CoCalc Public Fileswww / screms / report-2010.txt
Author: William A. Stein
Compute Environment: Ubuntu 18.04 (Deprecated)
1This is the annual report for SCREMS.
2
3William Stein:
4
5Purchased and maintain the SCREMS cluster.  Do research on elliptic
6curves and modular forms using the SCREMS hardware.  Creating and
7sharing databases, and designing, implementing, testing, and
8distributing free open source software as part of Sage using this
9hardware.
10
112008-2009:
12
13  * computed all newforms of weight 2 and gamma0 level up to 3200, of
14    prime level up to 10000, and of various other weights and
15    characters.
16
17  * Created the http://sagenb.org that runs on this hardware and
18    allows people to use the Sage software over the web.  This
19    supports computational work by many thousands of people.
20
21  * computed several additional terms for the Sloane sequence A164783
22
23  * Computation of torsion subgroups of modular abelian varieties
24    using new algorithm
25
26  * Computation of modular degrees and congruence moduli for joint
27    paper with Ribet and Agashe
28
29  * Computation of database of Brandt modules
30
31  * Tables of p-adic L-series and p-adic regulators needed to apply
32    Iwasawa theory to verification of the Birch and Swinnerton-Dyer
33    conjecture in specific cases.
34
352009-2010:
36
37  * Computed newforms up to level 5500 and weight 2
38
39  * Greatly expanded the power of http://sagenb.org; now there are
40    over 32,000 users.
41
42  * Major finding: Carried out the first ever computational
43    verification of Kolyvagin's conjecture (for several dozens curves)
44    -- this was a major computational project requiring hundreds of
45    hours of CPU time, done with help from Jennifer Balakrishnan.
46
47  * Major finding: Jointly with Sheldon Kamienny and Michael Stoll,
48    carried out a new computational classification of primes p such
49    that there is an elliptic curve over a quartic field with a
50    torsion point over order p. This extends Mazur's classical result
51    over QQ to all quartic fields.
52
53  * Did substantial work porting Sage to Microsoft Windows on the
54    SCREMS hardware.
55
56  * Publications:
57
58       * Heegner Points on Rank Two Elliptic Curves, preprint,
59         http://wstein.org/papers/kolyconj2/
60
61       * Toward a Generalization of the Gross-Zagier Conjecture,
62         International Mathematics Research Notices 2010; doi: 10.1093/imrn/rnq075
63
64
65Robert Miller:
66
672008-2010:
68
69  * Computational verification of the BSD formula for 16725 curves/QQ
70    of rank 0 and 1 of conductor up to 5000.
71
72  * Publication: his Ph.D. thesis
73
74  * Web resources:
75     - a database of codes:   http://rlmiller.org/de_codes/
76     - Large databases of Heegner indexes and other BSD data... (not online yet)
77
78Minh Nguyen:
79
80  * Used the SCREMS hardware for developing and testing software for
81    cryptography education. The code is now part of the Sage standard library.
82
83  * Wrote an undergraduate honours thesis as listed at:
84       http://www.sagemath.org/library-publications.html
85    The thesis explicitly acknowledges my use of the Sage cluster in
86    developing and testing the code described in the thesis itself.
87
88
89
90Jennifer Balakrishnan:
91
922008-2010:
93
94  * Computational verification of Kolyvagin's conjecture for a rank 3 curve
95
96  * Computation of p-adic L-series of Jacobians of hyperelliptic modular curves
97
98  * Computation of p-adic regulators of curves using techniques based on Coleman integration
99
100  * Everything going into my PhD thesis (2011) has been done on sage.math!
101   - Single Coleman integrals from non-Weierstrass/Weierstrass points on
102     hyperelliptic curves
103   - Local p-adic heights for hyperelliptic curves via Coleman integration
104   - double Coleman integrals on hyperelliptic curves
105   - experiments with the Chabauty method
106
107  * Major finding: fixed subtle error in Kim's nonabelian Chabauty method;
108    computations led to appendix/erratum to his original JAMS article
109
110  * Publications:
111
112    * "Explicit Coleman integration for hyperelliptic curves," ANTS IX
113      Proceedings, Springer LNCS 6197 (with Robert Bradshaw and Kiran
114      Kedlaya); explicitly acknowledged NSF support
115
116    * Appendix and erratum to "Massey products for elliptic curves of
117      rank 1" by Minhyong Kim (with Kiran Kedlaya and Minhyong Kim),
118      to appear in JAMS, acknowledged William Stein (but not NSF
119      explicitly).
120
121Andrey Novoseltsev:
122
1232009-2010:
124
125  * Relations between mirror maps for local Calabi-Yau manifolds and
126    their compactifications. This work (joint with Matthew Ballard,
127    Adrian Clingher, Charles Doran, Jacob Lewis) is related to the
128    Hodge Conjecture.
129
130  * Geometric transitions leading to the missing class in Doran-Morgan
131    classification of real variation of Hodge structure coming from
132    one-parameter families of Calabi-Yau manifolds (joint work with
133    Charles Doran and Jacob Lewis).
134
135  * In addition, the base framework for toric varieties was developed
136    and is now posted on Sage Trac with plans to merge it in the near
137    future and considerably improve the functionality by the end of
138    the summer.
139
140  * Publications: Results of another one were posted on arXiv and
141    accepted for publication in Contemporary Mathematics Proceedings
142    of AMS during the last year:
143
144       * "Closed form expressions for Hodge numbers of complete
145         intersection Calabi-Yau threefolds in toric varieties,"
146         Charles F. Doran, Andrey Y. Novoseltsev, arXiv:0907.2701v1
147         [math.CO], NSF support acknowledged.
148
149
150David Kirkby:
151
152Technical support personnel.
153
1542009-2010:
155
156  * Fully ported Sage to Solaris.  This was a major undertaking that
157    indirectly resulted in the porting of a large amount of standard
158    open source mathematics software and libraries to Solaris, which
159    makes them available to a wider range of users.
160
161Birne Binegar:
162
163Running computations related to representation theory (the ATLAS project).
164
1652008-2009:
166
167  * Computed the Kazhdan-Lusztig-Vogan polynomials for all simple
168    complex Lie algebras, with the exception of complex E8, viewed as
169    real Lie algebras up to real rank 16.  Computed the
170    Kazhdan-Lusztig-Vogan polynomials for SL(10,C) (real rank 20).
171
172  * Computed the W-graph structure for the set of irreducible
173    admissible representations of regular integral infinititesimal
174    character for the real forms of the simple real Lie groups up to
175    rank 8.
176
177  * Computed the Weyl group representations carried by the W-cells of
178    irreducible admissible representations of regular infinitesimal
179    character of the exceptional real Lie groups.
180
181  * Computed the associated varieties of the annihilators of
182    irreducible admissible representations of the exceptional real Lie
183    groups.
184
185  * Enumerated the set of irreducible admissible representations of
186    regular integral infinitesimal character of the exceptional real
187    groups and determined exactly when two irreducible admissible
188    representations of regular infinitesimal character share the same
189    primitive ideal.
190
1912009-2010:
192
193   * I've computed the Kazhdan-Lusztig-Vogan polynomials for real
194     forms G_R of simple complex Lie groups up to rank 8. From this
195     data I've also computed, for each real form G_R, I've computed
196
197     - the W-graph structure of the set G_R^ of equivalence classes of
198       irreducible admissible representations of G_R with regular
199       integral infinitesimal character
200     - the partitioning of G_R^ into cells of irreducible
201       representations sharing the same associated variety
202     - the partitioning of G_R^ cells into subcells of representations
203       sharing the same infinitiesimal character
204     - the cell representations of the Weyl group carried by the cells
205       of G_R^ (via the coherent continuation action)
206
207   * Websites:
208     - www.math.okstate.edu/~binegar/research.html
209     - http://lie.math.okstate.edu/UMRK/UMRK.html
210
211   * Databases:
212
213     * Constructed a PostgreSQL database UMRK (Unipotent Muffin
214       Research Kitchen) which houses all sorts of computational data
215       concerning simple Lie algebras, their subalgebras, their Weyl
216       groups, and their real forms. This data is accessible online
217       via simple web query forms (see the second link listed above).
218
219
220
221Chuck Doran:
222
223Running computations related to geometry, including Picard-Fuchs
224equations, families of curves and surfaces, tropical varieties, toric
225ideals, Fano compactifications, and K3 surfaces.
226
227Findings:
228
229  * Computing Picard-Fuchs equations of families of curves and surfaces
230
231  * Computing normal forms for anticanonical hypersurfaces in toric
232    Fano varieties
233
234  * Computing elliptic fibrations on toric K3 surfaces
235
236  * Computing tropical varieties
237
238  * Finding equations for elliptic space curves using invariant theory
239
240  * Constructed list of toric Fano compactifications of several
241    3-dimensional orbifolds
242
243  * Searched for 4-dimensional toric Fano varieties with special
244    properties
245
246  * Extensively tested and experimented with closed-form formulas for
247    Hodge numbers of complete intersections in toric varieties
248
249  * Found all torically induced elliptic fibrations of toric K3 surfaces
250
251
252Michael Rubinstein:
253
254  Running computations related to computing zeros of L-functions.
255
256  * Verify the Riemann Hypothesis for the first few hundred zeros for
257    all L-functions associated to the 1/2 million elliptic curves in
258    Cremona's database, and millions of zeros for the first few dozen
259    elliptic curves.
260
261  * Verify the moment conjecture for quadratic Dirichlet L-functions
262    for |d| < 10^10 (I will eventually get to 10^11). To get up to X
263    is an O(X^{3/2}) computation, so this would not have been possible
264    without a modern and powerful multicore machine.
265
266  * As a platform on which to develop and test code for computing with
267    L-functions. Compiling goes really quick on mod.math and allows me
268    to work more efficiently.
269
270
272
2732009-2010:
274
275   * The "trillion triangles" congruent number search that made good
276     use of the hardware (made the popular press, and featured on the
277     NSF website).
278
279   * Computational verification of the Birch and Swinnerton-Dyer conjecture
280     to 10,000 bits for a rank-2 curve.
281
282   * Wrote a Ph.D. thesis on L-functions, using these machines.
283
284   * Wrote paper on Coleman integration too:
285     http://www.ants9.org/accepted.html .
286
287
288Randall Rathbun:
289
2902009-2010:
291
292   * Finding perfect parallelepipeds, and corresponding with Clifford
293     Reiter on this.  Dr. Richard K Guy is being kept informed about
294     this project, which is a number theory question in section D18 of
295     UPINT, Diophantine Equations.  Reiter has published, but I will
296     probably write a paper to Experimental Mathematics or some other
297     internet journal.  I don't think anyone else is working on this,
298     and Clifford has acknowledged that the computer power has left
299     him in the dust so he appreciates the searches.
300
301
302Marshall Hampton:
303
3042009-2010:
305
306  Working on proving finiteness of central configurations in the
307  five-body problem in a certain generic sense.
308
309 * Computing Groebner bases for a celestial mechanics problem.  The
310   amount of RAM on the SCREMS-purchased hardware is crucial for this;
311   he doesn't have any other comparable resources I could do those on.
312   Already these computations have given me a (computer-assisted)
313   proof of the finiteness of central configurations in the five-body
314   problem in a certain generic sense.
315
316
317
318Fredrik Johansson:
319
320Developing the mpmath library, which is an open source Python library
321for computing special functions (and much more), which is important
322for computing with L-functions and modular forms. This work was funded
323by my NSF FRG DMS-0757627.
324
325  * During both Summer 2009 and Summer 2010, Fredrik developed the
326    mpmath Python library.  Much of the testing and computation took
327    place on the computer cluster that was purchased with the current
328    SCREMS grant: Fredrik writes "Using multiprocessing, the time for
329    the new torture test suite (about which see blog) dropped from 11
330    minutes to 28 seconds (which could be even less by partitioning
331    the tests into smaller pieces). This is very handy!"
332    Fredrik's salary during this time is paid for by the PI's NSF
333    FRG DMS-0757627.
334
335Fredrik Strömberg:
336
337Fredrik is the world's leading expert in large scale computations with
338Maass forms.  He has done many computational projects using the SCREMS
339hardware, in connection with the PI's NSF FRG DMS-0757627.
340
341  * Computation of vector-valued Poincare series for the Weil
342    representation with application to convolution-type L-series for
343    Siegel modular forms of genus 2 (joint with Nathan Ryan and Nils
344    Skoruppa)
345
346  * Have also computed more than 1500 examples of Maass waveforms
347    (with eigenvalues and at least 1000 Fourier coefficients) for
348    Gamma_0(N) with square-free N up to 119 and with >20 examples for
349    all N except 51 and 77 (where I have 12 and 13 examples)
350
351  * Major finding: Disproved a conjecture of Andrianov (for genus 2
352    and even weights between 20 and 30) by proving that the
353    convolution-type L-series of two "interesting forms" (i.e. not in
354    the Maass Spezialshar) is linearly independent from the Spinor
355    L-functions (of all Siegel forms in of the same genus and weight).
356
357Sourav Sen Gupta:
358
359Graduate student helping with computational projects related to
360research of Stein.
361
362 * Computed the congruence graphs associated to modular abelian
363   varieties of level up to 500 and made a database.
364
365
366Jacob Lewis:
367
368Graduate student helping with computational projects related to the
369research of Doran.
370
371Georg Weber:
372
373Weber is a number theory Ph.D. who works at a bank in Germany, who
374does computations related to Stein's research project using the SCREMS
375hardware, and also contributes to the Sage project.
376
377  * Computations of matrices of Hecke operators T_p for 'massive'
378    primes p (p > 10^10), e.g. for level N=53, using an algorithm he
379    developed.
380
381
382Tom Boothby:
383
384  Systems administer of the SCREMS cluster, which involves physically
385  organizing the hardware, maintaining the operating system, and
386  managing users.  Runs computations in support of Stein's research
387  projects.  Developing Sage software (e.g., release management).
388
3892008-2009:
390
391  * Computed analytic order of Shafarevich-Tate group of a rank 2
392    elliptic curve to 10,000 bits of precision.
393
394  * Compiled tables of data about newforms of level up to 10,000.
395
3962009-2010:
397
398  * Computed modular symbols of weight 2 for conductor up to 5000,
399    extending previous computation by thousands of conductors -- also,
400    computed 10k Fourier coefficients for all modular forms of
401    conductor up to 4800, with computation ongoing.
402
403  * Extended table of Birch and Swinnerton-Dyer quantities for modular
404    abelian varieties to conductor 300 (computation ongoing).
405
406  * Computed discriminants of Hecke algebras of weight 2 modular forms
407    for level up to 1000, and factored all but two particularly tough
408    ones, extending previous table whose conductor bound was 389.
409
410  * Computed component group of J0(N)(R) for N up to 1000, extending
411    previous table by 500.
412
413  * Implemented record-breaking algorithm to multiply matrices of
414    characteristic 3 to be included in Sage project.
415
416  * Implemented graph genus algorithm, greatly improving on previous
417    implementation in Sage.
418
419
420
421Martin Albrecht:
422
423  Cryptography graduate student in London who frequently collaborates
424  with Stein on the Sage software, and makes extensive use of the SCREMS
425  hardware.
426
4272008-2009:
428
429  * Experimentally verified the behaviour of algebraic-differential
430    cryptanalysis against the block cipher PRESENT.
431
432  * Broke the key predistribution scheme of Zhang et al. from MobiHoc
433    2007 for practical parameters
434
4352009-2010:
436
437  * Developed, tested and benchmarked fastest dense matrix
438    decomposition over GF(2)
439
440  * Developed and tested algorithm for solving polynomial systems with
441    noise
442
443  * Experimentally verified an attack against "Perturbation Based"
444    crypto systems
445
446  * Experimentally verified hybrid attack strategies against block
447    ciphers
448
449  * Papers:
450
451    * Martin Albrecht and Clément Pernet. Efficient Decomposition of
452      Dense Matrices over GF(2), accepted for presentation at ECrypt
453      Workshop on Tools for Cryptanalysis 2010. available locally and
454      on bitbucket. 2010.
455
456    * Martin Albrecht and Carlos Cid. Cold Boot Key Recovery using
457      Polynomial System Solving with Noise (extended abstract)
458      accepted for presentation at 2nd International Conference on
459      Symbolic Computation and Cryptography. 2010.
460
461    * Martin Albrecht, Carlos Cid, Thomas Dullien, Jean-Charles
462      Faugère and Ludovic Perret. Algebraic Precomputations in
463      Differential Cryptanalysis accepted for presentation at ECrypt
464      Workshop on Tools for Cryptanalysis 2010.  2010.
465
466    * Martin Albrecht, Craig Gentry, Shai Halevi and Jonathan
467      Katz. Attacking Cryptographic Schemes Based on "Perturbation
468      Polynomials" in Proceedings of the 16th ACM Conference on
469      Computer and Communications Security. pre-print available at
470      http://eprint.iacr.org/2009/098. 2009.
471
472    * Martin Albrecht, Algorithmic Algebraic Techniques and their
473      Application to Block Cipher Cryptanalysis, PhD thesis,
474      submission date: July 2010
475
476  * Web sites:
477
478    * http://m4ri.sagemath.org and
479    * http://www.bitbucket.org/malb/algebraic_attacks
480
481  * Software:
482
483    * The M4RI library and http://www.bitbucket.org/malb/algebraic_attacks
484
485Gonzalo Tornaria:
486
487  Mathematics researcher who has computed state-of-the-art
488  data about specific modular forms using cutting edge techniques that
489  push the SCREMS hardware to its limits.  He also attends many of the
490  workshops related to this grant.
491
4922008-2009:
493
494  * computed the 12 series for the weight 3/2 lift of 36A each to 10^10 places
495
496  * computed the congruent numbers up to 2e10, assuming BSD (this has
497    since been recently been pushed to 10^12).
498
499Dan Drake:
500
501   Mathematics researcher doing combinatorics who frequently
502   contributes to the Sage project.
503
504   * counted binary matrices that square to zero to correct a mistake
505     in the Online Encyclopedia of Integer Sequences, sequence A001147
506
507
508Mark Watkins:
509
510   Postdoc who is working on computations involving computing large
511   numbers of coefficients of modular forms in support of the number
512   theory research projects.
513
514   * Has done numerous computations using the SCREMS hardware that took
515     advantage of the huge RAM available on these computers.  E.g., work
516     on the congruent number problem, tables of L-functions and data about
517     elliptic curves, etc.
518
519Craig Citro
520
521   Postdoc working on computations involving databases of modular forms.
522
523Ondrej Certik
524
525   Graduate student developing software and testing code for the
526   FEMhub open source finite element method library (http://femhub.org/).
527
528
529-----
530
531ACTIVITIES:
532
533The goal of this project is to collect data about L-functions and
535geometry and mathematical physics, compute data about representations
536of Lie groups, and support the Sage mathematical software project.
537
538All involved groups have carried out numerous substantial computations
539on the SCREMS hardware, the Sage software project has undergone
540massive growth and testing using this hardware, and public web pages,
541databases, wikis, and interactive online computations.
542
543FINDINGS:
544
545We have obtained large new databases of modular forms, verified
546predictions of the Generalized Riemann Hypothesis in many new cases,
547computed new invariants of Lie groups, and developed and tested state
548of the art algorithms in number theory and cryptography.  Below we
549give a long (but non-comprehensive) list of specific findings in
550different areas.  This SCREMS grant resulted in the purchase of a lot
551of powerful computers, with about 180 users, many who are computing
552things that aren't all reported.
553
554[Here I copied all the findings bullet points from above for people.]
555
556
557Training and Development:
558
559Because the SCREMS-purchased computers are very high end, with
56024-processing cores each, several people who have worked on the
561project have become much more adept at parallel computing.  Also,
562general software engineering skills have been enhanced for dozens of
563mathematicians, by working on the Sage math software system.  Also,
564the free open source software that we are developing on this hardware
565is being used by thousands of mathematicians to help with their
567
568Outreach:
569
570The Sage project -- which is developed and hosted on this SCREMS
571hardware -- does creative community outreach.  For example, Stein has
572given internal talks to Sun Microsystems and Boeing about the Sage
573project, and recently ran many workshops on the use of Sage that used
574the SCREMS hardware during the workshop -- e.g., one was in in
575Barcelona, Spain and another was at a regional MAA meeting in
576Washington State.
577
578The public Sage notebook server (http://sagenb.org) is available to
579anybody in the world to use, and provides the full power of Sage.
580This SCREMS hardware is critically important to making that server
581available.
582
583Contributions within Discipline – What?
584
585Using the SCREMS-funded hardware, we have computed data in number
586theory, geometry, and representation that will provide a basis for
587much future research.  We have also developed much new software in
588these research areas that will be used by researchers.
589
590
591Contributions to Other Disciplines
592
593The Sage software, which we develop and share using the SCREMS-funded
594hardware, is a contribution to all areas of mathematics.
595
596Much of the data we've computed about zeros of L-functions is of
597potential relevance in physics (e.g., quantum dynamics), as is the
598data about representations of Lie groups.
599
600Contributions to Human Resource Development
601
602Students who have contributed to the Sage project or worked on the
603research computations that have been done on this hardware, have often
604learned advanced software engineering techniques.  Since so many
605people contribute to the Sage project (at this point, over 200, mostly
606grad students), we are in fact training a whole generation of
607mathematicians to be significantly more sophisticated at mathematical
608software engineering.
609
610Contributions to Resources for Research and Education
611
612The databases and wiki's that come out of this project are freely
613available resources for students and researchers around the world.
614
615==============================================
616
617==============================================
618
619
620
621Exactly what actually got submitted:
622
623
624Project Reporting ANNUAL REPORT FOR AWARD # 0821725
625U of Washington
626SCREMS: The Computational Frontiers of Number Theory, Representation Theory, and Mathematical Physics
627
628Participant Individuals:
629CoPrincipal Investigator(s) : Birne T Binegar; Charles F Doran; Michael Rubinstein
631Other -- specify(s) : Georg S Weber
632Graduate student(s) : Sourav Sen Gupta; Jacob Lewis
633Senior personnel(s) : Marshall Hampton
634Graduate student(s) : Tom Boothby; Martin Albrecht
635Senior personnel(s) : Gonzalo Tornaria; Dan Drake; Mark Watkins
636Post-doc(s) : Craig Citro
637
638Partner Organizations:
639
640Other collaborators:
641
642There are dozens of people -- too numerous to list -- who make use of
643the SCREMS hardware in various ways who were not listed above, and some
644contribute directly to the SCREMS proposed project goals.
645
646
647Activities and findings:
648
649Research and Education Activities:
650
651The goal of this project is to collect data about L-functions and modular
652forms, compute new data about objects at the crossroads of geometry and
653mathematical physics, compute data about representations of Lie groups,
654and support the Sage mathematical software project.
655
656All involved groups have carried out numerous substantial computations
657on the SCREMS hardware, the Sage software project has undergone massive
658growth and testing using this hardware, and public web pages, databases,
659wikis, and interactive online computations.
660
661
662Findings:
663
664We have obtained large new databases of modular forms, verified predictions
665of the Generalized Riemann Hypothesis in many new cases, computed new
666invariants of Lie groups, and developed and tested state of the art algorithms
667in number theory and cryptography.  Below we give a long (but non-comprehensive)
668list of specific findings in different areas.   This SCREMS grant resulted
669in the purchase of a lot of powerful computers, with about 180 users,
670many who are computing things that aren't all reported.
671
672STEIN:
673
674  * computed all newforms of weight 2 and gamma0 level up to 3200, of
675    prime level up to 10000, and of various other weights and
676    characters.
677
678  * Created the http://sagenb.org that runs on this hardware and
679    allows people to use the Sage software over the web.  This
680    supports computational work by many thousands of people.
681
682  * computed several additional terms for the Sloane sequence A164783
683
684  * Computation of torsion subgroups of modular abelian varieties
685    using new algorithm
686
687  * Computation of modular degrees and congruence moduli for joint
688    paper with Ribet and Agashe
689
690  * Computation of database of Brandt modules
691
692  * Tables of p-adic L-series and p-adic regulators needed to apply
693    Iwasawa theory to verification of the Birch and Swinnerton-Dyer
694    conjecture in specific cases.
695
696
697BINEGAR:
698
699  * Computed the Kazhdan-Lusztig-Vogan polynomials for all simple
700    complex Lie algebras, with the exception of complex E8, viewed as
701    real Lie algebras up to real rank 16.  Computed the
702    Kazhdan-Lusztig-Vogan polynomials for SL(10,C) (real rank 20).
703
704  * Computed the W-graph structure for the set of irreducible
705    admissible representations of regular integral infinititesimal
706    character for the real forms of the simple real Lie groups up to
707    rank 8.
708
709  * Computed the Weyl group representations carried by the W-cells of
710    irreducible admissible representations of regular infinitesimal
711    character of the exceptional real Lie groups.
712
713  * Computed the associated varieties of the annihilators of
714    irreducible admissible representations of the exceptional real Lie
715    groups.
716
717  * Enumerated the set of irreducible admissible representations of
718    regular integral infinitesimal character of the exceptional real
719    groups and determined exactly when two irreducible admissible
720    representations of regular infinitesimal character share the same
721    primitive ideal.
722
723
724DORAN/LEWIS:
725
726  * Computing Picard-Fuchs equations of families of curves and surfaces
727
728  * Computing normal forms for anticanonical hypersurfaces in toric
729    Fano varieties
730
731  * Computing elliptic fibrations on toric K3 surfaces
732
733  * Computing tropical varieties
734
735  * Finding equations for elliptic space curves using invariant theory
736
737  * Constructed list of toric Fano compactifications of several
738    3-dimensional orbifolds
739
740  * Searched for 4-dimensional toric Fano varieties with special
741    properties
742
743  * Extensively tested and experimented with closed-form formulas for
744    Hodge numbers of complete intersections in toric varieties
745
746  * Found all torically induced elliptic fibrations of toric K3 surfaces
747
748
749RUBINSTEIN:
750
751
752  * Verify the Riemann Hypothesis for the first few hundred zeros for
753    all L-functions associated to the 1/2 million elliptic curves in
754    Cremona's database, and millions of zeros for the first few dozen
755    elliptic curves.
756
757  * Verify the moment conjecture for quadratic Dirichlet L-functions
758    for |d| < 10^10 (I will eventually get to 10^11). To get up to X
759    is an O(X^{3/2}) computation, so this would not have been possible
760    without a modern and powerful multicore machine.
761
762  * As a platform on which to develop and test code for computing with
763    L-functions. Compiling goes really quick on mod.math and allows me
764    to work more efficiently.
765
766
767HAMPTON:
768
769
770 * Computing Groebner bases for a celestial mechanics problem.  The
771   amount of RAM on the SCREMS-purchased hardware is crucial for this;
772   he doesn't have any other comparable resources I could do those on.
773   Already these computations have given me a (computer-assisted)
774   proof of the finiteness of central configurations in the five-body
775   problem in a certain generic sense.
776
777
778JOHANSSON:
779
780  * During Summer 2009, Fredrik developed the mpmath Python library.
781    Much of the testing and computation took place on the computer
782    cluster that was purchased with the current SCREMS grant: Fredrik
783    writes 'Using multiprocessing, the time for the new torture test
784    suite (about which see blog) dropped from 11 minutes to 28 seconds
785    (which could be even less by partitioning the tests into smaller
786    pieces). This is very handy!'
787
788
789GUPTA:
790
791 * Computed the congruence graphs associated to modular abelian
792   varieties of level up to 500 and made a database.
793
794
795WEBER:
796
797  * Computations of matrices of Hecke operators T_p for 'massive'
798    primes p (p > 10^10), e.g. for level N=53, using an algorithm he
799    developed.
800
801BOOTHBY:
802
803   * Computed analytic order of Shafarevich-Tate group of a rank 2
804     elliptic curve to 10,000 bits of precision.
805
806   * Compiled tables of data about newforms of level up to 10,000.
807
808
809ALBRECHT:
810
811  * Experimentally verified the behaviour of algebraic-differential
812    cryptanalysis against the block cipher PRESENT.
813
814  * Broke the key predistribution scheme of Zhang et al. from MobiHoc
815    2007 for practical parameters
816
817
818
820
821  * computed the 12 series for the weight 3/2 lift of 36A each to 10^10
822places
823
824  * computed the congruent numbers up to 10^12, assuming BSD (this is
825an major accomplishment that will likely lead to substantial publicity).
826
827
828DRAKE:
829
830   * counted binary matrices that square to zero to correct a mistake
831     in the Online Encyclopedia of Integer Sequences, sequence A001147
832
833
834Training and Development:
835
836Because the SCREMS-purchased computers are very high end, with
83724-processing cores each, several people who have worked on the
838project have become much more adept at parallel computing.  Also,
839general software engineering skills have been enhanced for dozens of
840mathematicians, by working on the Sage math software system.  Also,
841the free open source software that we are developing on this hardware
842is being used by thousands of mathematicians to help with their
844
845
846Outreach Activities:
847
848The Sage project -- which is developed and hosted on this SCREMS
849hardware -- does creative community outreach.  For example, Stein has
850given internal talks to Sun Microsystems and Boeing about the Sage
851project, and recently ran many workshops on the use of Sage that used
852the SCREMS hardware during the workshop -- e.g., one was in in
853Barcelona, Spain and another was at a regional MAA meeting in
854Washington State.
855
856The public Sage notebook server (http://sagenb.org) is available to
857anybody in the world to use, and provides the full power of Sage.
858This SCREMS hardware is critically important to making that server
859available.
860
861Journal Publications:
862
863Book(s) of other one-time publications(s):
864
865Other Specific Products:
866
867   The hardware is valuable for hosting Cython, MPIR, M4RI, etc. as well as all the Sage stuff.
868
869Contributions:
870
871Contributions within Discipline:
872
873 Using the SCREMS-funded hardware, we have computed data in number
874theory, geometry, and representation that will provide a basis for
875much future research.  We have also developed much new software in
876these research areas that will be used by researchers.
877
878
879
880Contributions to Other Disciplines:
881
882 The Sage software, which we develop and share using the SCREMS-funded
883hardware, is a contribution to all areas of mathematics.
884
885Much of the data we've computed about zeros of L-functions is of potential
886relevance in physics (e.g., quantum dynamics), as is the data about representations
887of Lie groups.
888
889
890Contributions to Education and Human Resources:
891
892 Students who have contributed to the Sage project or worked on the
893research computations that have been done on this hardware, have often
894learned advanced software engineering techniques.  Since so many
895people contribute to the Sage project (at this point, over 200, mostly
896grad students), we are in fact training a whole generation of
897mathematicians to be significantly more sophisticated at mathematical
898software engineering.
899
900
901
902Contributions to Resources for Science and Technology:
903
904 The databases and wiki's that come out of this project are freely
905available resources for students and researchers around the world.
906
907
908*** 2009 - 2010 ***
909
910
911