Events in General and Computational Topology in the U.K.

• Galway at BMC2003                                               Pym Conference




Schedule of Seminars, Week Beginning:

• Friday, 17/1/03                 Friday, 24/1/03                 Friday, 31/1/03



• Friday, 7/2/03                   Friday, 14/2/03                 Friday, 21/2/03



• Friday, 28/2/03                 Friday, 7/3/03                   Friday, 14/3/03



• Friday, 25/4/03                 Friday, 2/5/03                   Friday, 9/5/03



• Friday, 16/5/03                 Friday, 23/5/03                 Friday, 30/5/03



• Friday, 6/6/03                  Friday, 13/6/03                  Friday, 20/6/03



• Friday, 27/6/03                 Friday, 25/7/03




The Birmingham Topology Seminar meets Fridays at 4 p.m. in G40, the Computer Science Building.

The Oxford Analytic Topology in Mathematics and Computer Science Seminar meets Mondays at 4 p.m. in L3, at the Mathematical Institute, 24-29 St. Giles', Oxford.

Links:

1. Oxford:          20 January       Keye Martin (Oxford)
                                                "Entropy as an object."

1. Birmingham:    24 January       Ralph Kopperman (CUNY)    [Theory seminar, 2 p.m., G40]
                                                 "Ask 'What can computer science do for topology?'".



2. Birmingham:    24 January       Steve Vickers (Birmingham)
                                                 TBA

For more information, click here.


3. Oxford:           27 January       Steve Matthews (Warwick)
                                                 "Partial metrics, topology, and domain theory."

1. Birmingham:    31 January       Harold Simmons (Manchester)
                                                 "What is, and what is not, point-free topology?"
For more information, click here.


2. Oxford:             3 February     Chris Good (Birmingham)
                                                 "Partial metrics, topology, and domain theory."

1. Birmingham:      7 February      Homeira Pajoohesh (Birmingham)
                                                 "Partial metrizability in quantales."
For more information, click here.


2. Oxford:          10 February      Pawel Waskiewicz (Krakow and Cork)
                                                  "Domain theory as a tool for topology."

1. Birmingham:    14 February     Pawel Waszkiewicz (Krakow and Cork)
                                                 TBA
For more information, click here.


2. Oxford:           17 February     Abbas Edalat (Imperial College)
                                                 "Domain theory and differential calculus."

1. Birmingham:    21 February     Mirna Dzamonja (UEA)
                                                  "Compact topological spaces and boolean algebras coming from functional analysis"
For more information, click here.


2. Oxford:           24 February     Julian Webster (Imperial College)
                                                 "Oriented matroids and geometric computation."

1. Birmingham:    28 February     G. M. Reed (Oxford)
                                                 TBA
For more information, click here.


2. Oxford:             3 March         Michel Schellekens (Cork)
                                                 "Quantitative domains."

1. Birmingham:     7 March          M. B. Smyth (Imperial College)
                                                 TBA
For more information, click here.


2. Oxford:          10 March         Adam Ostaszewski (L.S.E.)
                                                 TBA

1. Birmingham:     14 March       C. F. Townsend (Open University)
                                                 "Moving directed complete partial orders between toposes"

1. Oxford:           28 April          Bob Coecke
                                                "Probability as order."
   
        ABSTRACT:    I will establish the following equation:
   Quantitative Probability = Logic + Partiality of Knowledge + Entropy
   A finitary probability space (=all probability measures on {1, ... ,n}) can be fully and faithfully represented by the pair consisting of an abstract partially ordered set and Shannon entropy. The abstract partially ordered set itself can be obtained via a systematic purely order-theoretic procedure (which embodies introduction of partiality of knowledge) on an (algebraic) logic.
   This procedure actually applies to any poset. When taking the n-element powerset we obtain the above poset. When taking a finitary quantum logic (=the lattice of subspaces of a Hilbert space) we obtain the domain of quantum states introduced by Keye Martin and myself [2,3].
   We will also put all this in the perspective of order-theoretic research in the context of quantum physics [4,5].
   [1] B. Coecke: 'Entropic Geometry from Logic'. Electronic Notes in Theoretical Computer Science (MFPS'03 issue).      2003.
   [2] B. Coecke and K. Martin: 'A partial Order on Classical and Quantum States', PRG-RR-02-07, OUCL (92      pages).
   [3] 'A partial Order on Classical and Quantum States -- Extended abstract' (8 pages). 2002.
   [4] B. Coecke, D.J. Moore and A. Wilce: 'Operational Quantum Logic: An Overview'.
   [5] B. Coecke and D.J. Moore: 'Operational Galois Adjunctions'. In: B. Coecke et al, Current Research in Operational      Quantum Logic. Kluwer. 2000.
     All at: http://www.vub.ac.be/CLEA/Bob/Downloads.html.

1. Birmingham:      2 May           Vincent Schmitt (University of Leicester)
                                                 "Categories and metric spaces."
   
        ABSTRACT:   I shall present a notion of flatness that works for enriched categories. From this one may define a "free flat-cocompletion" of enrichments. I could apply this result using Lawvere's equivalence between metric spaces and enrichments. I showed that flat presheaves on A viewed as a category correspond exactly to particular filters on A viewed as a metric space. - I called these filters "flat". It happens that any Cauchy filter is flat. When the space A is symmetric, flat filters on A are exactly the Cauchy ones thus in this special case, the free flat-completion of A is exactly the (Lawvere-)Cauchy one. Another result is that flat filters are exactly the directed cocompletions of forward Cauchy sequences (with the right notion of morphisms though). I will also give a translation of the categorical completion in topological terms of the flat completion.
For more information, click here.


2. Oxford:           5 May              Peter Collins
                                                  "Hyperspaces, function spaces, and differential equations".

1. Birmingham:      9 May           Ionnis Raptis
                                                 "Noncommutative algebraic discretizations of smooth manifolds."
   
         ABSTRACT:   Sorkin's finitary (:locally finite) poset substitutes of topological manifolds will be revisited. Then we build the Gel'fand dual algebraic picture in terms of finite-dimensional noncommutative incidence Rota algebras. Casting Sorkin's posets as simplicial complexes a la Cech-Alexandrov, we present the associated Rota algebras as `discrete differential manifolds'---`differential functional algebras' with well mannered Gel'fand spatialization behaviour.Based on the recently developed Calculus and manifold-free sheaf-theoretic Abstract Differential Geometry (ADG) theory of Mallios, we first define finitary spacetime sheaves of incidence algebras as discrete differential (not just topological!) substitutes of sheaves of modules of smooth differential forms over differential manifolds, and we heuristically suggest a way of recovering the smooth spacetime continuum by suitable direct (inductive) and inverse (projective) limit constructions, with a concomitant new and significantly generalized notion of `emergent smoothness'. At the end, a physical interpretation, as Bohr's correspondence principle, will be given to these classical continuum limit procedures, and, time permitting, we will discuss the relevance of it all to current structural issues in both classical and quantum gravity research.
   Key words: finitary topological spaces, differential incidence algebras of locally finite posets, abstract differential geometry, sheaf theory, category theory, classical and quantum gravity.
For more information, click here.


2. Oxford:           12 May            no meeting.
   

1. Birmingham:      16 May           no meeting.
   
   
   

2. Oxford:            19 May            Achim Jung (U. of Birmingham)
                                                  "The probabilistic powerdomain on stably compact spaces."
   
        ABSTRACT:  At my visit to the Oxford Topology Seminar last year, I gave an introduction to stably compact spaces, and I explained some of their many nice properties. This time I plan to concentrate on one particular construction, known from Computer Science by the name "probabilistic powerdomain".
        I will briefly recap background from the general theory of stably compact spaces so that the talk is self-contained, and I will also explain some of the rationale behind the probabilistic powerdomain construction. The main purpose of the talk, however, will be to explain the connection between this construction and (regular) measures, and to exhibit a natural topology which turns the probabilistic powerdomain into another stably compact space. I will conclude with an open problem regarding the categorical properties of this construction.

1. Birmingham:      23 May           Hideki Tsuiki
                                                 "Subbases that give a canonical representation of the elements in a space."
For more information, click here.


2. Oxford:            26 May            (1) Mai Gehrke (New Mexico State University)
                Time: 3:00 p.m.            "Topologies on canonical extensions and their role in the extension of maps."
   
        ABSTRACT:  Even though canonical extensions are an alternative to topological duality for lattice ordered algebras, it turns out that these are greatly elucidated by the introduction of topology. This is especially true once we wnt to understand how to extend maps and operations, and when we want to know whether identities are preserved in the extension. In this talk we introduce the various topologies that play important roles, and show how they help us develop a fairly transparent theory of canonical extensions.



3.                          26 May            (2) Eric Goubault (DTSI/SLA CEA/Saclay)
                  Time: 4:15 p.m.           "Geometrical invariants of concurrent programs."
   
        ABSTRACT:  In this talk, I will present some of the latest results obtained by looking at parallel programs as geometric objects. They involve mainly the characterization, or the computation, of topological invariants (under some kind of "directed homeomorphism" or some kind of "directed" homotopy) in the style of algebraic topology (homotopology and homology).
        Some of these invariants are directly linked to important computer scientific properties such as deadlocks, unreachables, schedules of execution, etc. On the other hand, they involve nice category-theoretic structures, which we would like to "compute". Recent work on this with Lisbeth Fajstrup, Emmanuel Haucourt, and Martin Raussen paves the way towards nice calculations. At the other end of the spectrum, very important results have been obtained by Philippe Gaucher in the characterization of suitable invariants, and on homology.

1. Birmingham:      30 May           Mike Mislove
                                                
For more information, click here.


2. Oxford:             2 June              Jimmie Lawson (Louisiana State U.)
                            "Quotients of second countable spaces: a convenient category."
   
        ABSTRACT:  The topological category of quotients of second countable spaces has an interesting mathematical theory and also exhibits many useful features for modeling a variety of constructions in theoretical computer science. In this talk we discuss recent significant advances in the mathematical theory of this category of spaces and pose some open problems.

1. Birmingham:      6 June           to be announced.
   
For more information, click here.


2. Oxford:              9 June            T. Yung Kong (Queens College, CUNY)
                                                    "The Khalimsky Topologies are Precisely Those Simply-connected Topologies on Zⁿ Whose Connected
                                                     Sets Include All 2n-connected Sets but No (3ⁿ-1)-disconnected Sets".
   
        ABSTRACT:  The result stated in the title will be presented. Here the concepts of 2n- and (3ⁿ-1)-(dis)connected sets are the natural generalizations to Zⁿ of the standard concepts of 4- and 8-(dis)connected sets in 2D digital topology. Our proof involves some purely discrete arguments and a fact about simply connected polyhedra that is a well known consequence of the Simplicial Approximation Theorem, but also uses the following result (from an earlier paper by the speaker and Khalimsky): For any T₀ topological space in which each point lies in a finite open set and a finite closed set there exists a polyhedron, whose vertices are in 1-1 correspondence with the points of the space, such that the homotopy classes of continuous maps into the topological space from any metric space are in
   1-1 correspondence with the homotopy classes of continuous maps from that metric space into the polyhedron.

1. Birmingham:      13 June           Martin Escardo
                                                     "What is locale theory?".

******POSTPONED******



2. Oxford:              16 June            to be announced.
   

1. Birmingham:      20 June           to be announced.
   
For more information, click here.


2. Oxford:              23 June            to be announced.
   

1. Birmingham:      27 June          Abbas Edalat (Imperial College)
                                                     "A domain-theoretic model for quantum computation".
   
For more information, click here.


2. Oxford:              30 June           to be announced.
   

1. Birmingham:      25 July          Paul Taylor
                               2 p.m.            (Joint theory and topology seminar)
                                                    "Abstract Stone Duality".



2. Birmingham:      25 July          Martin Escardo
                               4 p.m.           "A gentle introduction to locales for topologists".
   

This years Galway Colloquium will take place in Birmingham, somewhat earlier than usual, on April 7th ,8th and 9th. Galway 2003 is running as a special session of the 55th British Maths Colloquium (BMC) at Birmingham.

Both events are keen to encourage graduate students to attend and give talks. Students studying for postgraduate degrees in the UK can register for free, receive a 50% reduction on accommodation and meals booked in advance (up to a limit of UKP50 and subject to availability of funds), and can attend the conference dinner at the reduced rate of UKP15.

Galway 2003 itself will start on Monday morning independently of the BMC and then in parallel as part of the BMC sessions. It is unlikely that we shall have any Galway lectures on the Thursday, though there will be a number of other lectures running. Since Galway 2003 participants will be BMC participants, you will of course be entitled to attend any of the lectures or sessions being held over the four days and there are sure to be some excellent presentations.

Invited Speakers:

We are delighted to say that this years invited speakers are:
Professor Jan van Mill (Vrije Universiteit, Amsterdam) and
Professor Steve Watson (York University, Canada)

So far, the following people have indicated that they will be attending:

Peter Collins (Oxford)
Chris Good (Birmingham)
Lylah Haynes (Birmingham)
Robin Knight (Oxford)
Ralph Kopperman (CUNY)
Declan McCartan (Queen's, Belfast)
Aisling McCluskey (Galway)
Brian McMaster (Queen's Belfast)
Brian Raines (Baylor, Texas)
Dona Strauss (Hull)
Rolf Suabedissen (Oxford).

Further information can be found on the web site: www.mat.bham.ac.uk/bmc. To register for Galway 2003 @ BMC 55, please register on the BMC website as instructed there mentioning Galway in the box 'General subject area of your presentation' under Splinter Group presentations. It does not matter if you decide not to give a talk later on, but at least we will have a know who is coming. You may well require accommodation for the Sunday night, as Galway lectures will start on Monday morning. Unfortunately there is no automatic registration for this. Please indicate in comments box and e-mail Chris Parker (cwp@for.mat.bham.ac.uk) to book accommodation for Sunday night.

This promises to be an exciting event and we really hope to see you here in April.

55th British Mathematics Colloquium University of Birmingham 7th to 10th of April, 2003

A conference on Groups and Semigroups in Analysis, in honour of J.S.Pym on the occasion of his retirement, will be held in Sheffield from May 30th-June 1st, 2003.

This could be followed by a link to the conference web site: http://www.math.uwo.ca/~milnes/JSPMay03.htm.