January 2005 - Categories - categories.org.au

Gerbes
by John Baez 30 Jan '05

30 Jan '05

Dear Categorists - I thought some of you might enjoy the material here on Larry Breen's conference, and on gerbes. Best, jb ...................................................................... Also available at http://math.ucr.edu/home/baez/week210.html January 25, 2005 This Week's Finds in Mathematical Physics - Week 210 John Baez As you've probably heard, the Huygens probe has successfully landed on Saturn's moon Titan and is sending back pictures: 1) Huygens Probe Descent http://saturn.jpl.nasa.gov/news/events/huygensDescent/index.cfm Titan averages a chilly -180 degrees Celsius, and its smoggy orange atmosphere is thicker than the Earth's, mostly nitrogen but 6 percent methane, together with substantial traces of all sorts of other hydrocarbons. The orange color may come from "tholins": polymers made by irradiating a mix of nitrogen and methane. Some other icy moons in the outer solar system are covered with this goop, but Titan is the only moon in the Solar System to have a substantial atmosphere. It even has clouds. As the Huygens probe parachuted to the surface, it photographed what look like twisty riverbeds flowing into a large lake! People have long suspected that Titan has lakes of made of methane and/or ethane, but now we may be seeing them. And when Huygens landed, its sensors reported that it broke through a crusty surface and sunk about 20 centimeters into something mushy: probably methane mud! The first color photo of the surface looks disappointingly like Mars at first sight. But, the surface is pumpkin-colored due to tholins or something, not rust red. The sky is orange too! The "rocks" could be water ice. And they've detected hints of volcanos that spew molten water and ammonia! So, it's a strange new world. Back here on Earth, there was a conference in December in honor of Larry Breen's 60th birthday: 2) Arithmetic, Geometry and Topology: Conference on occasion of Larry Breen's sixtieth birthday, http://www-math.univ-paris13.fr/~lb2004/ It was in Paris. This was my first visit to that city, but luckily I got to stay there an extra week after the conference, so I could focus on the math while it was going on. But I can't resist a digression! Paris won my heart, despite my suspicions that it had somehow been hyped all along. First of all, it's beautiful. Second, it's nice to be someplace where people take simple foods like bread, cheese, fruits and vegetables really seriously, and don't settle for the tasteless crud we so often eat in the US. None of this came as a surprise, of course. What surprised is that I've never seen a city with so many bookstores - and good ones, too! They're clustered thick near the Sorbonne, but the Latin Quarter is dotted with them, and there are even lots along the Boulevard St-Germain, which is the biggest most fashionable shopping street. I don't think there's any place in the English speaking world with so many bookstores. Not London, not New York... Cambridge Massachusetts used to have lots near Harvard Square, back when I was a grad student, but the high rents have long since squeezed them out, replacing bohemian diversity with clothing shops for boring rich people, like Abercrombie and Fitch. Somehow in Paris fancy clothing and books coexist. Umm, but what about the conference? Well, Breen's work is mainly on algebraic geometry a la Grothendieck, with a strong emphasis on category theory. Beautiful stuff, and lately it's it's begun to find applications to string theory - especially his work on gerbes. People at his conference spoke on all sorts of topics, most of which I didn't understand very well - some heavy-duty number theory, for example. I understood a few well enough to really enjoy them, like Mike Hopkins' talk on derived algebraic geometry, Clemens Berger's talk on geometric Reedy categories, and Ieke Moerdijk's talk on the homotopy theory of operads. But I won't try to explain these - I want to explain what a "gerbe" is, so I have my work cut out for me. One way to get going on the idea of gauge theory is to start with electromagnetism, where the concept of "phase" turns out to play a crucial role. If you move a charged particle through an electromagnetic field, its wavefunction gets multiplied by a unit complex number, or "phase" - and it turns out, rather wonderfully, that all effects of electricity and magnetism on charged particles is due to this! However, phases are funny. You can't actually measure the phase of a charged particle - at least, there's no such thing as a "phasometer" where you stick in a particle and the dial on the meter points to a unit complex number. Of course a unit complex number is just a fancy name for a point on the circle, and a dial is precisely the right shape for that... but you just can't build this machine. Instead, you can only measure the *change* in phase of a particle as it goes around a loop. Or, equivalently, the *difference* in phases when a particle takes two different paths from here to there. See, in quantum mechanics you can play tricks like the "double slit experiment", where you coax a particle's wavefunction to smear out and take two routes from here to there... and then when it arrives, it interferes with itself, and if you're smart you can see by these interference effects what the relative phase of the two paths is. Pretty weird, eh? I'm so used to this that it seems completely normal to me, but I should admit that this way of understanding the electromagnetic field came fairly late. Weyl had a hint of it in 1918 when he invented the term "gauge theory" in his quest to unify electromagnetism and gravity, but he was mixed up in some crucial ways that only got sorted out quite a bit later. For more details, try O'Raiferteagh's book "The Dawning of Gauge Theory", which I discussed in "week116". Anyway, the concept of relative phase, or difference in phase, is nicely captured by the concept of a "torsor". A unit complex number is a point on the unit circle in the complex plane. This circle is a group since we can multiply unit complex numbers and get unit complex numbers back. This group is called U(1). Like a dial, U(1) has standard names for all the points on it - and it has one god-given special point, the identity element, namely the number 1. A "U(1) torsor" is a lot like U(1), but subtly different. It's a circle where the points aren't given these standard names... but where you can still tell measure angles, and tell the difference between clockwise and counterclockwise. You can't get an element of U(1) from *one* point on a U(1) torsor. But, if you have *two* points on a U(1) torsor, you can say how much rotation it takes to get from one to the other, and this give an element of U(1). In other words, you can describe the "difference in phase" between these two points. For more on torsors, try this: 3) John Baez, Torsors made easy, http://math.ucr.edu/home/baez/torsors.html Anyway, the real idea behind electromagnetism is that sitting over each point in spacetime is a U(1) torsor. If a particle is sitting at some point in spacetime, its phase is not really a numbers: it's an element of the U(1) torsor sitting over that point! To get a *number*, we have to carry the particle around a loop! Its phase will change when we do this, so we get *two* points in a U(1) torsor, and their difference is an element of U(1). So while it sounds far-out, the key mathematical structure in electromagnetism is a bunch of U(1) torsors, one over each point in spacetime. This is called a "principal U(1) bundle" or sometimes just a "U(1) bundle" for short. If we wanted to describe some force other than electromagnetism, we could take this whole setup and replace U(1) with some other group. In fact, this idea works great: it's the main idea behind gauge theories, which do an excellent job of describing all the forces in nature. To set up a gauge theory, the first thing you need to do is pick a group G and pick a "principal G-bundle" over spacetime. Spacetime will be some manifold X. A principal G-bundle over X is gadget that assigns a G-torsor to each point of X. A G-torsor is a space where if you pick two points in it, you get an element of G which describes their "difference". I'm being fairly sloppy here, so don't take these as precise definitions! I give a precise definition of a G-torsor in the above webpage, and any decent book on differential geometry will give you a definition of a principal G-bundle. However, only rather highbrow books define principal G-bundles with the help of G-torsors... which is sad, because it's not that hard, and rather enlightening. Anyway, in gauge theory the forces of nature are described by "connections" on principal G-bundles. Let's say we have a principal G-bundle P which assigns to each point x of our manifold a G-torsor P(x). Then a "connection" on P is a gadget that says how any path from x to y gives a map from P(x) to P(y). If G is U(1), for example, this gadget says how the phase of a charged particle changes as we move it along any path from x to y. Now suppose we have a loop that starts and ends at x. Then our connection gives a map from P(x) to itself. If we start with a point in P(x), and apply this map, we get another point in P(x). Since P(x) is a G-torsor, these two points determine an element of G. This is how we get group elements from loops in gauge theory! Now let me sketch how gerbes enter the game. First I'll do the case where the group G is abelian, for example U(1). It's the nonabelian gerbes that really interest me... but the abelian case is a lot easier. The reason is that when G is abelian, the group element we get in the previous paragraph doesn't depend on the choice of a point of P(x). Gerbes show up when we try to invent a kind of "higher gauge theory" that describes how not just point particles but 1-dimensional objects transform when you move them around. For example, the strings in string theory, or the loops in loop quantum gravity. This leads to a mind-boggling self-referential twist, which is just the kind of thing I love: As we've seen, a connection describes how a point particle transforms when you carry it along a path: f x------------>-----y a path f from the point x to the point y: we write this as f: x -> y Now we need a gadget that'll describe how a *path* transforms when you carry it along a PATH OF PATHS: f ----------->----- / || \ x ||F y a path-of-paths F from the path f to the path g: \ \/ / we write this as F: f => g ----------->----- g To do this, we need to boost our level of thinking a notch, working not with "G-torsors" and "principal G-bundles" but instead with "G-2-torsors" and "G-gerbes". Here's how it goes: We start by picking an abelian group G and a manifold X. Then we pick a "G-gerbe" over M, say P. What's that? It's a thing that assigns to each point x of X a "G-2-torsor", say P(x). What's that? Well, it's a thing where if you pick two points in it, you get a G-TORSOR describing their difference! Get it? This is the beginning of a story that goes on forever: Two points in a G-torsor determine an element of G; two points in a G-2-torsor determine a G-torsor; two points in a G-3-torsor determine a G-2-torsor; . . . But, you'll probably be relieved to know we won't go beyond G-2-torsors today. Next, we pick a "connection" on P. What's that? Well, it's a gadget that for each path from x to y gives us a map from the G-2-torsor P(x) to the G-2-torsor P(y). If we call the path f: x -> y then we call this map P(f): P(x) -> P(y) Moroever, this sort of connection also gives a "map between maps" for each path-of-paths! So, from F: f => g it gives P(F): P(f) => P(g) I haven't explained enough stuff to say yet what these "maps between maps" are, so let's just see what happens if we have a loop f: x -> x and then a loop-of-loops F: f => f Our connection assigns a map to the loop f: x -> x, like this: P(f): P(x) -> P(x) If we start with a point in P(x), and apply this map, we get another point in P(x). Since P(x) is a G-2-torsor, these two points determine a G-torsor. This G-torsor doesn't depend on our initial choice of point. So, we can think of P(f) as being a G-torsor, if we like. Our connection also assigns a map to the loop-of-loops F: f => f, like this: P(F): P(f) => P(f) If we start with a point in P(f), and apply this map, we get another point in P(f). Since P(f) is a G-2-torsor, these two points determine an element of G. This element of G doesn't depend on our initial choice of point. So, we can think of P(F) as being an element of G, if we like. In short, the machinery functions just as you'd hope, giving a group element that describes how a loop of string "changes phase" as you carry it around a loop-of-loops! So far I've been strenously avoiding the language of categories and 2-categories, but if you're at all familiar with that language, you'll have guessed that it's precisely what we need to make everything I'm saying precise. It's actually incredibly beautiful... but I'm getting lazy, so I'll explain it very tersely now, in a way that only true lovers of abstraction will enjoy: If G is a group, it acts on itself by left translation. So, it becomes a left G-set. Any left G-set isomorphic to this one is called a "G-torsor". There's a category G-Tor whose objects are G-torsors and whose morphisms are maps compatible with the action of G. Since all G-torsors are isomorphic, and the automorphism group of any one is just G, this category G-Tor is equivalent to G (regarded as a 1-object category). If G is abelian, every left G-set becomes a right G-set too. This allows us to define a "tensor product" of G-sets. The tensor product of G-torsors is a G-torsor, so G-Tor becomes a monoidal category. In fact, it's a "2-group": a monoidal category where all the objects and morphisms are invertible. This allows us to iterate what we've just done: Since G-Tor is a 2-group, it acts on itself by left translation. So, it becomes a "left G-category". Any left G-category isomorphic to this one is called a "G-2-torsor". There's a 2-category G-2-Tor whose objects are G-2-torsors, whose morphisms are functors compatible the action of G, and whose morphisms are natural transformations compatible with the action of G. Since all G-2-torsors are isomorphic, and the automorphism 2-group of any one is just G-Tor, this 2-category is equivalent to G-Tor (regarded as a 1-object 2-category). And so on! This infinite hierarchy only works when G is abelian; when G is nonabelian we need a different hierarchy, which uses "bitorsors", where G acts on both left and right, instead of "torsors". To learn more about this stuff, here are some references. I'll stick to ones I didn't already list in "week71" and "week151". First, for physicists, some work on the role of gerbes and 2-gerbes in string theory and M-theory: 4) Paolo Aschieri, Luigi Cantini and Branislav Jurco, Nonabelian bundle gerbes, their differential geometry and gauge theory, available as hep-th/0312154. 5) Paolo Aschieri and Branislav Jurco, Gerbes, M5-brane anomalies and E8 gauge theory, available as hep-th/0409200. Second, for mathematicians, some classic works by Breen: 6) Lawrence Breen, Bitorseurs et cohomologie non-abelienne, in The Grothendieck Festschrift, eds. P. Cartier et al, Progress in Mathematics vol. 86, Birkhauser, Boston, 1990, pp. 401-476. 7) Lawrence Breen, Theorie de Schreier superieure, Ann. Sci. Ecole Norm. Sup. 25 (1992), 465-514. 8) Lawrence Breen, Classification of 2-stacks and 2-gerbes, Asterisque 225, Societe Mathematique de France, 1994. 2-gerbes are what you get if you climb the hierarchy one more step. They should be good for describing the parallel transport of 2-dimensional surfaces, or "2-branes" - and indeed they make an appearance in Aschieri and Jurco's paper for precisely that reason. Another key reference is Breen's paper with Messing about connections on nonabelian gerbes: 9) Lawrence Breen and William Messing, The Differential Geometry of Gerbes, available as math.AG/0106083. and Breen's lecture notes from the IMA workshop on higher categories: 10) Larry Breen, n-Stacks and n-gerbes: homotopy theory. Notes available at http://www.ima.umn.edu/categories/#thur I've been working on this stuff myself lately, from a somewhat different viewpoint. So far I've written papers with Aaron Lauda and Alissa Crans about 2-groups and Lie 2-algebras: 11) John Baez and Aaron Lauda, Higher-dimensional algebra V: 2-groups, Theory and Applications of Categories 12 (2004), 423-491. Available online at http://www.tac.mta.ca/tac/volumes/12/14/12-14abs.html or as math.QA/0307200. 12) John Baez and Alissa Crans, Higher-dimensional algebra VI: Lie 2-algebras, Theory and Applications of Categories 12 (2004), 492-528. Available online at http://www.tac.mta.ca/tac/volumes/12/15/12-15abs.html or as math.QA/0307263. Aaron Lauda was getting a masters degree in physics at UCR when we started our paper on 2-groups. Now he's a grad student in math at the University of Cambridge, working on things related to topological quantum field theory with the category theorist Martin Hyland. Alissa Crans did her PhD in math at UCR, and our paper on Lie 2-algebras contains a lot of stuff from her thesis. Now she has a job at Loyola Marymount University, in Los Angeles. I've had a huge amount of fun working with both of them! Luckily Alissa lives nearby, and I visit Cambridge most summers. So, we can all keep working on other projects together - and we are. I also have some gerbe-related projects going on with my grad student Toby Bartels, Danny Stevenson (who is teaching at UCR now) and Urs Schreiber, a fellow moderator of sci.physics.research who will soon be a postdoc at Hamburg with Christoph Schweiger. Urs will be visiting UCR for two weeks in February, and we plan to figure a lot of stuff out. So, I've got gerbes on the brain, and I'll probably be saying more about them in the future, unless I burn up all my expository energy writing papers. In fact, one of the best places to learn about the differential geometry of abelian gerbes and 2-gerbes is Danny's thesis: 13) Danny Stevenson, The geometry of bundle gerbes, Ph.D. thesis, University of Adelaide, 2000. Available as math.DG/0004117. He's also written lots of other papers on gerbes, which you can find on the arXiv. Physicists may find these the most interesting: 14) Michael K. Murray and Danny Stevenson, Higgs fields, bundle gerbes and string structures, Comm. Math. Phys. 236 (2003), 541-555. Also available as math.DG/0106179. 15) Alan L. Carey, Stuart Johnson, Michael K. Murray, Danny Stevenson and Bai-Ling Wang, Bundle gerbes for Chern-Simons and Wess-Zumino-Witten models, available as math.DG/0410013. Toby is doing his thesis on categorified bundles, or "2-bundles", and you can already get a preview here: 16) Toby Bartels, Categorified gauge theory: 2-bundles, available as math.CT/0410328. 2-bundles are meant to be an alternative to gerbes: although I've done my best to hide it above, a gerbe is really more like a categorified *sheaf* than a bundle. And, just as a bundle has a sheaf of sections, we're hoping that a 2-bundle has a stack of sections, which in certain cases will be a gerbe. That's one of the things we need to figure out, though. And, while I'm listing the papers of the gerbe gang, I should admit that Urs and I have written a paper about connections on 2-bundles. But, I want to polish this paper a bit before talking about it here. As for 2-groups, various people have been studying their representations lately, and this should become an important part of higher gauge theory, just as group representations are crucial in gauge theory: 17) Magnus Forrester-Barker, Representations of crossed modules and cat^1-groups, Ph.D. thesis, Department of Mathematics, University of Wales, Bangor, 2004. Available at http://www.informatics.bangor.ac.uk/public/mathematics/research/ftp/theses/… 18) John Barrett and Marco Mackaay, Categorical representations of categorical groups, available as math.CT/0407463. 19) Josep Elgueta, Representation theory of 2-groups on finite dimensional 2-vector spaces, available as math.CT/0408120. Hendryk Pfeiffer's papers on higher gauge theory are also very interesting. Since he works on lattice gauge theory and spin foam models, the first two papers here develop higher gauge theory on a discrete spacetime, and then compare it to higher gauge theory on a manifold: 20) Hendryk Pfeiffer, Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics, Annals Phys. 308 (2003), 447-477. Also available as hep-th/0304074. 21) Florian Girelli and Hendryk Pfeiffer, Higher gauge theory - differential versus integral formulation, Jour. Math. Phys. 45 (2004), 3949-3971. Also available as hep-th/0309173. 22) Hendryk Pfeiffer, 2-groups, trialgebras and their Hopf categories of representations, available as math.QA/0411468. The third one partially fulfills an old dream of Crane and Frenkel - a dream I vaguely hinted at way back in "week50". Their dream was to find a concept of "trialgebra" such that a trialgebra has a Hopf category of representations, which in turn can have a monoidal 2-category of representations of its own. This is a kind of aggravated version of a pattern already familiar in algebra, where a Hopf algebra (or bialgebra) has a monoidal category of representations. Pfeiffer doesn't define general trialgebras, but only "cocommutative trialgebras" and "commutative cotrialgebras". A cocommutative trialgebra is a category in the category of cocommutative Hopf algebras, while a commutative cotrialgebra is a category in the opposite of the category of commutative Hopf algebras. Zounds - say that three times fast! He shows you can get these two gadgets from 2-groups in analogy to how you get cocommutative or commutative Hopf algebras from groups, by taking the group algebra or the algebra of functions on a group. He also proves a Tannaka- Krein theorem that lets you reconstruct commutative cotrialgebras from their Hopf categories of representations. Really cool stuff! ----------------------------------------------------------------------- Previous issues of "This Week's Finds" and other expository articles on mathematics and physics, as well as some of my research papers, can be obtained at http://math.ucr.edu/home/baez/ For a table of contents of all the issues of This Week's Finds, try http://math.ucr.edu/home/baez/twf.html A simple jumping-off point to the old issues is available at http://math.ucr.edu/home/baez/twfshort.html If you just want the latest issue, go to http://math.ucr.edu/home/baez/this.week.html

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MFPS Final Call for Papers
by Michael Mislove 29 Jan '05

29 Jan '05

Dear Colleagues, Below is the Final Call for Papers for MFPS 21, which will take place at the University of Birmingham, UK from Wednesday, May 18 through Saturday, May 21, 2005. Best regards, Mike Mislove =============================================== Professor Michael Mislove Phone: +1 504 862-3441 Department of Mathematics FAX: +1 504 865-5063 Tulane University URL: http://www.math.tulane.edu/~mwm New Orleans, LA 70118 USA =============================================== Final Call for Papers MFPS XXI Twenty-first Conference on the Mathematical Foundations of Programming Semantics University of Birmingham Edgbaston, Birmingham UK May 18 - May 21, 2005 Partially Supported by US Office of Naval Research The Twenty-first Conference on the Mathematical Foundations of Programming Semantics will take place at the University of Birmingham, UK from Wednesday, May 18 through Saturday, May 21, 2005. The invited speakers for MFPS XXI are Samson Abramsky, Oxford Andrej Bauer, IMFM, Slovenia Roberto Gorrieri, Bologna Cliff Jones, Newcastle Catuscia Palamidessi, INRIA Gordon Plotkin, Edinburgh John Reynolds, CMU In addition to the invited addresses, there will be three special sessions: o Special Session on Quantum Computing organized by Samson Abramsky, Michael Mislove (Tulane) and Prakash Panangaden (McGill). o Special Session on Security organized by Catherine Meadows (NRL) o Special Session on Domain Theory and Topology, organized by Martin Escardo and Achim Jung (Birmingham). The remainder of the program will be composed of papers selected by the Program Committee from submissions received in response to this Call for Papers. The Program Committee is being chaired by Martin Escardo (Birmingham). It also includes: o Ulrich Berger, Swansea o Lars Birkedal, ITU, Denmark o Stephen Brookes, CMU o Thierry Coquand, Goteberg o Pierre-Louis Curien, LIAFA, Paris VII o Vincent Danos, Paris o Marcelo Fiore, Cambridge o Achim Jung Birmingham, U.K. o Catherine Meadows, NRL o Michael Mislove, Tulane o Luke Ong, Oxford o Prakash Panangaden, McGill o Brigitte Pientka, McGill o Phil Scott, Ottawa o Roberto Segala, Verona o Alex Simpson, Edinburgh o James Worrell, Tulane o Steve Zdancewic, Penn Submissions should consist of original work that has not been published elsewhere. Submissions should be no longer than 12 pages, and they should be in the form of either PostScript or pdf files that can be printed on a standard printer. They can be made using the link that is available on the MFPS 21 Home Page http://www.math.tulane.edu/~mfps/mfps21.htm Submissions must be received by midnight, Pacific Standard Time on Friday, February 15, 2005. Authors will be notified of acceptance by March 25, 2005. The conference Proceedings will appear as a volume of the Electronic Notes on Theoretical Computer Science. Information about proper formatting of submissions for the Proceedings will accompany the notices of acceptance. Information about ENTCS is available at http://www.elsevier.com/locate/entcs The MFPS conferences are devoted to those areas of mathematics, logic and computer science which are related to the semantics of programming languages. The series particularly has stressed providing a forum where both mathematicians and computer scientists can meet and exchange ideas about problems of common interest. We also encourage participation by researchers in neighboring areas, since we strive to maintain breadth in the scope of the series. The Organizing Committee for MFPS consists of Stephen Brookes (CMU), Achim Jung (Birmingham), Catherine Meadows (NRL), Michael Mislove (Tulane) and Prakash Panangaden (McGill). The local arrangements for MFPS XXI are being overseen by Achim Jung. In addition to supporting the conference overall, the support we anticipate from the Office of Naval Research makes funds available to help offset expenses of graduate students. Women and minorities also are encouraged to inquire about possible support to attend the meeting. Participation Information Further information about MFPS XXI can be found at the URL http://www.math.tulane.edu/~mfps/mfps21.htm Registration information will be available at these sites shortly after the list of accepted papers is available. If you have problems accessing the link above, then send email to mfps(a)math.tulane.edu. 30-Jan-2005 16:49:19 -0400,24236;000000000001-00000000

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PhD positions
by Jiri Rosicky 26 Jan '05

26 Jan '05

The Department of Algebra and Geometry at the Masaryk University, Brno, Czech Republic, announces free PhD positions. The scholarships are available for three years, beginning in October 2005. They cover modest living expenses and are supported by the project `Algebra and geometry: the reunion and trends in current Mathematics' of the Grant Agency of the Czech Republic. The research topics are: category theory, algebraic number theory, semigroups and languages, differential geometry, global analysis, algebraic topology. Possible supervisors include: J.Rosicky, R.Kucera, L.Polak, J.Slovak, M.Cadek, J.Janyska. The closing date for applications is April 15, 2005. The study will begin in September 2005. Further basic information on the project is available at www.math.muni.cz/~slovak/phd-grant, the web pages of the Masaryk University are at http://www.muni.cz/to.en/, or http://www.muni.cz/to.en/misc/about.html (including a short Euro News profile http://wwwdata.muni.cz/to.en/media/video_mu.avi) 28-Jan-2005 17:09:36 -0400,5292;000000000000-00000000

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CFP Student session LACL 2005
by Renaud Marlet 25 Jan '05

25 Jan '05

Call for papers ***************************************************** Student Session - LACL'2005 Logical Aspects of Computational Linguistics ***************************************************** Deadline : March 15, 2005 LACL'2005 is the 5th edition of a series of international conferences on logical and formal methods in computational linguistics. It addresses in particular the use of proof theoretic and model theoretic methods for describing natural language syntax and semantics, as well as the implementation of natural language processing software relying on such models. *** STUDENT SESSION *** For the first time, LACL'2005 will feature a student session. Students (not having defended yet their PhD thesis or defending it in 2005) are invited to submit short papers (2 or 3 pages) on the same topics as LACL. Submitted papers may present only partial but promising work. This student session offers a good opportunity for students to acquaint themselves with the world of research : digest writing exercise, feedback from the program committee, oral presentation exercise, feedback from LACL attendants. Students whose articles will be selected for the student session will benefit from reduced registration fees for the LACL conference. *** PAPER SELECTION *** Submitted articles will be reviewed by a program committee made of a a group of experienced researcher as well as a group of chosen PhD students. Each article will be reviewed by at least one experienced researcher and one of these PhD students. *** PAPER PRESENTATION *** Students whose papers will be selected will present their work in a poster session at the LACL conference. The papers will also be grouped and edited as an INRIA research report. *** TOPICS *** Computer scientists, linguists, mathematicians and philosophers are invited to present their work on the use of logical methods in computational linguistics and natural language processing, in natural language analysis, generation or acquisition. * LOGICAL FOUNDATIONS OF SYNTACTIC FORMALISMS: - categorial grammars, - minimalist grammars, - dependency grammars, - tree adjoining grammars, - model theoretic syntax, - formal language theory for natural language processing, - data-driven approaches, * LOGIC FOR SEMANTICS OF LEXICAL ITEMS, SENTENCES, DISCOURSE AND DIALOG: - discourse representation theory, - Montague semantics, - compositionality, - dynamic logic, - game semantics, - situation semantics, - generative lexicon, * APPLICATIONS OF THESE MODELS TO NATURAL LANGUAGE PROCESSING: - software for natural language analysis, - software for acquiring linguistic resources, - software for natural language generation, - software for information extraction, - question answering and human computer interaction in natural language, - evaluation and scalability *** SUBMISSION FORMAT *** Papers are be 2 to 3 pages long, including bibliography and possible figures and appendices. Articles, in PDF format, should be sent by email to lacl(a)labri.fr, with the keywords "student session" in the mail subject. *** IMPORTANT DATES *** - Paper submission deadline : March 15th, 2005 - Notification of acceptance : March 31st, 2005 - Camera-ready papers due : April 15th, 2005 - Student session : during LACL (April 28-30th, 2005) *** SCIENTIFIC INQUIRIES *** - Philippe Blache, blache(a)lpl.univ-aix.fr - Edward Stabler, stabler(a)ucla.edu *** PRACTICAL INQUIRIES *** - Renaud Marlet, marlet(a)labri.fr - Maxime Amblard, amblard(a)labri.fr *** PROGRAM COMMITTEE *** Ph. Blache, E. Stabler (chairs), members of the LACL 2005 program committee, group of chosen PhD students (in the course of being defined). *** ORGANIZING COMMITTEE *** R. Marlet, M. Amblard, J. Busquets, R. Moot *** MORE DETAILS *** http://lacl.labri.fr/student-session (at work) 25-Jan-2005 11:57:37 -0400,4662;000000000000-00000000

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CSL'05 - Second Call for Papers
by Andrzej Murawski 25 Jan '05

25 Jan '05

CALL FOR PAPERS CSL'05, University of Oxford, 22-25 August 2005 http://web.comlab.ox.ac.uk/oucl/conferences/CSL05/ THE EVENT Computer Science Logic (CSL) is the annual conference of the European Association for Computer Science Logic (EACSL). The 14th Annual Conference (and 19th International Workshop), CSL2005, will take place in the week 22 - 25 August 2005; it will be organised by the Computing Laboratory at the University of Oxford. SCOPE The conference is intended for computer scientists whose research activities involve logic, as well as for logicians working on issues significant for computer science. Suggested topics of interest include: automated deduction and interactive theorem proving, constructive mathematics and type theory, equational logic and term rewriting, modal and temporal logic, model checking, logical aspects of computational complexity, finite model theory, computational proof theory, logic programming and constraints, lambda calculus and combinatory logic, categorical logic and topological semantics, domain theory, database theory, specification, extraction and transformation of programs, logical foundations of programming paradigms, linear logic, higher-order logic. INVITED SPEAKERS Matthias Baaz (U. of Technology, Vienna) Ulrich Berger (U. of Wales, Swansea) Maarten Marx (U. of Amsterdam) Anatol Slissenko (Universit� Paris 12) SUBMISSION The proceedings will be published in the Springer Lecture Notes in Computer Science. Papers accepted by the Programme Committee must be presented at the conference by one of the authors, and final copy prepared according to Springer's guidelines. Submitted papers must be in Springer's LNCS style and of no more than 15 pages, presenting work not previously published. They must not be submitted concurrently to another conference with refereed proceedings. The PC chair should be informed of closely related work submitted to a conference or journal by 1 April 2005. Papers authored or coauthored by members of the Programme Committee are not allowed. Submitted papers must be in English and provide sufficient detail to allow the programme committee to assess the merits of the paper. Full proofs may appear in a technical appendix which will be read at the reviewer's discretion. The title page must contain: title and author(s), physical and e-mail addresses, identification of the corresponding author, an abstract of no more than 200 words, and a list of keywords. IMPORTANT DATES Deadline for abstracts 25 March, 2005 Deadline for papers 1 April, 2005 Notification 15 May, 2005 Final versions due 1 June, 2005 ACKERMANN AWARD The EACSL Board has decided to launch the Ackermann Award: The EACSL Outstanding Dissertation Award for Logic in Computer Science. The first awards will be presented to the recipients at CSL'05. Further details of the Award can be found at http://www.dimi.uniud.it/~eacsl/award.html PROGRAMME COMMITTEE Albert Atserias (Universitat Polit�cnica de Catalunya) David Basin (Eidgen�ssische Technische Hochschule Z�rich) Martin Escardo (U. of Birmingham) Martin Grohe (Humboldt-Universitat zu Berlin) Ryu Hasegawa (U. of Tokyo) Martin Hofmann (Ludwig-Maximilians-Universit�t M�nchen) Ulrich Kohlenbach (Darmstadt U. of Technology) Orna Kupferman (Hebrew U. of Jerusalem) Paul-Andre Mellies (CNRS / Universit� Paris 7) Aart Middeldorp (U. of Innsbruck, Austria) Dale Miller (INRIA / Ecole Polytechnique) Damian Niwinski (U. of Warsaw) Peter O'Hearn (Queen Mary, U. of London) Luke Ong (U. of Oxford, Chair) Alexander Rabinovich (U. of Tel Aviv) Thomas Schwentick (Philipps-Universit�t Marburg) Alex Simpson (U. of Edinburgh) Nicolai Vorobjov (U. of Bath) Andrei Voronkov (U. of Manchester) 26-Jan-2005 11:48:51 -0400,1731;000000000000-00000000

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by cat-dist＠mta.ca 21 Jan '05

21 Jan '05

s X-URL: http://www.science.uva.nl/ Date: Wed, 19 Jan 2005 13:10:58 +0100 To: info(a)folli.org Subject: categories: Beth Dissertation Prize: call for submissions From: Alberto Policriti <policriti(a)dimi.uniud.it> Sender: cat-dist(a)mta.ca Precedence: bulk *** Our apologies for multiple copies! *** E. W. Beth Dissertation Prize: call for submissions. Since 2002, FoLLI (the European Association for Logic, Language, and Information, www.folli.org) awards the E. W. Beth Dissertation Prize to outstanding dissertations in the fields of Logic, Language, and Information. Submissions are invited for 2004. The prize will be awarded to the best dissertation which resulted in a Ph.D. in the year 2004. The dissertations will be judged on the impact they made in their respective fields, breadth and originality of the work, and also on the interdisciplinarity of the work. Ideally the winning dissertation will be of interest to researchers in all three fields. Who qualifies: Those who were awarded a Ph.D. degree in the areas of Logic, Language, or Information between January 1st, 2004 and December 31st, 2004. There is no restriction on the nationality of the candidate or the university where the Ph.D. was granted. However, after a careful consideration, FoLLI has decided to accept only dissertations written in English. Prize: The prize consists of =B7 a certificate =B7 an invitation to present the thesis during ESSLLI 05 =B7 a donation of 2500 euros provided by the E. W. Beth Foundation. =B7 fee waive for ESSLLI 05 attendance =B7 the possibility to publish the thesis (or a revised version of it) in the new series of books in Logic, Language and Information to be published by Springer-Verlag as part of LNCS or LNCS/LNAI. (Further information on this series will be posted on the FoLLI site soon.) How to submit: We only accept electronic submissions. The following documents are required: 1. the thesis in pdf or ps format (doc/rtf not accepted); 2. a ten page abstract of the dissertation in ascii or pdf format; 3. a letter of nomination from the thesis supervisor. Self-nominations are not admitted: each nomination must be sponsored by the thesis supervisor. The letter of nomination should concisely describe the scope and significance of the dissertation and state when the degree was officially awarded; 4. two additional letters of support, including at least one letter from a referee not affiliated with the academic institution that awarded the Ph.D. degree. All documents must be submitted electronically to beth_award(a)dimi.uniud.it. Hard copy submissions are not admitted. If you experience any problems with the email submission or do not receive a notification from us within three working days, please write to policriti(a)dimi.uniud.it or folli(a)inf.unibz.it * Important dates: Deadline for Submissions: March 15, 2005. Notification of Decision: June 30, 2005. The prize will be officially assigned to the winner at ESSLLI'05 (http://www.macs.hw.ac.uk/esslli05/) the 17th European Summer School in Logic, Language, and Information, to be held in Edinburgh, Scotland, August 9-19, 2005. Prize winner will be expected to attend the ceremony and to give a presentation of her/his Ph.D. dissertation at ESSLLI?05. Committee =B7 Anne Abeill=E9 (Universit=E9 Paris 7) =B7 Johan van Benthem (University of Amsterdam) =B7 Veronica Dahl (Simon Fraser University) =B7 Nissim Francez (The Technion, Haifa) =B7 Valentin Goranko (University of Johannesburg) =B7 Alessandro Lenci (University of Pisa) =B7 Ewa Orlowska (Institute of Telecommunications, Poland) =B7 Gerald Penn (University of Toronto) =B7 Alberto Policriti (chair) (Universit=E0 di Udine) =B7 Christian Retor=E9 (Universit=E9 Bordeaux 1 ) =B7 Rob van der Sandt (University of Nijmegen) =B7 Wolfgang Thomas (RWTH Aachen)

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A question for topos theorists.
by jean benabou 20 Jan '05

20 Jan '05

I have recently come across a question, which seems to me natural, and before trying to solve it, I wanted to know if an answer was already known. If E is a category with pullbacks so is the category Cat(E) having as objects the internal categories of E and and as maps the internal functors F: A ---> B. I shall say that such an F is a "Pi-functor" if the pullback functor: Cat(E)/B --->Cat(E)/A has a right adjoint Pi/F: Cat(E)/A---->Cat(E)/B When E=Set there is a well known Conduché-Giraud condition characterizing such functors. Is there such a characterization when E is an (elementary) topos? If there is, what is the condition and where can it be found? Best wishes to all, Jean

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Quantale workshop this Friday in Oxford.
by Bob Coecke 20 Jan '05

20 Jan '05

For those of you in the Oxford, London, English midlands area, or elsewere, there will be a workshop this Friday (the 21st) on Logic from Quantales in Oxford. Please check: http://se10.comlab.ox.ac.uk:8080/InformaticPhenomena/LogicfromQuantales_en.… for the program, directions etc. Best wishes, Bob. 25-Jan-2005 11:57:36 -0400,4861;000000000000-00000000

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A Special Programme on Logic and Algorithm
by vardi＠cs.rice.edu 20 Jan '05

20 Jan '05

The Isaac Newton Institute for Mathematical Science in Cambridge, UK (http://www.newton.cam.ac.uk/) will hold a Special Programme on Logic and Algorithms (LAA) during the first half of 2006. A brief statement on the programme's focus areas can be seen at http://www.newton.cam.ac.uk/programmes/LAA/. For a list of workshops, see http://www.newton.cam.ac.uk/programmes/LAA/ws.html. To receive further announcements on LAA events, see instructions at http://www.newton.cam.ac.uk/programmes/LAA/list.html. Anuj Dawar and Moshe Y. Vardi 20-Jan-2005 15:07:43 -0400,959;000000000001-00000000

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Heyting semilattices again
by Prof. Peter Johnstone 18 Jan '05

18 Jan '05

Many thanks to the people who pointed me in the direction of the literature on free Heyting semilattices. With its help, I have now managed to answer the question that led me to think about them in the first place: There are exactly 489 different Mal'cev operations in the theory of Heyting semilattices. (There are infinitely many in Heyting algebras, and I had idly wondered whether the same might be true if you leave out disjunction.) Note that 489 = 3 x 163: this is not a coincidence, though why Eddington's favourite prime appears in this context I don't know. Rather to my surprise, there is only one Pixley operation (that is, a Mal'cev operation p satisfying the additional equation p(x,y,x) = y). There are many different ways of describing it, but they all turn out to be equal as members of the free Heyting semilattice HS(3). Peter Johnstone 20-Jan-2005 15:07:43 -0400,2069;000000000000-00000000

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