Tue 27th May-Tue 3rd Jun 2008 "Workshop on Commutative algebra, complexes and computer algebra" Organised by Gavin Brown, David Eisenbud, Diane Maclagan, Miles Reid and Frank Schreyer Confirmed participants include Mats Boij, Martin Bright, Gavin Brown, Nils Bruin, John Cremona, David Eisenbud, Tom Fisher, Gunnar Floystad, Anne Fruehbis-Krueger, Dan Grayson, Mike Harrison, KWAK Sijong, Cristina Lopez-Martin, Dianne Maclagan, David Mond, Stavros Papadakis, Miles Reid, Greg Sankaran, Hans Schoenemann, Frank Schreyer, SHIMADA Ichiro, Greg Smith, Bernd Sturmfels, Jan Tuitman, Graduate students: Maria Teresa Aranes, Carlos Barros, Martha Bernal, Stephen Couglan, Sarah Davis, Homero Gallegos, HAN Kang Jin, Umar Hayat, Bradford Gary Hovinen, Sohail Iqbal, Almar Kaid, Henning Lohne, Anna Morra. Alvaro Nolla, Muhammad Imran Qureshi, Lisema Rammea, Nils Rasmussen, Thotsaphon Thongjunthug, ZHOU Shengtian, please register online at https://www.warwick.ac.uk/mrc/events.php Preliminary program =================== Some of the schedule will be decided during the meeting. The talks will include => A series of lectures by Boij, Eisenbud and Schreyer on the recent breakthrough by Boij and Soederberg on Betti tables of varieties in PP^n. => Talks by Maclagan and Greg Smith on Smooth multigraded Hilbert schemes => A series by Brown, Papadakis and Reid on unprojection and Gorenstein rings in small codimension. => Several talks will include short demonstrations of M2, Singular or Magma. [Tue 27th and Wed 28th May, 4 or 5 intro talks for graduate students Our students have run seminars on the first chapters of David Eisenbud, The geometry of syzygies] Tue 27th May 10:00 Coffee and registration [Arithmetic geometry talk: 10-11 Anna Morra (Bordeaux) Counting cubic extensions with given quadratic resolvent] 11:30 in B3.03 M. Reid (Warwick), Introduction to complexes 14:00 Gunnar Floystad (Bergen), GL(n)-equivariant constructions of pure resolutions 16:00 David Eisenbud, Introduction to Boij-Soederberg theory 18:00 Buffet dinner in common room Wed 28th May 9:30 M Reid (Warwick): Kustin--Miller unprojection 11:00 Diane Maclagan and Greg Smith, intro to smooth multigraded Hilbert schemes (1) 13:00 Guerilla lunch in common room 14:00 Diane Maclagan and Greg Smith, intro to smooth multigraded Hilbert schemes (2) 16:00 F. Schreyer: Boij-Soederberg theory Thu 29th May 9:30 Stavros Papadakis (Lisboa): Unprojection with complexes 11:00 Mats Boij (KTH Stockholm): Betti numbers of modules up to scalar multiples 14:00 David Eisenbud (Berkeley): asymptotic regularity and fibers of finite morphisms (eg projections) with Harris and Huneke 16:00 KWAK Sijeong (KIAST, Taejon): Algebra and geometry under projection and applications 7:00 Dinner at Ally's Balti, Earlsdon Fri 30th May 9:30 Dan Grayson (Urbana-Champaign), Computing in the intersection ring of flag bundles 11:00 Gavin Brown and Jarek Buczynski (Kent), Magma demonstration 11:35 Anne Fruehbis-Krueger (Hannover) and Hans Schoenemann (Kaiserslautern), Singular demonstration 14:00 Gunnar Floystad, The colorful Helly theorem and colorful resolutions of ideals 16:00 Colloquium: Sturmfels, Powers of linear forms 17:15 Drinks party in common room Sat 31st May 10:30 Reid: The Gorenstein codimension 4 problem 12:00 Papadakis: Stellar subdivisions and Stanley-Reisner rings Program for Mon 2nd--Tue 3rd Jun activities by and for grad students, prelim program 9:30 Umar Hayat, Resolution of quotients by SL(2,CC) groups and their subgroups 11:00 Brad Hovinnen, A nonclassical formula for the classical discriminant 14:00 Alvaro Nolla, Representation of quivers and resolution of dihedral orbifolds? 16:00 TBA 18:00 Buffet dinner in common room Tue 3rd Jun 9:30 TBA 11:00 TBA 13:00 Guerilla lunch in common room possible talks Stavros Papadakis, More examples of unprojections Miles Reid, More applications of graded rings to birational geometry Piotr Zwiernik, Introduction to statistics for algebraic geometers Hospitality/excursions There will be one or two buffet dinner parties on Tue 27th May and Mon 2nd Jun, a group dinner for all on Thu 29th May, and a colloquium snacks/wine party of Fri 30th May. We may put on one or two visits to Stratford (for RSC) or Sat or Sun excursions to Oxford/Warwick/Stratford depending on who is interested. Royal Shakespeare Company at Stratford-upon-Avon Tue 27 May The Taming of the Shrew Wed 28 May The Taming of the Shrew Thu 29 May The Taming of the Shrew Fri 30 May A Midsummer Night's Dream Sat 31 May The Merchant of Venice Mon 2 Jun A Midsummer Night's Dream Tue 3 Jun The Merchant of Venice The RSC program at Stratford is on http://www.rsc.org.uk/whatson/calendar.aspx?monthDropDown=2008:05:31&date=31%20May%202008 (I heard a recent radio program with reviews of the plays, claiming that the production of Shrew is not misogynous, Merchant not antisemitic and Dream not discriminatory to fairies.) Birmingham Symphony Hall Sat 31st May, 7:00 Tchaikovsky: 1812 Overture Haydn: Symphony No. 100 (Military) Prokofiev: Alexander Nevsky from the grant application: Organised by Schreyer, Brown, Eisenbud and Reid Complexes are central to algebraic geometry and commutative algebra. Whereas computer algebra systems currently contain packages for syzygy modules and projective resolutions, these are now being complemented by routines for general coherent cohomology, together with homological functors such as Hom and Ext, Castelnuovo--Mumford regularity (as an explicit form of Serre vanishing) and Kustin--Miller unprojection, all subjects with strong theoretical connections. Following Bayer and Mumford's seminal paper `What can be computed in algebraic geometry?', recent work on the asymptotic regularity of ideals relate these to other asymptotic invariants (see [CEL]). Combined with classical methods, theoretical progress and some ingenuity, computer algebra is approaching Mumford's goal of describing classes of surface of general type and their moduli explicitly via computer algebra. Green's conjecture on the syzygies of a canonical curve were an entry point for algebraic geometers into computer algebra. Farkas' recent work introduces divisors on M_g as jumping loci of Koszul cohomology; this suggests generalisations of the Green--Lazarfeld conjecture on syzygies. At the same time, these jumping loci provide estimates for the `slope problem' and hence methods for the Kodaira dimension of moduli spaces. Analysing the precise dividing line between unirational moduli spaces and moduli spaces that are of general type is another challenge for computer algebra methods: Monte Carlo methods (or `needle in a haystack') over finite fields provides a probabilistic substitute for unirational parametrisations of moduli spaces or special loci in them. Although not primarily concerned with implementation in software, we hope that people from computer algebra systems such as Magma, Macaulay2 and Singular will take part in our workshops, and may be inspired to complete their implementations of Eisenbud, Floystad and Schreyer's algorithms for coherent cohomology [EFS], Papadakis' algorithm for Kustin--Miller unprojection and so on. The COM activity of WAG07-08 follows the explicit component XPL: to a large extent, these are different methods to tackle the same subject. COM will run in May and Jun 2008. A workshop is planned for Tue 27th May--Tue 3rd Jun 2008. Confirmed participants: Brown, Eisenbud, Farkas, Reid, Schreyer Targetted: Bayer, Cremona, Decker, Graf v. Bothmer, Fl{\o}ystad, Greuel, Hess, Kreuzer, Lazarsfeld, Papadakis, Popescu, Robbiano, Ryder, Schicho, Steel, Voisin, Walter,