The Abel Prize 2013–2017

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Yakov G . Sinai , Abel Prize Laureate 2014

A dynamical billiard is an idealization of the game of billiard, but where the table can have shapes other than the rectangular and even be multidimensional. We use only one billiard ball, and the billiard may even have regions where the ball is kept out. Formally, a dynamical billiard is a dynamical system where a massless and point shaped particle moves inside a bounded region. The particle i...

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Abel Prize 2017 for Yves Meyer

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Abel Prize 2009 as a necessitation to discussion on geometry, or

Contemporary geometers do not acknowledge nonaxomatizable geometries. This fact means that our knowledge of geometry is poor. A perfect knowledge of geometry is important for ”consumers of geometry” (physicists dealing with geometry of microcosm), because poor knowledge of geometry forces physicists to refuse from the orthodox geometrical paradigm and to use the quantum paradigm, which is a sim...

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The Abel-Zeilberger Algorithm

We use both Abel’s lemma on summation by parts and Zeilberger’s algorithm to find recurrence relations for definite summations. The role of Abel’s lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger alg...

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Computing the Abel map

A Riemann surface is associated with its Jacobian through the Abel map. Using a plane algebraic curve representation of the Riemann surface, we provide an algorithm for the numerical computation of the Abel map. Since our plane algebraic curves are of arbitrary degree and may have arbitrary singularities, the Abel map of any connected compact Riemann surface may be obtained in this way.

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ژورنال

عنوان ژورنال: Notices of the American Mathematical Society

سال: 2021

ISSN: 0002-9920,1088-9477

DOI: 10.1090/noti2193