24 search results for “polynomials” in the Public website
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Isogeny graphs, modular polynomials, and applications
This thesis has three main parts. The first part gives an algorithm to compute Hilbert modular polynomials for ordinary abelian varieties with maximal real multiplication. Hilbert modular polynomials of a given level b give a way of finding all of the abelian varieties that are b-isogeneous to any given…
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Algorithms for finite rings
Promotores: H.W. Lenstra, K. Belabas (University of Bordeaux)
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Logarithmic approach to the double ramification cycle
This thesis discusses several questions regarding the double ramification cycle as a Chow class on the moduli space of stable n-pointed genus g curves using tools from so-called logarithmic geometry.
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Counting problems for number rings
Promotor: H.W. Lenstra
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Expansions of quantum group invariants
In my research, we developed a method to distinguish knots. A knot is a mathematical depiction of the everyday knot that occurs in ropes and cords.
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Computational aspects of class group actions and applications to post-quantum cryptography
Most of current public-key cryptography is considered insecure against attacks from sufficiently powerful quantum computers. Post-quantum cryptography studies methods to secure information resistant against such attacks. One proposal is isogeny-based cryptography, which bases its security on computational…
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Complex multiplication of abelian surfaces
Promotor: Peter Stevenhagen
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Faster number theory, safer cryptography
Developing a method to simplify polynomials in complex curves
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ASML Graduation Prize for mathematics student Pim Spelier – Incentive Prize for first-year student Jorre The
Alumnus Pim Spelier is one of the two winners of the ASML Graduation prizes for mathematics students. He used a new method to solve single polynomial equations. Bachelor student Jorre The wins one of the ORTEC Incentive prizes for the best study results during the first year. On 30 November, the Royal…
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On the amount of sieving in factorization methods
Promotoren: R. Tijdeman, A.K. Lenstra, Co-promotor: H.J.J. te Riele
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On continued fraction algorithms
Promotor: Robert Tijdeman, Co-promotor: Cornelis Kraaikamp
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Dynamical Gibbs-non-Gibbs transitions: a study via coupling and large deviations
Promotores: F.H.J. Redig, W.T.F. den Hollander
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On the computation of norm residue symbols
An algorithm is discussed to compute the exponential representation of principal units in a finite extension field F of the p-adic rationals.
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Links between cohomology and arithmetic
Promotor: S.J. Edixhoven
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Model-assisted robust optimization for continuous black-box problems
Uncertainty and noise are frequently-encountered obstacles in real-world applications of numerical optimization. The practice of optimization that deals with uncertainties and noise is commonly referred to as robust optimization.
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Geometric quadratic Chabauty and other topics in number theory
This thesis is is made of three parts. The first part describes a generalization of the Chabauty's method, that can be used to determine the rational points of a curve such that s+g>r+1, where g is the genusof the curve, r is the rank of the Mordell-Weil group of the jacobian of the curve and s is…
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Modular curves, Arakelov theory, algorithmic applications
Promotor: S.J. Edixhoven, Co-promotor: R.S. de Jong
- Math requirement
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NWO tenure track grant in arithmetic algebraic geometry
Within the context of the four national mathematics clusters, NWO has awarded seven proposals for tenure track positions. One of these was on 'Moduli, metrics, models, and arithmetic of Shimura varieties' by Bas Edixhoven from the Leiden Mathematical Institute.
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Lieuwe Vinkhuijzen third in VERSEN Master Thesis Award
PhD candidate Lieuwe Vinkhuijzen received the VERSEN Master Thesis Award 3rd prize for his master’s thesis on quantum computing. ‘A forward-looking thesis that solves problems in software engineering; not in the next decade, but beyond’, according to the jury.
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New professor David Holmes engages with age-old counting problems
As of 1 October, David Holmes has been appointed full professor of Pure Mathematics at the Mathematical Institute (MI). His work lies at the intersection of algebra, geometry and number theory.
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Four Leiden consortia awarded large NWO grants
No less than four Leiden research teams have been awarded a grant by NWO. On 27 July NWO honoured 21 applications in the Open Competition ENW-XL. NWO awards the grants to consortia in the exact and natural sciences who are doing unconnected fundamental research that is 'driven by curiosity'.
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Theses
Below thesis archives will be moved shortly (work in progress) to the Leiden Repository. Once this is done, theses submitted by MI students (from 2008 onwards) can be accessed via the Repository and will be removed from this site.
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