18 zoekresultaten voor “polynomials” in de Publieke 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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Counting problems for number rings
Promotor: H.W. Lenstra
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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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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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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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Links between cohomology and arithmetic
Promotor: S.J. Edixhoven
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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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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
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Explicit Computation of the Height of a Gross-Schoen Cycle
Arithmetic geometry concerns the number-theoretic properties of geometric objects defined by polynomials. Mathematicians are interested in the rational solutions to these geometric objects.
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ASML afstudeerprijs voor wiskundestudent Pim Spelier – aanmoedingsprijs voor eerstejaarsstudent Jorre The
Alumnus Pim Spelier is één van de twee winnaars van de ASML afstudeerprijs voor wiskundestudenten. Hij gebruikte een nieuwe methode om enkele polynomiale vergelijkingen op te lossen. Bachelorstudent Jorre The wint één van de ORTEC Aanmoedigingsprijzen voor de beste studieresultaten tijdens het eerste…
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NWO tenure track grant voor het Mathematisch Instituut
In het raamwerk van de nationale clusters in de wiskunde heeft NWO zeven voorstellen voor een tenure track positie goedgekeurd. Een van deze voorstellen is: 'Moduli, metrics, models, and arithmetic of Shimura varieties' door Bas Edixhoven van het Leidse Mathematische Instituut.
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Lieuwe Vinkhuijzen wint derde prijs VERSEN Master Thesis Award
Promovendus Lieuwe Vinkhuijzen heeft de VERSEN Master Thesis derde prijs gewonnen voor zijn masterscriptie over quantumcomputers. ‘Een vooruitstrevende scriptie, die problemen in software engineering oplost; niet in het volgende decennium, maar nog verder in de toekomst’, aldus de jury.