Preparation of the Partner University Fund application

Last year, we applied with Anne Schilling for a PUF grant around Sage-Combinat:

The application failed, but the organizers warmly recommended to apply again this year. This is a three years grant that can fund travel, short to long term accommodation, meeting expenses to encourage exchanges between France and the USA, especially for grad students and postdocs, and possibly some hardware. The application deadline is December 15th, with the grant starting around March/April.

Here is the current draft of project, as a call for suggestions. Please highlight your edits and comments in bold!

1 / PROJECT TITLE OF THE PROJECT: *-Combinat: boosting open source research-driven mathematical software for algebraic combinatorics US INSTITUTION: UC Davis FRENCH INSTITUTION: Faculté d'Orsay, Université Paris-Sud Level(s)*: Master PhD Postdoctoral Research Subject Area(s)*: *Projects may include several subject areas Mathematics, IT and applications XXX 4.3 / OTHER GRANT(S) REQUESTED OR ALREADY OBTAINED FOR THIS PROJECT The *-Combinat platform was adopted for the computational aspects of two NSF Focused Research Groups: - "Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects" led by Jennifer Morse, Anne Schilling, and Mark Shimozono (2007-2010) - "Combinatorics of crystals: geometric, physical, and computational applications" led by Cristian Lenart, Anne Schilling, Mark Shimozono, and Julianna Tymoczko (2010-2013, submitted). These many-faceted international projects involve and tie together various problems from combinatorics, geometry, representation theory, physics, and computation. Many investigations in these areas are largely fueled by extensive computational experimentation. The robust implementation of algorithms derived from the projects leads to the development of new libraries for computer algebra systems. The open source dissemination of this new software not only advances the research program but also has an outreach impact on the mathematics, physics, and computer science communities. As part of the first NSF project, Nicolas M. Thiéry spent the academic year 2007-2008 at UC Davis and spent again 6 months there in Spring 2009. Anne Schilling was invited through the Kastler foundation to the University Marne-la-Vallee in November 2006 (hosted by Jean-Christophe Novelli) and to Universite Orsay, Paris-Sud in November 2008 (hosted by Nicolas M. Thiéry). *-Combinat is also the software underlying the French Non thematic ANR project "blanc" ANR-06-BLAN-0380 which involves, among others, Florent Hivert, Jean-Christophe Novelli, and Franco Saliola. Combinatorial Hopf algebras, operads and props: Combinatorial Hopf algebras are Hopf algebras whose bases are indexed by combinatorial objects. They can be seen as generalizations of the Hopf algebra of symmetric functions. The latter plays a fundamental role in numerous theories such as group representations (as characters of finite and Lie groups, spherical functions of complex groups, real and p-adic), algebraic topology (cobordism rings), algebraic geometry (Schubert calculus) and mathematical physics (integrable system, vertex operators). In the last couple of years, several such Hopf algebras appeared in seemingly unrelated domains. They appear naturally in operads theory since each operad verifying some simple conditions gives rise to a Hopf algebra. They also appear in combinatorics when one tries to lift certain computations on polynomials to a non-commutative level to get combinatorial interpretations of multiplicities. Moreover, since the work of Connes and Kreimer on renormalization, they appear regularly in mathematical physics. The goal of this ANR project is to not only provide the theoretical foundation of combinatorial Hopf algebras but also to find new algorithms needed for computer exploration during research, and which can be used for applications in physics (computation of perturbation series to a high order). 5 / PROJECT DESCRIPTION AND RATIONALE (TEXT BOXES BELOW ARE EXPANDABLE. HOWEVER PLEASE REMAIN AS CONCISE AS POSSIBLE) 5.1 / Objectives of the partnership Algebraic combinatorics is a field of mathematics which is interdisciplinary by nature and has deep connections with many other areas, and in particular computer science and theoretical physics. Due to the concrete and constructive approach, computer exploration has been playing an increasing role as a guide for research ever since Marcel-Paul Schützenberger introduced it in 50's. The involved computations vary a lot, requiring a wide range of tools as well as, more often than not, specific development by the researchers. Given the increasing scale and level of complexity, it has become essential to share the development efforts and capitalize on those in a well organized body of code. This is the purpose of the *-Combinat project, which was founded in 2000 by Florent Hivert and Nicolas M. Thiéry; it has now reached maturity, and has become a major tool in the field with 30+ researchers involved worldwide. This project is by nature research driven and already led to 50+ publications. In 2000, there was no viable open-source mathematical platform, and the project started as the package MuPAD-Combinat (http://mupad-combinat.sf.net) for the computer algebra system MuPAD (http://www.mupad.de). Meanwhile, Sage appeared (http://www.sagemath.org/), a completely open source general purpose mathematical software (similar to Maple, MuPAD, Mathematica, and up to some point matlab) based on the popular python programming language. Sage is gaining strong momentum in the math community, and we decided in June 2008 to migrate our project under the name Sage-Combinat (see http://wiki.sagemath.org/combinat). This move by itself attracted many new developers, and half of the code has readily been ported. However there still is a massive amount of work left, which must be carried out swiftly in order to support continuous use by the community for research. At the same time, care needs to be taken in laying out strong foundations for the future, and new features are continuously needed. The purpose of the PUF project is to provide short to mid-term funding to boost the international development of Sage-Combinat around the bipole France-America during this critical period. The key is communication and coordination; therefore the primary needs are mobility (in particular of graduate students and postdocs), organization of regular workshops, and hardware for collaborative development tools. 5.2 / History of the partnership (if applicable) Anne Schilling joined the *-Combinat development team after meeting with Nicolas Thiéry in the international conference FPSAC in July 2006. Shortly after, Anne Schilling was invited for one month in Marne-la-Vallée, where she worked with Jean-Christophe Novelli on problems related to symmetric functions and started the discussion about implementation details for a crystal library in *-Combinat with Nicolas Thiéry. Later on, *-Combinat was chosen as research platform for a three year (2007-2010) NSF Focused Research Group under the lead of Anne Schilling and others; see http://garsia.math.yorku.ca/dokuwiki/doku.php?id=start. This project financed the visit of Nicolas M. Thiéry in Davis in 2007-2008 and in Spring 2009. This visit fueled an active research collaboration between UC Davis, Orsay, the University of Marne-la-Vallée and of Rouen. It was also the occasion to build an active software development collaboration, in particular with the University of Washington and Stanford University. The decision to migrate *-Combinat to Sage was taken during this period at the Mathematical Sciences Research Institute in Berkeley. 5.3 / Departments/units involved Math department, University of California at Davis, USA Math department, University of Washington in Seattle, USA Math department, University of Pennsylvania, USA Math department, University of Minnesota, USA Math department, Stanford University, USA Laboratoire de Mathématiques d'Orsay, Université Paris Sud, France Département d'informatique, Université de Rouen, France Institut Gaspard Monge, Université de Marne-la-Vallée, France Laboratoire Bordelais de Recherche en Informatique, Université Bordeaux 1, France 5.4 / Description of activites, including levels, timetable, and milestones Here are some of the key areas that we want to improve in Sage-Combinat: - Symmetric functions: this is the original flagship of Sage-Combinat; the current implementation is feature reach, but heavy refactoring is needed for further. - Enumerative combinatorics: Sage-Combinat contains more than one hundred predefined enumerated sets (partitions, permutations, ...). Deep refactoring and infrastructure work (combinatorial factories, bijections) is crucial for further extensions. - (affine) root systems, Coxeter and Weyl groups, Hecke algebras, generalization to pseudo-reflection groups. - Crystals, Lie algebras and their characters - Combinatorial Species - Posets - Infrastructure for combinatorial Hopf and Kac algebras, with noncommutative symmetric functions, ... - Representation theory of semigroups and finite dimensional algebras. For most of them, we have or will have soon a specific development plan (design, algorithmic, personnel). For example, the upcoming Sage days 20 at CIRM, in February 2009 will include sessions about root systems, Hecke algebras, and semi groups, with specialists of those fields on board (Andrew Mathas, author of Specht, Meinholf Geck, coauthor of the Chevie package for GAP, and Jean-Éric Pin, author of the SemiGroups package). As per *-Combinat's tradition, all the development work is done with a combination of a long term vision and of short term goals which are strongly tied to research needs. Hence, even though all the topics above will undoubtedly be needed at some point by the participants, it would be impossible, and in fact prejudicial, to set specific timelines. The main purpose of this PUF project is to obtain flexible funding for short to long term visits across the Atlantic. There are two typical scenarios there: in the first one, two or more researchers (student, postdoc, or faculty) are working on distinct research projects which require the same computational tool. A short visit or very focused workshop (3-8 people) will help them coordinate to setup the design and foundations. By nature such workshops cannot be planned long in advance; however experience gathered over the previous years calls for about two of them every year on each side of the Atlantic. In the second scenario, researchers gather to work together on a common research project which requires software development. This includes for example long visits of Tom Denton to Orsay (Spring 2010 and 2011), as part of his PhD (representation theory of crystals and monoids) coadvised by Schilling and Thiéry. Postdoc positions are also well suited for this, in particular since there is an exceptionally large pool of excellent candidates for postdocs in Orsay; this includes Jason Bandlow (symmetric functions), Brant Jones (crystals and Hecke algebras), Robert Miller (graphs), Steve Pon (affine Stanley symmetric functions), and Qiang Wang (posets, root systems). Reciprocally, Nicolas Borie (root systems, Hecke algebras, invariants) will be available in 2010-2011 for a postdoc in Davis. All of them are regular contributors to Sage, and have expressed great interest in participating in this project. Parallel to this, regular workshops gathering the whole community will be organized, including a yearly Sage-Combinat satellite workshops to FPSAC, the primary international conference in algebraic combinatorics. Those workshops focus on coding sessions in an extreme programming setup, and introducing new users and developers to the system. They also are the occasion to set and advertise important milestones in the development. The previous such workshop was held in July 2009 at RISC in Austria (http://www.risc.uni-linz.ac.at/about/conferences/fpsac2009/), and gathered 30 researchers. The upcoming ones are: - FPSAC'10: San Francisco, USA, 2010 - FPSAC'11: Reykjavik, Iceland, 2011 - FPSAC'12: Nagoya, Japon, 2012 - FPSAC'13: Paris, France, 2013 The collaborative nature of the project requires advanced software development tools (ticket server, distributed version control), as well as heavy computational resources (compilation, regression testing, time or memory demanding calculations). So far, we have been using a server courtesy of the Sage team at the University of Washington (combinat.sagemath.org). Scaling further will require its replacement by a modern machine, which the Sage team agreed to host as part of the Sage computation farm (which includes four GNU/Linux servers with 24 cores and 128Gb of RAM). Unused resources will be made available to the Sage-Combinat and Sage community at large. The Sage team is committed to the ongoing administration of this server so that it will continue to be a resource for the Sage-Combinat community well after the end of this project (see the attached letter by William Stein). Budget rationale: The main lines of the PUF-funded part of the budget follows the activities listed above. This include one postdoc to France in Year 1 ($60000), one post doc to the US in Year 2 ($45000), half a postdoc to France in Year 3 ($40000), the purchase of a Sage-Combinat server ($20000), regular funding for Sage-Combinat workshops and meetings, software development laptops for the long term visitors. It would have been desirable to purchase the server right at the start of the project, but the exceptional situation for postdocs (due to the current state of the job market in the US) convinced us to hire in priority a postdoc to France. Most of the cofunding consists of the salaries of the main participants N. M. Thiéry (1/2), F. Hivert (1/2), Nicolas Borie (1/2), Anne Schilling (...), TODO: other people in Davis proportionally to their involvement in the project, as well as the associated overhead. We did not include in the budget some other major sources of cofunding that are not yet secured. For example, the planned budget of the NSF-FRG project "Combinatorics of crystals: geometric, physical, and computational applications" which was submitted in September 2009, includes cofunding of Sage-Combinat workshops and small meetings, laptops for software development, postdocs involved in the development of Sage-Combinat, etc. We also expect cofunding for Tom Denton's stay in France from the American embassy and from the "Île de France" Région. Finally, Sage-Combinat will be used in a variety of research projects, which will fund personnel to participate to Sage-Combinat's development and workshops. We did not include either the contribution \emph{in kind} of the University of Seattle through the hosting and administration of the Sage-Combinat server, which is extremely valuable yet hard to estimate. 5.5 / Description of how the project will be sustained after the grant period A major policy of *-Combinat is that its core developers have permanent positions. In general, all the code is written by researchers for their own research; therefore this activity is an integral part of their research work. At the same time the code is made visible and useable to others through the open-source environment. This development model has proved its pertinence and validity over the eight years of MuPAD-Combinat development, and by the time PUF will be over Sage-Combinat will have reached its cruise speed. Further development will then occur as part of many standard research projects. 5.6 / If exchanges are INVOLVED, housing and other arrangements 5.7 / Originality, innovativeness of the project There is a long tradition of software packages for algebraic combinatorics, and to name but a few: - SF, posets, coxeter/weyl (J. Stembridge, University of Michigan) - Symmetrica (University of Bayreuth) - ACE, mu-EC (University of Marne-la-Vallée) - combstruct, gfun, ... (INRIA) Each of those packages is developed by a small university team, if not a single person, to tackle (very efficiently!) a specific problem (symmetric functions, decomposable objects, generating series, ...). The originality of *-Combinat lies in the following simultaneous focus: - Offer a wide variety of interoperable and extensible tools, integrated in a general purpose mathematical software, as needed for daily computer exploration in algebraic combinatorics - Be developed by a community of researchers spread around the world and across institutions Reaching this scale is a true challenge, as there is a simultaneous need for mathematical and algorithmic expertise and for strong computer science experience, in particular concerning the design and the development model. For example, *-Combinat puts great emphasis in high level programing techniques (object orientation and polymorphism, iterators, functional programming) to obtain concise, expressive, and easy to maintain code. The migration to Sage is the occasion to reach yet another scale, with a wider community and a long desired interoperability with tools from other areas of mathematics (e.g. fast sparse exact linear algebra, group theory, ...). This migration also makes *-Combinat into the first large scale top-to-bottom open source package for algebraic combinatorics. 6 / OUTCOMES OF THE PROJECT 6.1 / Expected outcomes of this project: Joint and dual degrees, educational initiatives, PUBLICATIONS; COMMUNICATIONS; symposiums - Coadvised PhD (and possible dual degree) for Tom Denton (Orsay and UC Davis). In general, all the mobility will be very beneficial to the students and postdocs. - In keeping with the *-Combinat tradition, all the software development is associated to mathematical research and leads to a continuous stream of joint research publications. - All the code produced by the Sage-Combinat community is released as open source and integrated into Sage. This will give indirectly a substantial push to the Sage project which has an enormous potential for research and teaching at all university levels, as well as industrial applications. - Yearly large Sage-Combinat workshop, and regular smaller meetings. 6.2 / Regional perspectives: Existing or PLANNED PARTICIPATION in European/ North American programs; names and partners 6.3 / Other international perspectives The NSF-FRG projects are international cooperative research ventures, with core group members located in Canada, the United States, Chile, and France, and interdisciplinary, involving mathematicians, physicists, and computer scientists. 6.4 / Present or considered Industrial Perspectives MuPAD-Combinat has been used for statistical software testing, but was put aside recently due to licensing issue. The migration to an open source platform will solve this, and open the door to further applications. 6.5 / Monitoring of the partnership (suggested internal steps/procedures) All the code is shared via a public mercurial patch queue server (http://combinat.sagemath.org/patches), and is immediately available as open source. Stable patches are integrated into Sage after a formal review process, and can be monitored via the Sage trac server (http://trac.sagemath.org/). The overall development progress and the induced publications will be tracked on the Sage-Combinat Wiki (http://wiki.sagemath.org/combinat). 7 / ADDITIONAL INFORMATION (for joint research projects only) Additional information can be uploaded together with the application 7.1 / TEAMS’ PRESENTATIONS U.S : NAMES AND SHORT BIOS University of California at Davis: Anne Schilling * University of California at Davis, Professor 2006-current University of California at Davis, Associate Professor 2004-2006 University of California at Davis, Assistant Professor 2000-2004 Massachusetts Institute of Technology, CLE Moore Instructor 1999-2001 University of Amsterdam, postdoc 1997-1999 Brant C. Jones * University of California at Davis, VIGRE Assistant Professor, 2007-present University of Washington, PhD, 2002-2007 Synygy Inc. (Chester, PA), Senior Software Developer, 2002 PricewaterhouseCoopers (Fort Lee, NJ), Computer Systems Consultant, 1997-2001 Bard College, B.A. in Mathematics, 1993-1997 Andrew S. Berget * University of California, Davis. VIGRE Postdoctoral Fellow (2009-) University of Minnesota, PhD (2004-2009) Wang Qiang * University of California at Davis, graduate student 2004-2010 San Jose State University, mathematics student 2002-2004 Software Engineer 1994-2001 Dalian University of Technology, China, B.E. in Software Engineering 1990-1994 Steve Pon * University of California at Davis, PhD, 2005-2010 University of California at San Diego, B.A. mathematics 2004 Tom Denton * University of California at Davis, graduate student 2006-current University of Oregon, mathematics student 2003-2006 University of Washington in Seattle: Sara Billey * University of Washington in Seattle, associate professor, 2003-present Massachusetts Instituted of Technology, assistant/associate professor, 1998-2003 Massachusetts Instituted of Technology, postdoc, 1994-1998 University of California at San-Diego, PhD, 1994 William Stein * Founder and head of Sage UW, Assoc. Professor (with tenure), 2006-present, UCSD, Assoc. Professor (with tenure), 2005-2006 Harvard University, Benjamin Peirce Assistant Professor, 2001-2005 Harvard University, NSF Postdoc, 2000-2001 UC Berkeley, 1995-2000 Andrew Crites University of Washington, graduate teaching assistant, 2005-current Mike Hansen Translator of 30k lines of MuPAD-Combinat code to Sage University of Washington, graduate student, 2008-2009 Robert L. Miller * University of Washington, PhD, 2005-present Syracuse University, 2001-2005 University of Pennsylvania: Jason Bandlow * University of Pennsylvania, lecturer, 2008-2011 University of California at Davis, NSF postdoc, 2007-2008 University of California at San-Diego, PhD, 2007 University of Minnesota: Vic Reiner * University of Minnesota, professor, 2001–present University of Minnesota, associate professor, 1997–2001 University of Minnesota, assistant professor, 1993–1997 University of Minnesota, Dunham Jackson assistant professor, 1990–1993 Massachusetts Institute of Technology, Ph.D. in Mathematics 1986–1990 Stanford University: Daniel Bump * Professor of Mathematics, Stanford 1995-present Associate Professor, Stanford 1990-1995 Assistant Professor, Stanford 1986-1990 Member, Institute for Advanced Study (Princeton) 1985-1986 Lecturer, The University of Texas (Austin) 1983-1985 PhD 1982 The University of Chicago France : NAMES AND SHORT BIOS Université Paris Sud: Nicolas M. Thiéry * Habilitation à diriger des recherches, December 2008 University of California at Davis, researcher, 2007-2008 and Spring 2009 Université Paris Sud, maître de conférences, 2004-current IDEALX, Senior software developer, spring 2004 Université Lyon I, maître de conférences, 2001-2004 Colorado School of Mines, Postdoc, 1999-2000 Université Lyon I, PhD, 1996-1999 École Normale Supérieure (Paris), 1992-1996 Nicolas Borie * Université Paris Sud, graduate student 2008- Université de Rouen: Florent Hivert * Cofounder of *-Combinat Professor, Université de Rouen, 2005-present Habilitation à diriger des recherches, December 2004 Independent University of Moscou, Russia, chargé de recherches CNRS, 2003-2004 Université de Marne-la-Vallée, maître de conférences, 1999-2005 Université de Marne-la-Vallée, PhD, 1996-1999 École Normale Supérieure (Paris), 1991-1995 Université de Marne-la-Vallée: Jean-Christophe Novelli * Université de Marne-la-Vallée, professeur, 2007-present Independent University of Moscou, Russia, détaché du CNRS, 2002-2003 Université de Marne-la-Vallée, chargé de recherche CNRS, 1999-2007 Habilitation à diriger des recherches, September 2001, Université Paris VI, PhD, 1995-1999 École Normale Supérieure (Paris), 1993-1997 Adrien Boussicault* Université de Marne-la-Vallée, PhD, 2005-2009 Marc Sage* Université de Marne-la-Vallée, graduate student, 2007-current École Normale Supérieure 2004-2008 Pierre Loic Meliot* Université de Marne-la-Vallée, graduate student, 2007-current École Normale Supérieure 2004-2008 Université Bordeaux 1: Valentin Feray Université Bordeaux 1, chargé de recherche CNRS, 2009-current Université de Marne-la-Vallée, PhD, 2006-2009 École Normale Supérieure 2003-2007 7.2 / EQUIPMENT AVAILABLE FOR THE PROJECT us: Sage computational farm at Seattle (sagemath.org), which includes four GNU/Linux servers with 24 cores and 128Gb of RAM. france: N/a 7.3 /Significant publications relative to the project us: - Florent Hivert, Anne Schilling, and Nicolas M. Thiéry. Hecke group algebras as degenerate affine Hecke algebras. Journal of Combinatorial Theory, Series A 116 (2009) 844--863 http://arxiv.org/abs/0804.3781 - Jason Bandlow, Anne Schilling, and Nicolas M. Thiéry. On the uniqueness of promotion operators on tensor products of type a crystals. Algebraic Combinatorics, to appear ( arXiv:0806.3131 [math.CO] ) http://arxiv.org/abs/0806.3131 - Anne Schilling Combinatorial structure of Kirillov-Reshetikhin crystals of type D_n(1), B_n(1), A_{2n-1}(2), J. Algebra 319 (2008) 2938-2962, http://arxiv.org/abs/0704.2046 - Brant Jones and Anne Schilling Affine structures and a tableau model for E_6 crystals preprint arXiv:0909.2442 [math.CO], submitted. FRANCE: - Florent Hivert and Nicolas M. Thiéry MuPAD-Combinat, an open-source package for research in algebraic combinatorics. Sém. Lothar. Combin.,51 :Art. B51z, 70 pp. (electronic), 2004. http://igd.univ-lyon1.fr/~slc/wpapers/s51thiery.html - Anne Schilling and Jean-Christophe Novelli The forgotten monoid RIMS Kokyuroku Bessatsu B8 (2008) 71-83 http://arxiv.org/abs/0706.2996 - Tom Denton, Florent Hivert, Anne Schilling, Nicolas M. Thiéry The representation theory of J-trivial monoids. in preparation