Detailed project information

In de cryptografie is het essentieel het exacte aantal oplossingen van bepaalde vergelijkingen te weten. Deze aantallen zijn groot: getallen van honderden cijfers. Technieken uit de meetkunde worden met behulp van zeer snelle algoritmen toepasbaar gemaakt op dit probleem.

Articles

• Dr. J.G. Bosman (2005). On the computation of coefficients of modular forms, II. explicit calculations.. Oberwolfach Reports. pp. 
• Prof. dr. S.J. Edixhoven (2005). On the computation of the coefficients of a modular form, I. introduction . Oberwolfach Reports. pp. 
• Prof. dr. S.J. Edixhoven (2005). Special points on products of modular curves.. Duke Math. J.. pp. 325-348
• Dr. R.S. de Jong (2005). Arakelov invariants of Riemann surfaces.. Documenta Mathematica. pp. 311-329
• Dr. R.S. de Jong (2005). Faltings' delta-invariant of a hyperelliptic Riemann surface.. G. van der Geer, B. Moonen, R. Schoof (eds.), Number Fields and Function Fields -- Two Parallel Worlds. Progress in Mathematics.. pp. 
• Prof. dr. S.J. Edixhoven (2005). On the computation of the coefficients of a modular form, IV. the Arakelov contribution. Oberwolfach Reports. pp. 
• Dr. R.S. de Jong (2005). Computing the coefficients of a modular form III. Application of Arakelov intersection theory. Oberwolfach Reports. pp. 
• Prof. dr. S.J. Edixhoven (2006). Comparison of integral structures on spaces of modular forms of weight two, and computation of spaces of forms mod 2 of weight one, with appendices by Jean-François Mestre and Gabor Wiese.. Journal of the Inst. of Math. Jussieu. pp. 1-34
• Prof. dr. S.J. Edixhoven (2006). On the computation of the coefficients of a modular form.. Lecture Notes in Comput. Sci.. pp. 30-39
• Dr. J.G. Bosman, Prof. dr. S.J. Edixhoven (2006). On the computation of coefficients of a modular form.. Together with J-M. Couveignes, R. de Jong, F. Merkl.. arxiv. pp. 
• W. Veys, Dr. J.A.W. Schepers (2007). Stringy Hodge numbers for a class of isolated singularities and for threefolds. Int. Math. Res. Not.. pp. 
• Dr. J.G. Bosman (2007). A polynomial with Galois group SL2(F16). LMS J. Comput. Math.. pp. 378-388
• Prof. dr. S.J. Edixhoven, Dr. R.S. de Jong, Dr. J.A.W. Schepers (2008). Covers of surfaces with fixed branch locus.. arxiv. pp. 
• Dr. F.R.A. Doray, Dr. O.N. Karpenkov, Dr. J.A.W. Schepers (2008). Geometry of configuration spaces of tensegrities.. arxiv. pp. 
• A. Stolk (2009). An Algebraic Framework for Discrete Tomography: Revealing the Structure of Dependencies. With co-author Joost Batenburg. Ingediend bij gerefereed tijdschrift.. preprint server arxiv. pp. 
• S.J. Edixhoven, R.S. de Jong, J.A.W. Schepers (2010). Covers of surfaces with fixed branch locus. Internat. J. Math.. pp. 859-874

Proefschriften

• Dr. J.G. Bosman (2008). Explicit computations with modular Galois representations. Universiteit Leiden. promotiedatum 15-12-2008
• Dr. J.G. Bosman (2009). Explicit computations with modular Galois representations.. Universiteit Leiden. promotiedatum 15-12-2008
• Dr. P.J. Bruin (2010). Modular curves, Arakelov theory, algorithmic applications. Universiteit Leiden. promotiedatum 1-9-2010
• P.J. Bruin (2010). Modular curves, Arakelov theory, algorithmic applications. Universiteit Leiden. promotiedatum 1-9-2010

Bijdragen aan boeken

• Prof. dr. S.J. Edixhoven, Prof. dr. G.B.M. van der Geer, Dr. B.J.J. Moonen (2008). Modular forms. in: Modular forms on Schiermonnikoog.. : . pp. 
• S.J. Edixhoven (2010). On the computation of the coefficients of modular forms.. in: Proceedings of the Fifth European Congress of Mathematics. Zurich: . pp. 17-29. ISBN 978-3-03719-077-7 .