This is the annual report for SCREMS.12William Stein:34Purchased and maintain the SCREMS cluster. Do research on elliptic5curves and modular forms using the SCREMS hardware. Creating and6sharing databases, and designing, implementing, testing, and7distributing free open source software as part of Sage using this8hardware.9102008-2009:1112* computed all newforms of weight 2 and gamma0 level up to 3200, of13prime level up to 10000, and of various other weights and14characters.1516* Created the http://sagenb.org that runs on this hardware and17allows people to use the Sage software over the web. This18supports computational work by many thousands of people.1920* computed several additional terms for the Sloane sequence A1647832122* Computation of torsion subgroups of modular abelian varieties23using new algorithm2425* Computation of modular degrees and congruence moduli for joint26paper with Ribet and Agashe2728* Computation of database of Brandt modules2930* Tables of p-adic L-series and p-adic regulators needed to apply31Iwasawa theory to verification of the Birch and Swinnerton-Dyer32conjecture in specific cases.33342009-2010:3536* Computed newforms up to level 5500 and weight 23738* Greatly expanded the power of http://sagenb.org; now there are39over 32,000 users.4041* Major finding: Carried out the first ever computational42verification of Kolyvagin's conjecture (for several dozens curves)43-- this was a major computational project requiring hundreds of44hours of CPU time, done with help from Jennifer Balakrishnan.4546* Major finding: Jointly with Sheldon Kamienny and Michael Stoll,47carried out a new computational classification of primes p such48that there is an elliptic curve over a quartic field with a49torsion point over order p. This extends Mazur's classical result50over QQ to all quartic fields.5152* Did substantial work porting Sage to Microsoft Windows on the53SCREMS hardware.5455* Publications:5657* Heegner Points on Rank Two Elliptic Curves, preprint,58http://wstein.org/papers/kolyconj2/5960* Toward a Generalization of the Gross-Zagier Conjecture,61International Mathematics Research Notices 2010; doi: 10.1093/imrn/rnq075626364Robert Miller:65662008-2010:6768* Computational verification of the BSD formula for 16725 curves/QQ69of rank 0 and 1 of conductor up to 5000.7071* Publication: his Ph.D. thesis7273* Web resources:74- a database of codes: http://rlmiller.org/de_codes/75- Large databases of Heegner indexes and other BSD data... (not online yet)7677Minh Nguyen:7879* Used the SCREMS hardware for developing and testing software for80cryptography education. The code is now part of the Sage standard library.8182* Wrote an undergraduate honours thesis as listed at:83http://www.sagemath.org/library-publications.html84The thesis explicitly acknowledges my use of the Sage cluster in85developing and testing the code described in the thesis itself.86878889Jennifer Balakrishnan:90912008-2010:9293* Computational verification of Kolyvagin's conjecture for a rank 3 curve9495* Computation of p-adic L-series of Jacobians of hyperelliptic modular curves9697* Computation of p-adic regulators of curves using techniques based on Coleman integration9899* Everything going into my PhD thesis (2011) has been done on sage.math!100- Single Coleman integrals from non-Weierstrass/Weierstrass points on101hyperelliptic curves102- Local p-adic heights for hyperelliptic curves via Coleman integration103- double Coleman integrals on hyperelliptic curves104- experiments with the Chabauty method105106* Major finding: fixed subtle error in Kim's nonabelian Chabauty method;107computations led to appendix/erratum to his original JAMS article108109* Publications:110111* "Explicit Coleman integration for hyperelliptic curves," ANTS IX112Proceedings, Springer LNCS 6197 (with Robert Bradshaw and Kiran113Kedlaya); explicitly acknowledged NSF support114115* Appendix and erratum to "Massey products for elliptic curves of116rank 1" by Minhyong Kim (with Kiran Kedlaya and Minhyong Kim),117to appear in JAMS, acknowledged William Stein (but not NSF118explicitly).119120Andrey Novoseltsev:1211222009-2010:123124* Relations between mirror maps for local Calabi-Yau manifolds and125their compactifications. This work (joint with Matthew Ballard,126Adrian Clingher, Charles Doran, Jacob Lewis) is related to the127Hodge Conjecture.128129* Geometric transitions leading to the missing class in Doran-Morgan130classification of real variation of Hodge structure coming from131one-parameter families of Calabi-Yau manifolds (joint work with132Charles Doran and Jacob Lewis).133134* In addition, the base framework for toric varieties was developed135and is now posted on Sage Trac with plans to merge it in the near136future and considerably improve the functionality by the end of137the summer.138139* Publications: Results of another one were posted on arXiv and140accepted for publication in Contemporary Mathematics Proceedings141of AMS during the last year:142143* "Closed form expressions for Hodge numbers of complete144intersection Calabi-Yau threefolds in toric varieties,"145Charles F. Doran, Andrey Y. Novoseltsev, arXiv:0907.2701v1146[math.CO], NSF support acknowledged.147148149David Kirkby:150151Technical support personnel.1521532009-2010:154155* Fully ported Sage to Solaris. This was a major undertaking that156indirectly resulted in the porting of a large amount of standard157open source mathematics software and libraries to Solaris, which158makes them available to a wider range of users.159160Birne Binegar:161162Running computations related to representation theory (the ATLAS project).1631642008-2009:165166* Computed the Kazhdan-Lusztig-Vogan polynomials for all simple167complex Lie algebras, with the exception of complex E8, viewed as168real Lie algebras up to real rank 16. Computed the169Kazhdan-Lusztig-Vogan polynomials for SL(10,C) (real rank 20).170171* Computed the W-graph structure for the set of irreducible172admissible representations of regular integral infinititesimal173character for the real forms of the simple real Lie groups up to174rank 8.175176* Computed the Weyl group representations carried by the W-cells of177irreducible admissible representations of regular infinitesimal178character of the exceptional real Lie groups.179180* Computed the associated varieties of the annihilators of181irreducible admissible representations of the exceptional real Lie182groups.183184* Enumerated the set of irreducible admissible representations of185regular integral infinitesimal character of the exceptional real186groups and determined exactly when two irreducible admissible187representations of regular infinitesimal character share the same188primitive ideal.1891902009-2010:191192* I've computed the Kazhdan-Lusztig-Vogan polynomials for real193forms G_R of simple complex Lie groups up to rank 8. From this194data I've also computed, for each real form G_R, I've computed195196- the W-graph structure of the set G_R^ of equivalence classes of197irreducible admissible representations of G_R with regular198integral infinitesimal character199- the partitioning of G_R^ into cells of irreducible200representations sharing the same associated variety201- the partitioning of G_R^ cells into subcells of representations202sharing the same infinitiesimal character203- the cell representations of the Weyl group carried by the cells204of G_R^ (via the coherent continuation action)205206* Websites:207- www.math.okstate.edu/~binegar/research.html208- http://lie.math.okstate.edu/UMRK/UMRK.html209210* Databases:211212* Constructed a PostgreSQL database UMRK (Unipotent Muffin213Research Kitchen) which houses all sorts of computational data214concerning simple Lie algebras, their subalgebras, their Weyl215groups, and their real forms. This data is accessible online216via simple web query forms (see the second link listed above).217218219220Chuck Doran:221222Running computations related to geometry, including Picard-Fuchs223equations, families of curves and surfaces, tropical varieties, toric224ideals, Fano compactifications, and K3 surfaces.225226Findings:227228* Computing Picard-Fuchs equations of families of curves and surfaces229230* Computing normal forms for anticanonical hypersurfaces in toric231Fano varieties232233* Computing elliptic fibrations on toric K3 surfaces234235* Computing tropical varieties236237* Finding equations for elliptic space curves using invariant theory238239* Constructed list of toric Fano compactifications of several2403-dimensional orbifolds241242* Searched for 4-dimensional toric Fano varieties with special243properties244245* Extensively tested and experimented with closed-form formulas for246Hodge numbers of complete intersections in toric varieties247248* Found all torically induced elliptic fibrations of toric K3 surfaces249250251Michael Rubinstein:252253Running computations related to computing zeros of L-functions.254255* Verify the Riemann Hypothesis for the first few hundred zeros for256all L-functions associated to the 1/2 million elliptic curves in257Cremona's database, and millions of zeros for the first few dozen258elliptic curves.259260* Verify the moment conjecture for quadratic Dirichlet L-functions261for |d| < 10^10 (I will eventually get to 10^11). To get up to X262is an O(X^{3/2}) computation, so this would not have been possible263without a modern and powerful multicore machine.264265* As a platform on which to develop and test code for computing with266L-functions. Compiling goes really quick on mod.math and allows me267to work more efficiently.268269270Robert Bradshaw:2712722009-2010:273274* The "trillion triangles" congruent number search that made good275use of the hardware (made the popular press, and featured on the276NSF website).277278* Computational verification of the Birch and Swinnerton-Dyer conjecture279to 10,000 bits for a rank-2 curve.280281* Wrote a Ph.D. thesis on L-functions, using these machines.282283* Wrote paper on Coleman integration too:284http://www.ants9.org/accepted.html .285286287Randall Rathbun:2882892009-2010:290291* Finding perfect parallelepipeds, and corresponding with Clifford292Reiter on this. Dr. Richard K Guy is being kept informed about293this project, which is a number theory question in section D18 of294UPINT, Diophantine Equations. Reiter has published, but I will295probably write a paper to Experimental Mathematics or some other296internet journal. I don't think anyone else is working on this,297and Clifford has acknowledged that the computer power has left298him in the dust so he appreciates the searches.299300301Marshall Hampton:3023032009-2010:304305Working on proving finiteness of central configurations in the306five-body problem in a certain generic sense.307308* Computing Groebner bases for a celestial mechanics problem. The309amount of RAM on the SCREMS-purchased hardware is crucial for this;310he doesn't have any other comparable resources I could do those on.311Already these computations have given me a (computer-assisted)312proof of the finiteness of central configurations in the five-body313problem in a certain generic sense.314315316317Fredrik Johansson:318319Developing the mpmath library, which is an open source Python library320for computing special functions (and much more), which is important321for computing with L-functions and modular forms. This work was funded322by my NSF FRG DMS-0757627.323324* During both Summer 2009 and Summer 2010, Fredrik developed the325mpmath Python library. Much of the testing and computation took326place on the computer cluster that was purchased with the current327SCREMS grant: Fredrik writes "Using multiprocessing, the time for328the new torture test suite (about which see blog) dropped from 11329minutes to 28 seconds (which could be even less by partitioning330the tests into smaller pieces). This is very handy!"331Fredrik's salary during this time is paid for by the PI's NSF332FRG DMS-0757627.333334Fredrik Strömberg:335336Fredrik is the world's leading expert in large scale computations with337Maass forms. He has done many computational projects using the SCREMS338hardware, in connection with the PI's NSF FRG DMS-0757627.339340* Computation of vector-valued Poincare series for the Weil341representation with application to convolution-type L-series for342Siegel modular forms of genus 2 (joint with Nathan Ryan and Nils343Skoruppa)344345* Have also computed more than 1500 examples of Maass waveforms346(with eigenvalues and at least 1000 Fourier coefficients) for347Gamma_0(N) with square-free N up to 119 and with >20 examples for348all N except 51 and 77 (where I have 12 and 13 examples)349350* Major finding: Disproved a conjecture of Andrianov (for genus 2351and even weights between 20 and 30) by proving that the352convolution-type L-series of two "interesting forms" (i.e. not in353the Maass Spezialshar) is linearly independent from the Spinor354L-functions (of all Siegel forms in of the same genus and weight).355356Sourav Sen Gupta:357358Graduate student helping with computational projects related to359research of Stein.360361* Computed the congruence graphs associated to modular abelian362varieties of level up to 500 and made a database.363364365Jacob Lewis:366367Graduate student helping with computational projects related to the368research of Doran.369370Georg Weber:371372Weber is a number theory Ph.D. who works at a bank in Germany, who373does computations related to Stein's research project using the SCREMS374hardware, and also contributes to the Sage project.375376* Computations of matrices of Hecke operators T_p for 'massive'377primes p (p > 10^10), e.g. for level N=53, using an algorithm he378developed.379380381Tom Boothby:382383Systems administer of the SCREMS cluster, which involves physically384organizing the hardware, maintaining the operating system, and385managing users. Runs computations in support of Stein's research386projects. Developing Sage software (e.g., release management).3873882008-2009:389390* Computed analytic order of Shafarevich-Tate group of a rank 2391elliptic curve to 10,000 bits of precision.392393* Compiled tables of data about newforms of level up to 10,000.3943952009-2010:396397* Computed modular symbols of weight 2 for conductor up to 5000,398extending previous computation by thousands of conductors -- also,399computed 10k Fourier coefficients for all modular forms of400conductor up to 4800, with computation ongoing.401402* Extended table of Birch and Swinnerton-Dyer quantities for modular403abelian varieties to conductor 300 (computation ongoing).404405* Computed discriminants of Hecke algebras of weight 2 modular forms406for level up to 1000, and factored all but two particularly tough407ones, extending previous table whose conductor bound was 389.408409* Computed component group of J0(N)(R) for N up to 1000, extending410previous table by 500.411412* Implemented record-breaking algorithm to multiply matrices of413characteristic 3 to be included in Sage project.414415* Implemented graph genus algorithm, greatly improving on previous416implementation in Sage.417418419420Martin Albrecht:421422Cryptography graduate student in London who frequently collaborates423with Stein on the Sage software, and makes extensive use of the SCREMS424hardware.4254262008-2009:427428* Experimentally verified the behaviour of algebraic-differential429cryptanalysis against the block cipher PRESENT.430431* Broke the key predistribution scheme of Zhang et al. from MobiHoc4322007 for practical parameters4334342009-2010:435436* Developed, tested and benchmarked fastest dense matrix437decomposition over GF(2)438439* Developed and tested algorithm for solving polynomial systems with440noise441442* Experimentally verified an attack against "Perturbation Based"443crypto systems444445* Experimentally verified hybrid attack strategies against block446ciphers447448* Papers:449450* Martin Albrecht and Clément Pernet. Efficient Decomposition of451Dense Matrices over GF(2), accepted for presentation at ECrypt452Workshop on Tools for Cryptanalysis 2010. available locally and453on bitbucket. 2010.454455* Martin Albrecht and Carlos Cid. Cold Boot Key Recovery using456Polynomial System Solving with Noise (extended abstract)457accepted for presentation at 2nd International Conference on458Symbolic Computation and Cryptography. 2010.459460* Martin Albrecht, Carlos Cid, Thomas Dullien, Jean-Charles461Faugère and Ludovic Perret. Algebraic Precomputations in462Differential Cryptanalysis accepted for presentation at ECrypt463Workshop on Tools for Cryptanalysis 2010. 2010.464465* Martin Albrecht, Craig Gentry, Shai Halevi and Jonathan466Katz. Attacking Cryptographic Schemes Based on "Perturbation467Polynomials" in Proceedings of the 16th ACM Conference on468Computer and Communications Security. pre-print available at469http://eprint.iacr.org/2009/098. 2009.470471* Martin Albrecht, Algorithmic Algebraic Techniques and their472Application to Block Cipher Cryptanalysis, PhD thesis,473submission date: July 2010474475* Web sites:476477* http://m4ri.sagemath.org and478* http://www.bitbucket.org/malb/algebraic_attacks479480* Software:481482* The M4RI library and http://www.bitbucket.org/malb/algebraic_attacks483484Gonzalo Tornaria:485486Mathematics researcher who has computed state-of-the-art487data about specific modular forms using cutting edge techniques that488push the SCREMS hardware to its limits. He also attends many of the489workshops related to this grant.4904912008-2009:492493* computed the 12 series for the weight 3/2 lift of 36A each to 10^10 places494495* computed the congruent numbers up to 2e10, assuming BSD (this has496since been recently been pushed to 10^12).497498Dan Drake:499500Mathematics researcher doing combinatorics who frequently501contributes to the Sage project.502503* counted binary matrices that square to zero to correct a mistake504in the Online Encyclopedia of Integer Sequences, sequence A001147505506507Mark Watkins:508509Postdoc who is working on computations involving computing large510numbers of coefficients of modular forms in support of the number511theory research projects.512513* Has done numerous computations using the SCREMS hardware that took514advantage of the huge RAM available on these computers. E.g., work515on the congruent number problem, tables of L-functions and data about516elliptic curves, etc.517518Craig Citro519520Postdoc working on computations involving databases of modular forms.521522Ondrej Certik523524Graduate student developing software and testing code for the525FEMhub open source finite element method library (http://femhub.org/).526527528-----529530ACTIVITIES:531532The goal of this project is to collect data about L-functions and533modular forms, compute new data about objects at the crossroads of534geometry and mathematical physics, compute data about representations535of Lie groups, and support the Sage mathematical software project.536537All involved groups have carried out numerous substantial computations538on the SCREMS hardware, the Sage software project has undergone539massive growth and testing using this hardware, and public web pages,540databases, wikis, and interactive online computations.541542FINDINGS:543544We have obtained large new databases of modular forms, verified545predictions of the Generalized Riemann Hypothesis in many new cases,546computed new invariants of Lie groups, and developed and tested state547of the art algorithms in number theory and cryptography. Below we548give a long (but non-comprehensive) list of specific findings in549different areas. This SCREMS grant resulted in the purchase of a lot550of powerful computers, with about 180 users, many who are computing551things that aren't all reported.552553[Here I copied all the findings bullet points from above for people.]554555556Training and Development:557558Because the SCREMS-purchased computers are very high end, with55924-processing cores each, several people who have worked on the560project have become much more adept at parallel computing. Also,561general software engineering skills have been enhanced for dozens of562mathematicians, by working on the Sage math software system. Also,563the free open source software that we are developing on this hardware564is being used by thousands of mathematicians to help with their565research (we have about 5000 downloads of Sage per month).566567Outreach:568569The Sage project -- which is developed and hosted on this SCREMS570hardware -- does creative community outreach. For example, Stein has571given internal talks to Sun Microsystems and Boeing about the Sage572project, and recently ran many workshops on the use of Sage that used573the SCREMS hardware during the workshop -- e.g., one was in in574Barcelona, Spain and another was at a regional MAA meeting in575Washington State.576577The public Sage notebook server (http://sagenb.org) is available to578anybody in the world to use, and provides the full power of Sage.579This SCREMS hardware is critically important to making that server580available.581582Contributions within Discipline – What?583584Using the SCREMS-funded hardware, we have computed data in number585theory, geometry, and representation that will provide a basis for586much future research. We have also developed much new software in587these research areas that will be used by researchers.588589590Contributions to Other Disciplines591592The Sage software, which we develop and share using the SCREMS-funded593hardware, is a contribution to all areas of mathematics.594595Much of the data we've computed about zeros of L-functions is of596potential relevance in physics (e.g., quantum dynamics), as is the597data about representations of Lie groups.598599Contributions to Human Resource Development600601Students who have contributed to the Sage project or worked on the602research computations that have been done on this hardware, have often603learned advanced software engineering techniques. Since so many604people contribute to the Sage project (at this point, over 200, mostly605grad students), we are in fact training a whole generation of606mathematicians to be significantly more sophisticated at mathematical607software engineering.608609Contributions to Resources for Research and Education610611The databases and wiki's that come out of this project are freely612available resources for students and researchers around the world.613614==============================================615616==============================================617618619620Exactly what actually got submitted:621622623Project Reporting ANNUAL REPORT FOR AWARD # 0821725624U of Washington625SCREMS: The Computational Frontiers of Number Theory, Representation Theory, and Mathematical Physics626627Participant Individuals:628CoPrincipal Investigator(s) : Birne T Binegar; Charles F Doran; Michael Rubinstein629Graduate student(s) : Fredrik Johansson630Other -- specify(s) : Georg S Weber631Graduate student(s) : Sourav Sen Gupta; Jacob Lewis632Senior personnel(s) : Marshall Hampton633Graduate student(s) : Tom Boothby; Martin Albrecht634Senior personnel(s) : Gonzalo Tornaria; Dan Drake; Mark Watkins635Post-doc(s) : Craig Citro636637Partner Organizations:638639Other collaborators:640641There are dozens of people -- too numerous to list -- who make use of642the SCREMS hardware in various ways who were not listed above, and some643contribute directly to the SCREMS proposed project goals.644645646Activities and findings:647648Research and Education Activities:649650The goal of this project is to collect data about L-functions and modular651forms, compute new data about objects at the crossroads of geometry and652mathematical physics, compute data about representations of Lie groups,653and support the Sage mathematical software project.654655All involved groups have carried out numerous substantial computations656on the SCREMS hardware, the Sage software project has undergone massive657growth and testing using this hardware, and public web pages, databases,658wikis, and interactive online computations.659660661Findings:662663We have obtained large new databases of modular forms, verified predictions664of the Generalized Riemann Hypothesis in many new cases, computed new665invariants of Lie groups, and developed and tested state of the art algorithms666in number theory and cryptography. Below we give a long (but non-comprehensive)667list of specific findings in different areas. This SCREMS grant resulted668in the purchase of a lot of powerful computers, with about 180 users,669many who are computing things that aren't all reported.670671STEIN:672673* computed all newforms of weight 2 and gamma0 level up to 3200, of674prime level up to 10000, and of various other weights and675characters.676677* Created the http://sagenb.org that runs on this hardware and678allows people to use the Sage software over the web. This679supports computational work by many thousands of people.680681* computed several additional terms for the Sloane sequence A164783682683* Computation of torsion subgroups of modular abelian varieties684using new algorithm685686* Computation of modular degrees and congruence moduli for joint687paper with Ribet and Agashe688689* Computation of database of Brandt modules690691* Tables of p-adic L-series and p-adic regulators needed to apply692Iwasawa theory to verification of the Birch and Swinnerton-Dyer693conjecture in specific cases.694695696BINEGAR:697698* Computed the Kazhdan-Lusztig-Vogan polynomials for all simple699complex Lie algebras, with the exception of complex E8, viewed as700real Lie algebras up to real rank 16. Computed the701Kazhdan-Lusztig-Vogan polynomials for SL(10,C) (real rank 20).702703* Computed the W-graph structure for the set of irreducible704admissible representations of regular integral infinititesimal705character for the real forms of the simple real Lie groups up to706rank 8.707708* Computed the Weyl group representations carried by the W-cells of709irreducible admissible representations of regular infinitesimal710character of the exceptional real Lie groups.711712* Computed the associated varieties of the annihilators of713irreducible admissible representations of the exceptional real Lie714groups.715716* Enumerated the set of irreducible admissible representations of717regular integral infinitesimal character of the exceptional real718groups and determined exactly when two irreducible admissible719representations of regular infinitesimal character share the same720primitive ideal.721722723DORAN/LEWIS:724725* Computing Picard-Fuchs equations of families of curves and surfaces726727* Computing normal forms for anticanonical hypersurfaces in toric728Fano varieties729730* Computing elliptic fibrations on toric K3 surfaces731732* Computing tropical varieties733734* Finding equations for elliptic space curves using invariant theory735736* Constructed list of toric Fano compactifications of several7373-dimensional orbifolds738739* Searched for 4-dimensional toric Fano varieties with special740properties741742* Extensively tested and experimented with closed-form formulas for743Hodge numbers of complete intersections in toric varieties744745* Found all torically induced elliptic fibrations of toric K3 surfaces746747748RUBINSTEIN:749750751* Verify the Riemann Hypothesis for the first few hundred zeros for752all L-functions associated to the 1/2 million elliptic curves in753Cremona's database, and millions of zeros for the first few dozen754elliptic curves.755756* Verify the moment conjecture for quadratic Dirichlet L-functions757for |d| < 10^10 (I will eventually get to 10^11). To get up to X758is an O(X^{3/2}) computation, so this would not have been possible759without a modern and powerful multicore machine.760761* As a platform on which to develop and test code for computing with762L-functions. Compiling goes really quick on mod.math and allows me763to work more efficiently.764765766HAMPTON:767768769* Computing Groebner bases for a celestial mechanics problem. The770amount of RAM on the SCREMS-purchased hardware is crucial for this;771he doesn't have any other comparable resources I could do those on.772Already these computations have given me a (computer-assisted)773proof of the finiteness of central configurations in the five-body774problem in a certain generic sense.775776777JOHANSSON:778779* During Summer 2009, Fredrik developed the mpmath Python library.780Much of the testing and computation took place on the computer781cluster that was purchased with the current SCREMS grant: Fredrik782writes 'Using multiprocessing, the time for the new torture test783suite (about which see blog) dropped from 11 minutes to 28 seconds784(which could be even less by partitioning the tests into smaller785pieces). This is very handy!'786787788GUPTA:789790* Computed the congruence graphs associated to modular abelian791varieties of level up to 500 and made a database.792793794WEBER:795796* Computations of matrices of Hecke operators T_p for 'massive'797primes p (p > 10^10), e.g. for level N=53, using an algorithm he798developed.799800BOOTHBY:801802* Computed analytic order of Shafarevich-Tate group of a rank 2803elliptic curve to 10,000 bits of precision.804805* Compiled tables of data about newforms of level up to 10,000.806807808ALBRECHT:809810* Experimentally verified the behaviour of algebraic-differential811cryptanalysis against the block cipher PRESENT.812813* Broke the key predistribution scheme of Zhang et al. from MobiHoc8142007 for practical parameters815816817818TORNARIA/HARVEY/BRADSHAW/WATKINS/HART:819820* computed the 12 series for the weight 3/2 lift of 36A each to 10^10821places822823* computed the congruent numbers up to 10^12, assuming BSD (this is824an major accomplishment that will likely lead to substantial publicity).825826827DRAKE:828829* counted binary matrices that square to zero to correct a mistake830in the Online Encyclopedia of Integer Sequences, sequence A001147831832833Training and Development:834835Because the SCREMS-purchased computers are very high end, with83624-processing cores each, several people who have worked on the837project have become much more adept at parallel computing. Also,838general software engineering skills have been enhanced for dozens of839mathematicians, by working on the Sage math software system. Also,840the free open source software that we are developing on this hardware841is being used by thousands of mathematicians to help with their842research (we have about 5000 downloads of Sage per month).843844845Outreach Activities:846847The Sage project -- which is developed and hosted on this SCREMS848hardware -- does creative community outreach. For example, Stein has849given internal talks to Sun Microsystems and Boeing about the Sage850project, and recently ran many workshops on the use of Sage that used851the SCREMS hardware during the workshop -- e.g., one was in in852Barcelona, Spain and another was at a regional MAA meeting in853Washington State.854855The public Sage notebook server (http://sagenb.org) is available to856anybody in the world to use, and provides the full power of Sage.857This SCREMS hardware is critically important to making that server858available.859860Journal Publications:861862Book(s) of other one-time publications(s):863864Other Specific Products:865866The hardware is valuable for hosting Cython, MPIR, M4RI, etc. as well as all the Sage stuff.867868Contributions:869870Contributions within Discipline:871872Using the SCREMS-funded hardware, we have computed data in number873theory, geometry, and representation that will provide a basis for874much future research. We have also developed much new software in875these research areas that will be used by researchers.876877878879Contributions to Other Disciplines:880881The Sage software, which we develop and share using the SCREMS-funded882hardware, is a contribution to all areas of mathematics.883884Much of the data we've computed about zeros of L-functions is of potential885relevance in physics (e.g., quantum dynamics), as is the data about representations886of Lie groups.887888889Contributions to Education and Human Resources:890891Students who have contributed to the Sage project or worked on the892research computations that have been done on this hardware, have often893learned advanced software engineering techniques. Since so many894people contribute to the Sage project (at this point, over 200, mostly895grad students), we are in fact training a whole generation of896mathematicians to be significantly more sophisticated at mathematical897software engineering.898899900901Contributions to Resources for Science and Technology:902903The databases and wiki's that come out of this project are freely904available resources for students and researchers around the world.905906907*** 2009 - 2010 ***908909910911