Abstract analytic number theory
Double Dirichlet series soon became multiple Dirichlet series. It has gradually emerged that the local structure of these multiple Dirichlet series shows a rich connection to combinatorial representation theory. This program will explore this interface between automorphic forms and combinatorial representation theory, and will develop computational tools for facilitating investigations.
On the automorphic side, Whittaker functions on p-adic groups and their covers are the fundamental objects. Whittaker functions and their relatives are expressible in terms of combinatorial structures on the associated L-group, its flag Sage is a mathematics software system developed by and for the mathematics community, whose mission is to create a viable free open source alternative to Magma, Maple, Mathematica and Matlab. Its wide span of features, in particular in number theory, combinatorics, and representation theory, together with its friendly community based development, fosters collaborations across disciplines, from the design and implementation of new computer exploration tools to research.
NUMBER THEORY BOOKS, OR BEFORE
This workshop will bring together experienced Sage and Sage-Combinat developers and experts of multiple Dirichlet series and computational algebraic combinatorics. Like every workshop in the Sage Days series, it will welcome whoever wants to discover Sage, learn more about it, or contribute to it. Schubert calculus is the modern approach to classical problems in enumerative algebraic geometry, specifically on flag varieties and their many generalizations.
Crystals are combinatorial tools based on quantum groups which arise in the study of representations of Lie algebras. Whittaker functions are special functions on Lie groups or p-adic groups, for example GL n,F where F might be the real or complex numbers, or a p-adic field. The area of intersection between these three topics is combinatorial representation theory.
Common tools such as Demazure operators, the Bruhat partial order, and Macdonald polynomials appear in all three areas. Some connections between these three areas are quite new. This workshop will explore these connections.
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Abstract Recent years have seen a flurry of activity in the field of Weyl group multiple Dirichlet series. Speaker Poster Presenter Attendee. Workshop Schedule Monday, April 15, Tuesday, April 16, Wednesday, April 17, Thursday, April 18, Friday, April 19, Jan 28 - May 3, Close View Event Page.
Feb 11 - 15, Whittaker Functions, Schubert calculus and Crystals. Mar 4 - 8, Cryptographic applications of analytic number theory: complexity lower bounds and pseudorandomness Igor Shparlinski. Department of Computing. Abstract The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation.
Number theory. Lower bound. Pseudorandom numbers.
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Complexity Theory. Cryptographic applications of analytic number theory: complexity lower bounds and pseudorandomness. Progress in computer science and applied logic; Vol. Shparlinski, Igor.
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