Sharedwww / screms / report-2010.txtOpen in CoCalc
Author: William A. Stein
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This is the annual report for SCREMS.
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William Stein:
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Purchased and maintain the SCREMS cluster. Do research on elliptic
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curves and modular forms using the SCREMS hardware. Creating and
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sharing databases, and designing, implementing, testing, and
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distributing free open source software as part of Sage using this
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hardware.
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2008-2009:
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* computed all newforms of weight 2 and gamma0 level up to 3200, of
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prime level up to 10000, and of various other weights and
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characters.
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* Created the http://sagenb.org that runs on this hardware and
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allows people to use the Sage software over the web. This
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supports computational work by many thousands of people.
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* computed several additional terms for the Sloane sequence A164783
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* Computation of torsion subgroups of modular abelian varieties
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using new algorithm
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* Computation of modular degrees and congruence moduli for joint
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paper with Ribet and Agashe
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* Computation of database of Brandt modules
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* Tables of p-adic L-series and p-adic regulators needed to apply
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Iwasawa theory to verification of the Birch and Swinnerton-Dyer
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conjecture in specific cases.
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2009-2010:
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* Computed newforms up to level 5500 and weight 2
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* Greatly expanded the power of http://sagenb.org; now there are
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over 32,000 users.
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* Major finding: Carried out the first ever computational
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verification of Kolyvagin's conjecture (for several dozens curves)
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-- this was a major computational project requiring hundreds of
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hours of CPU time, done with help from Jennifer Balakrishnan.
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* Major finding: Jointly with Sheldon Kamienny and Michael Stoll,
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carried out a new computational classification of primes p such
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that there is an elliptic curve over a quartic field with a
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torsion point over order p. This extends Mazur's classical result
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over QQ to all quartic fields.
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* Did substantial work porting Sage to Microsoft Windows on the
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SCREMS hardware.
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* Publications:
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* Heegner Points on Rank Two Elliptic Curves, preprint,
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http://wstein.org/papers/kolyconj2/
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* Toward a Generalization of the Gross-Zagier Conjecture,
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International Mathematics Research Notices 2010; doi: 10.1093/imrn/rnq075
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Robert Miller:
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2008-2010:
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* Computational verification of the BSD formula for 16725 curves/QQ
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of rank 0 and 1 of conductor up to 5000.
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* Publication: his Ph.D. thesis
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* Web resources:
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- a database of codes: http://rlmiller.org/de_codes/
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- Large databases of Heegner indexes and other BSD data... (not online yet)
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Minh Nguyen:
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* Used the SCREMS hardware for developing and testing software for
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cryptography education. The code is now part of the Sage standard library.
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* Wrote an undergraduate honours thesis as listed at:
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http://www.sagemath.org/library-publications.html
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The thesis explicitly acknowledges my use of the Sage cluster in
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developing and testing the code described in the thesis itself.
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Jennifer Balakrishnan:
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2008-2010:
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* Computational verification of Kolyvagin's conjecture for a rank 3 curve
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* Computation of p-adic L-series of Jacobians of hyperelliptic modular curves
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* Computation of p-adic regulators of curves using techniques based on Coleman integration
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* Everything going into my PhD thesis (2011) has been done on sage.math!
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- Single Coleman integrals from non-Weierstrass/Weierstrass points on
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hyperelliptic curves
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- Local p-adic heights for hyperelliptic curves via Coleman integration
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- double Coleman integrals on hyperelliptic curves
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- experiments with the Chabauty method
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* Major finding: fixed subtle error in Kim's nonabelian Chabauty method;
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computations led to appendix/erratum to his original JAMS article
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* Publications:
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* "Explicit Coleman integration for hyperelliptic curves," ANTS IX
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Proceedings, Springer LNCS 6197 (with Robert Bradshaw and Kiran
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Kedlaya); explicitly acknowledged NSF support
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* Appendix and erratum to "Massey products for elliptic curves of
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rank 1" by Minhyong Kim (with Kiran Kedlaya and Minhyong Kim),
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to appear in JAMS, acknowledged William Stein (but not NSF
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explicitly).
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Andrey Novoseltsev:
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2009-2010:
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* Relations between mirror maps for local Calabi-Yau manifolds and
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their compactifications. This work (joint with Matthew Ballard,
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Adrian Clingher, Charles Doran, Jacob Lewis) is related to the
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Hodge Conjecture.
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* Geometric transitions leading to the missing class in Doran-Morgan
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classification of real variation of Hodge structure coming from
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one-parameter families of Calabi-Yau manifolds (joint work with
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Charles Doran and Jacob Lewis).
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* In addition, the base framework for toric varieties was developed
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and is now posted on Sage Trac with plans to merge it in the near
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future and considerably improve the functionality by the end of
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the summer.
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* Publications: Results of another one were posted on arXiv and
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accepted for publication in Contemporary Mathematics Proceedings
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of AMS during the last year:
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* "Closed form expressions for Hodge numbers of complete
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intersection Calabi-Yau threefolds in toric varieties,"
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Charles F. Doran, Andrey Y. Novoseltsev, arXiv:0907.2701v1
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[math.CO], NSF support acknowledged.
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David Kirkby:
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Technical support personnel.
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2009-2010:
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* Fully ported Sage to Solaris. This was a major undertaking that
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indirectly resulted in the porting of a large amount of standard
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open source mathematics software and libraries to Solaris, which
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makes them available to a wider range of users.
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Birne Binegar:
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Running computations related to representation theory (the ATLAS project).
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2008-2009:
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* Computed the Kazhdan-Lusztig-Vogan polynomials for all simple
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complex Lie algebras, with the exception of complex E8, viewed as
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real Lie algebras up to real rank 16. Computed the
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Kazhdan-Lusztig-Vogan polynomials for SL(10,C) (real rank 20).
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* Computed the W-graph structure for the set of irreducible
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admissible representations of regular integral infinititesimal
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character for the real forms of the simple real Lie groups up to
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rank 8.
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* Computed the Weyl group representations carried by the W-cells of
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irreducible admissible representations of regular infinitesimal
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character of the exceptional real Lie groups.
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* Computed the associated varieties of the annihilators of
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irreducible admissible representations of the exceptional real Lie
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groups.
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* Enumerated the set of irreducible admissible representations of
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regular integral infinitesimal character of the exceptional real
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groups and determined exactly when two irreducible admissible
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representations of regular infinitesimal character share the same
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primitive ideal.
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2009-2010:
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* I've computed the Kazhdan-Lusztig-Vogan polynomials for real
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forms G_R of simple complex Lie groups up to rank 8. From this
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data I've also computed, for each real form G_R, I've computed
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- the W-graph structure of the set G_R^ of equivalence classes of
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irreducible admissible representations of G_R with regular
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integral infinitesimal character
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- the partitioning of G_R^ into cells of irreducible
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representations sharing the same associated variety
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- the partitioning of G_R^ cells into subcells of representations
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sharing the same infinitiesimal character
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- the cell representations of the Weyl group carried by the cells
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of G_R^ (via the coherent continuation action)
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* Websites:
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- www.math.okstate.edu/~binegar/research.html
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- http://lie.math.okstate.edu/UMRK/UMRK.html
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* Databases:
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* Constructed a PostgreSQL database UMRK (Unipotent Muffin
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Research Kitchen) which houses all sorts of computational data
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concerning simple Lie algebras, their subalgebras, their Weyl
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groups, and their real forms. This data is accessible online
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via simple web query forms (see the second link listed above).
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Chuck Doran:
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Running computations related to geometry, including Picard-Fuchs
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equations, families of curves and surfaces, tropical varieties, toric
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ideals, Fano compactifications, and K3 surfaces.
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Findings:
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* Computing Picard-Fuchs equations of families of curves and surfaces
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* Computing normal forms for anticanonical hypersurfaces in toric
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Fano varieties
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* Computing elliptic fibrations on toric K3 surfaces
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* Computing tropical varieties
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* Finding equations for elliptic space curves using invariant theory
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* Constructed list of toric Fano compactifications of several
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3-dimensional orbifolds
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* Searched for 4-dimensional toric Fano varieties with special
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properties
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* Extensively tested and experimented with closed-form formulas for
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Hodge numbers of complete intersections in toric varieties
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* Found all torically induced elliptic fibrations of toric K3 surfaces
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Michael Rubinstein:
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Running computations related to computing zeros of L-functions.
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* Verify the Riemann Hypothesis for the first few hundred zeros for
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all L-functions associated to the 1/2 million elliptic curves in
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Cremona's database, and millions of zeros for the first few dozen
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elliptic curves.
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* Verify the moment conjecture for quadratic Dirichlet L-functions
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for |d| < 10^10 (I will eventually get to 10^11). To get up to X
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is an O(X^{3/2}) computation, so this would not have been possible
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without a modern and powerful multicore machine.
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* As a platform on which to develop and test code for computing with
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L-functions. Compiling goes really quick on mod.math and allows me
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to work more efficiently.
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Robert Bradshaw:
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2009-2010:
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* The "trillion triangles" congruent number search that made good
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use of the hardware (made the popular press, and featured on the
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NSF website).
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* Computational verification of the Birch and Swinnerton-Dyer conjecture
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to 10,000 bits for a rank-2 curve.
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* Wrote a Ph.D. thesis on L-functions, using these machines.
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* Wrote paper on Coleman integration too:
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http://www.ants9.org/accepted.html .
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Randall Rathbun:
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2009-2010:
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* Finding perfect parallelepipeds, and corresponding with Clifford
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Reiter on this. Dr. Richard K Guy is being kept informed about
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this project, which is a number theory question in section D18 of
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UPINT, Diophantine Equations. Reiter has published, but I will
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probably write a paper to Experimental Mathematics or some other
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internet journal. I don't think anyone else is working on this,
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and Clifford has acknowledged that the computer power has left
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him in the dust so he appreciates the searches.
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Marshall Hampton:
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2009-2010:
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Working on proving finiteness of central configurations in the
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five-body problem in a certain generic sense.
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* Computing Groebner bases for a celestial mechanics problem. The
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amount of RAM on the SCREMS-purchased hardware is crucial for this;
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he doesn't have any other comparable resources I could do those on.
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Already these computations have given me a (computer-assisted)
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proof of the finiteness of central configurations in the five-body
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problem in a certain generic sense.
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Fredrik Johansson:
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Developing the mpmath library, which is an open source Python library
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for computing special functions (and much more), which is important
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for computing with L-functions and modular forms. This work was funded
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by my NSF FRG DMS-0757627.
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* During both Summer 2009 and Summer 2010, Fredrik developed the
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mpmath Python library. Much of the testing and computation took
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place on the computer cluster that was purchased with the current
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SCREMS grant: Fredrik writes "Using multiprocessing, the time for
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the new torture test suite (about which see blog) dropped from 11
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minutes to 28 seconds (which could be even less by partitioning
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the tests into smaller pieces). This is very handy!"
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Fredrik's salary during this time is paid for by the PI's NSF
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FRG DMS-0757627.
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Fredrik Strömberg:
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Fredrik is the world's leading expert in large scale computations with
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Maass forms. He has done many computational projects using the SCREMS
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hardware, in connection with the PI's NSF FRG DMS-0757627.
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* Computation of vector-valued Poincare series for the Weil
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representation with application to convolution-type L-series for
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Siegel modular forms of genus 2 (joint with Nathan Ryan and Nils
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Skoruppa)
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* Have also computed more than 1500 examples of Maass waveforms
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(with eigenvalues and at least 1000 Fourier coefficients) for
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Gamma_0(N) with square-free N up to 119 and with >20 examples for
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all N except 51 and 77 (where I have 12 and 13 examples)
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* Major finding: Disproved a conjecture of Andrianov (for genus 2
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and even weights between 20 and 30) by proving that the
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convolution-type L-series of two "interesting forms" (i.e. not in
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the Maass Spezialshar) is linearly independent from the Spinor
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L-functions (of all Siegel forms in of the same genus and weight).
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Sourav Sen Gupta:
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Graduate student helping with computational projects related to
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research of Stein.
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* Computed the congruence graphs associated to modular abelian
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varieties of level up to 500 and made a database.
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Jacob Lewis:
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Graduate student helping with computational projects related to the
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research of Doran.
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Georg Weber:
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Weber is a number theory Ph.D. who works at a bank in Germany, who
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does computations related to Stein's research project using the SCREMS
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hardware, and also contributes to the Sage project.
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* Computations of matrices of Hecke operators T_p for 'massive'
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primes p (p > 10^10), e.g. for level N=53, using an algorithm he
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developed.
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Tom Boothby:
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Systems administer of the SCREMS cluster, which involves physically
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organizing the hardware, maintaining the operating system, and
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managing users. Runs computations in support of Stein's research
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projects. Developing Sage software (e.g., release management).
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2008-2009:
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* Computed analytic order of Shafarevich-Tate group of a rank 2
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elliptic curve to 10,000 bits of precision.
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* Compiled tables of data about newforms of level up to 10,000.
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2009-2010:
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* Computed modular symbols of weight 2 for conductor up to 5000,
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extending previous computation by thousands of conductors -- also,
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computed 10k Fourier coefficients for all modular forms of
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conductor up to 4800, with computation ongoing.
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* Extended table of Birch and Swinnerton-Dyer quantities for modular
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abelian varieties to conductor 300 (computation ongoing).
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* Computed discriminants of Hecke algebras of weight 2 modular forms
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for level up to 1000, and factored all but two particularly tough
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ones, extending previous table whose conductor bound was 389.
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* Computed component group of J0(N)(R) for N up to 1000, extending
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previous table by 500.
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* Implemented record-breaking algorithm to multiply matrices of
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characteristic 3 to be included in Sage project.
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* Implemented graph genus algorithm, greatly improving on previous
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implementation in Sage.
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Martin Albrecht:
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Cryptography graduate student in London who frequently collaborates
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with Stein on the Sage software, and makes extensive use of the SCREMS
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hardware.
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2008-2009:
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* Experimentally verified the behaviour of algebraic-differential
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cryptanalysis against the block cipher PRESENT.
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* Broke the key predistribution scheme of Zhang et al. from MobiHoc
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2007 for practical parameters
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2009-2010:
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* Developed, tested and benchmarked fastest dense matrix
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decomposition over GF(2)
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* Developed and tested algorithm for solving polynomial systems with
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noise
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* Experimentally verified an attack against "Perturbation Based"
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crypto systems
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* Experimentally verified hybrid attack strategies against block
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ciphers
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* Papers:
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* Martin Albrecht and Clément Pernet. Efficient Decomposition of
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Dense Matrices over GF(2), accepted for presentation at ECrypt
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Workshop on Tools for Cryptanalysis 2010. available locally and
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on bitbucket. 2010.
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* Martin Albrecht and Carlos Cid. Cold Boot Key Recovery using
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Polynomial System Solving with Noise (extended abstract)
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accepted for presentation at 2nd International Conference on
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Symbolic Computation and Cryptography. 2010.
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* Martin Albrecht, Carlos Cid, Thomas Dullien, Jean-Charles
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Faugère and Ludovic Perret. Algebraic Precomputations in
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Differential Cryptanalysis accepted for presentation at ECrypt
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Workshop on Tools for Cryptanalysis 2010. 2010.
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* Martin Albrecht, Craig Gentry, Shai Halevi and Jonathan
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Katz. Attacking Cryptographic Schemes Based on "Perturbation
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Polynomials" in Proceedings of the 16th ACM Conference on
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Computer and Communications Security. pre-print available at
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http://eprint.iacr.org/2009/098. 2009.
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* Martin Albrecht, Algorithmic Algebraic Techniques and their
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Application to Block Cipher Cryptanalysis, PhD thesis,
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submission date: July 2010
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* Web sites:
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* http://m4ri.sagemath.org and
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* http://www.bitbucket.org/malb/algebraic_attacks
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* Software:
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* The M4RI library and http://www.bitbucket.org/malb/algebraic_attacks
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Gonzalo Tornaria:
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Mathematics researcher who has computed state-of-the-art
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data about specific modular forms using cutting edge techniques that
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push the SCREMS hardware to its limits. He also attends many of the
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workshops related to this grant.
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2008-2009:
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* computed the 12 series for the weight 3/2 lift of 36A each to 10^10 places
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* computed the congruent numbers up to 2e10, assuming BSD (this has
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since been recently been pushed to 10^12).
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Dan Drake:
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Mathematics researcher doing combinatorics who frequently
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contributes to the Sage project.
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* counted binary matrices that square to zero to correct a mistake
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in the Online Encyclopedia of Integer Sequences, sequence A001147
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Mark Watkins:
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Postdoc who is working on computations involving computing large
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numbers of coefficients of modular forms in support of the number
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theory research projects.
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* Has done numerous computations using the SCREMS hardware that took
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advantage of the huge RAM available on these computers. E.g., work
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on the congruent number problem, tables of L-functions and data about
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elliptic curves, etc.
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Craig Citro
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Postdoc working on computations involving databases of modular forms.
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Ondrej Certik
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Graduate student developing software and testing code for the
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FEMhub open source finite element method library (http://femhub.org/).
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-----
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ACTIVITIES:
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The goal of this project is to collect data about L-functions and
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modular forms, compute new data about objects at the crossroads of
535
geometry and mathematical physics, compute data about representations
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of Lie groups, and support the Sage mathematical software project.
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All involved groups have carried out numerous substantial computations
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on the SCREMS hardware, the Sage software project has undergone
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massive growth and testing using this hardware, and public web pages,
541
databases, wikis, and interactive online computations.
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FINDINGS:
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We have obtained large new databases of modular forms, verified
546
predictions of the Generalized Riemann Hypothesis in many new cases,
547
computed new invariants of Lie groups, and developed and tested state
548
of the art algorithms in number theory and cryptography. Below we
549
give a long (but non-comprehensive) list of specific findings in
550
different areas. This SCREMS grant resulted in the purchase of a lot
551
of powerful computers, with about 180 users, many who are computing
552
things that aren't all reported.
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[Here I copied all the findings bullet points from above for people.]
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Training and Development:
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Because the SCREMS-purchased computers are very high end, with
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24-processing cores each, several people who have worked on the
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project have become much more adept at parallel computing. Also,
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general software engineering skills have been enhanced for dozens of
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mathematicians, by working on the Sage math software system. Also,
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the free open source software that we are developing on this hardware
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is being used by thousands of mathematicians to help with their
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research (we have about 5000 downloads of Sage per month).
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Outreach:
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The Sage project -- which is developed and hosted on this SCREMS
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hardware -- does creative community outreach. For example, Stein has
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given internal talks to Sun Microsystems and Boeing about the Sage
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project, and recently ran many workshops on the use of Sage that used
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the SCREMS hardware during the workshop -- e.g., one was in in
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Barcelona, Spain and another was at a regional MAA meeting in
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Washington State.
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The public Sage notebook server (http://sagenb.org) is available to
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anybody in the world to use, and provides the full power of Sage.
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This SCREMS hardware is critically important to making that server
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available.
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Contributions within Discipline – What?
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Using the SCREMS-funded hardware, we have computed data in number
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theory, geometry, and representation that will provide a basis for
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much future research. We have also developed much new software in
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these research areas that will be used by researchers.
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Contributions to Other Disciplines
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The Sage software, which we develop and share using the SCREMS-funded
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hardware, is a contribution to all areas of mathematics.
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Much of the data we've computed about zeros of L-functions is of
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potential relevance in physics (e.g., quantum dynamics), as is the
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data about representations of Lie groups.
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Contributions to Human Resource Development
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Students who have contributed to the Sage project or worked on the
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research computations that have been done on this hardware, have often
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learned advanced software engineering techniques. Since so many
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people contribute to the Sage project (at this point, over 200, mostly
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grad students), we are in fact training a whole generation of
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mathematicians to be significantly more sophisticated at mathematical
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software engineering.
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Contributions to Resources for Research and Education
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The databases and wiki's that come out of this project are freely
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available resources for students and researchers around the world.
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==============================================
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==============================================
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Exactly what actually got submitted:
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Project Reporting ANNUAL REPORT FOR AWARD # 0821725
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U of Washington
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SCREMS: The Computational Frontiers of Number Theory, Representation Theory, and Mathematical Physics
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Participant Individuals:
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CoPrincipal Investigator(s) : Birne T Binegar; Charles F Doran; Michael Rubinstein
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Graduate student(s) : Fredrik Johansson
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Other -- specify(s) : Georg S Weber
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Graduate student(s) : Sourav Sen Gupta; Jacob Lewis
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Senior personnel(s) : Marshall Hampton
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Graduate student(s) : Tom Boothby; Martin Albrecht
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Senior personnel(s) : Gonzalo Tornaria; Dan Drake; Mark Watkins
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Post-doc(s) : Craig Citro
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Partner Organizations:
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Other collaborators:
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There are dozens of people -- too numerous to list -- who make use of
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the SCREMS hardware in various ways who were not listed above, and some
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contribute directly to the SCREMS proposed project goals.
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Activities and findings:
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Research and Education Activities:
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The goal of this project is to collect data about L-functions and modular
652
forms, compute new data about objects at the crossroads of geometry and
653
mathematical physics, compute data about representations of Lie groups,
654
and support the Sage mathematical software project.
655
656
All involved groups have carried out numerous substantial computations
657
on the SCREMS hardware, the Sage software project has undergone massive
658
growth and testing using this hardware, and public web pages, databases,
659
wikis, and interactive online computations.
660
661
662
Findings:
663
664
We have obtained large new databases of modular forms, verified predictions
665
of the Generalized Riemann Hypothesis in many new cases, computed new
666
invariants of Lie groups, and developed and tested state of the art algorithms
667
in number theory and cryptography. Below we give a long (but non-comprehensive)
668
list of specific findings in different areas. This SCREMS grant resulted
669
in the purchase of a lot of powerful computers, with about 180 users,
670
many who are computing things that aren't all reported.
671
672
STEIN:
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* 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.
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* Created the http://sagenb.org that runs on this hardware and
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allows people to use the Sage software over the web. This
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supports computational work by many thousands of people.
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* computed several additional terms for the Sloane sequence A164783
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* Computation of torsion subgroups of modular abelian varieties
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using new algorithm
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* Computation of modular degrees and congruence moduli for joint
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paper with Ribet and Agashe
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* Computation of database of Brandt modules
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* Tables of p-adic L-series and p-adic regulators needed to apply
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Iwasawa theory to verification of the Birch and Swinnerton-Dyer
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conjecture in specific cases.
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BINEGAR:
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* Computed the Kazhdan-Lusztig-Vogan polynomials for all simple
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complex Lie algebras, with the exception of complex E8, viewed as
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real Lie algebras up to real rank 16. Computed the
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Kazhdan-Lusztig-Vogan polynomials for SL(10,C) (real rank 20).
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* Computed the W-graph structure for the set of irreducible
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admissible representations of regular integral infinititesimal
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character for the real forms of the simple real Lie groups up to
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rank 8.
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* Computed the Weyl group representations carried by the W-cells of
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irreducible admissible representations of regular infinitesimal
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character of the exceptional real Lie groups.
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* Computed the associated varieties of the annihilators of
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irreducible admissible representations of the exceptional real Lie
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groups.
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* Enumerated the set of irreducible admissible representations of
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regular integral infinitesimal character of the exceptional real
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groups and determined exactly when two irreducible admissible
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representations of regular infinitesimal character share the same
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primitive ideal.
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DORAN/LEWIS:
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* Computing Picard-Fuchs equations of families of curves and surfaces
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* Computing normal forms for anticanonical hypersurfaces in toric
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Fano varieties
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* Computing elliptic fibrations on toric K3 surfaces
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* Computing tropical varieties
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* Finding equations for elliptic space curves using invariant theory
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* Constructed list of toric Fano compactifications of several
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3-dimensional orbifolds
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* Searched for 4-dimensional toric Fano varieties with special
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properties
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* Extensively tested and experimented with closed-form formulas for
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Hodge numbers of complete intersections in toric varieties
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* Found all torically induced elliptic fibrations of toric K3 surfaces
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RUBINSTEIN:
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* Verify the Riemann Hypothesis for the first few hundred zeros for
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all L-functions associated to the 1/2 million elliptic curves in
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Cremona's database, and millions of zeros for the first few dozen
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elliptic curves.
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* Verify the moment conjecture for quadratic Dirichlet L-functions
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for |d| < 10^10 (I will eventually get to 10^11). To get up to X
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is an O(X^{3/2}) computation, so this would not have been possible
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without a modern and powerful multicore machine.
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* As a platform on which to develop and test code for computing with
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L-functions. Compiling goes really quick on mod.math and allows me
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to work more efficiently.
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HAMPTON:
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* Computing Groebner bases for a celestial mechanics problem. The
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amount of RAM on the SCREMS-purchased hardware is crucial for this;
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he doesn't have any other comparable resources I could do those on.
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Already these computations have given me a (computer-assisted)
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proof of the finiteness of central configurations in the five-body
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problem in a certain generic sense.
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JOHANSSON:
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* During Summer 2009, Fredrik developed the mpmath Python library.
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Much of the testing and computation took place on the computer
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cluster that was purchased with the current SCREMS grant: Fredrik
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writes 'Using multiprocessing, the time for the new torture test
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suite (about which see blog) dropped from 11 minutes to 28 seconds
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(which could be even less by partitioning the tests into smaller
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pieces). This is very handy!'
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GUPTA:
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* Computed the congruence graphs associated to modular abelian
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varieties of level up to 500 and made a database.
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WEBER:
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* Computations of matrices of Hecke operators T_p for 'massive'
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primes p (p > 10^10), e.g. for level N=53, using an algorithm he
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developed.
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BOOTHBY:
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* Computed analytic order of Shafarevich-Tate group of a rank 2
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elliptic curve to 10,000 bits of precision.
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* Compiled tables of data about newforms of level up to 10,000.
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ALBRECHT:
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* Experimentally verified the behaviour of algebraic-differential
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cryptanalysis against the block cipher PRESENT.
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814
* Broke the key predistribution scheme of Zhang et al. from MobiHoc
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2007 for practical parameters
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TORNARIA/HARVEY/BRADSHAW/WATKINS/HART:
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* computed the 12 series for the weight 3/2 lift of 36A each to 10^10
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places
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* computed the congruent numbers up to 10^12, assuming BSD (this is
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an major accomplishment that will likely lead to substantial publicity).
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DRAKE:
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* counted binary matrices that square to zero to correct a mistake
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in the Online Encyclopedia of Integer Sequences, sequence A001147
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Training and Development:
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Because the SCREMS-purchased computers are very high end, with
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24-processing cores each, several people who have worked on the
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project have become much more adept at parallel computing. Also,
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general software engineering skills have been enhanced for dozens of
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mathematicians, by working on the Sage math software system. Also,
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the free open source software that we are developing on this hardware
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is being used by thousands of mathematicians to help with their
843
research (we have about 5000 downloads of Sage per month).
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Outreach Activities:
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The Sage project -- which is developed and hosted on this SCREMS
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hardware -- does creative community outreach. For example, Stein has
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given internal talks to Sun Microsystems and Boeing about the Sage
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project, and recently ran many workshops on the use of Sage that used
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the SCREMS hardware during the workshop -- e.g., one was in in
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Barcelona, Spain and another was at a regional MAA meeting in
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Washington State.
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The public Sage notebook server (http://sagenb.org) is available to
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anybody in the world to use, and provides the full power of Sage.
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This SCREMS hardware is critically important to making that server
859
available.
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861
Journal Publications:
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863
Book(s) of other one-time publications(s):
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Other Specific Products:
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The hardware is valuable for hosting Cython, MPIR, M4RI, etc. as well as all the Sage stuff.
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Contributions:
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Contributions within Discipline:
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Using the SCREMS-funded hardware, we have computed data in number
874
theory, geometry, and representation that will provide a basis for
875
much future research. We have also developed much new software in
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these research areas that will be used by researchers.
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Contributions to Other Disciplines:
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The Sage software, which we develop and share using the SCREMS-funded
883
hardware, is a contribution to all areas of mathematics.
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Much of the data we've computed about zeros of L-functions is of potential
886
relevance in physics (e.g., quantum dynamics), as is the data about representations
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of Lie groups.
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Contributions to Education and Human Resources:
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Students who have contributed to the Sage project or worked on the
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research computations that have been done on this hardware, have often
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learned advanced software engineering techniques. Since so many
895
people contribute to the Sage project (at this point, over 200, mostly
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grad students), we are in fact training a whole generation of
897
mathematicians to be significantly more sophisticated at mathematical
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software engineering.
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Contributions to Resources for Science and Technology:
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The databases and wiki's that come out of this project are freely
905
available resources for students and researchers around the world.
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907
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*** 2009 - 2010 ***
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