcmaster.ca/bernhard-banaschewski-1926-2022/

Publications on ResearchGate

CECAT Workshops and Conferences

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August 8 - 12, 2022

Held at Chapman University, Beckman Hall, Orange, CA 92866

Conference website

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

Conference Organizers: José Gil-Férez, Peter Jipsen, Alexander Kurz, M. Andrew Moshier

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

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

Monday, February 5th, 2018

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

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

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)

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

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

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

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

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

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

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

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

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

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

» Center of Excellence in Computation, Algebra, and Topology

Members

Drew Moshier

Michael Fahy

Peter Jipsen

Alexander Kurz

Oghenetega Ighedo

Jonathan Weinberger

Rick Ball

Guram Bezhanishvili

Frederick K. Dashiell, Jr.

Achim Jung

Aleš Pultr

Joanne Walters-Wayland

Melvin Henriksen

Bernhard Banaschewski

CECAT Workshops and Conferences

BLAST 2022

11th Annual CECAT Workshop in Pointfree Mathematics

4th SYSMICS Workshop on Duality in Algebra and Logic

Colloquium Talk

9th Annual CECAT Workshop in Pointfree Mathematics

Special Session on Algebraic Logic

9th Annual CECAT Workshop in Pointfree Mathematics

8th Annual CECAT Workshop in Pointfree Mathematics

7th Annual CECAT Workshop in Pointfree Mathematics

6th Annual CECAT Workshop in Pointfree Mathematics

BLAST 2013

5th Annual CECAT Workshop in Pointfree Mathematics

4th Annual CECAT Workshop in Pointfree Topology and Analysis

3rd Annual CECAT Workshop in Pointfree Topology

2nd CECAT Workshop on Contemporary Topology

1st CECAT Workshop on Contemporary Topology