Microsoft Research

This presentation has two parts. The first half discusses the major factorization algorithms when ECM was discovered in 1985, stressing the similarities between ECM and P +- 1.

Joint work with Noam Berger, Nevin Kapur and Vijay V.

Prof.

The parametrization of ideal classes of quadratic rings by binary quadratic forms has been an important tool for computing class numbers of quadratic fields.

This talk will consist of a series of light mini-talks inspired by Atkin's papers on recognizing primes (1982, 'On a primality test of Solovay and Strassen'; 1995, 'Intelligent primality test

Computing genus 2 curves from invariants on the Hilbert moduli space Joint work with Tonghai Yang (University of Wisconsin USA); he was originally scheduled to present this work.

Solid GroundΓÇÖs ( solid-ground.org/Pages/Default.aspx) core beliefs are that we can build a community free from poverty, prejudice and neglect in which all members can have the skills and

As described in the book, The Fourth Paradigm: Data-Intensive Scientific Discovery, scientific breakthroughs will be increasingly powered by advanced computing capabilities that help researchers

I will present two families of mathematical problems that are very simple to describe, that seem natural to study from geometric, algebraic or combinatorial points of view, and are seemingly

Pairing based cryptography has resulted in a number of breakthrough results, including some major developments in the area of zero knowledge proof systems.

Recently, Gaudry and Diem have proposed an index calculus method for the resolution of the DLP on elliptic curves defined over extension fields.

Vélu's formulas allow to compute an isogeny between elliptic curves from the coordinates of the points in the kernel.

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The embedded security community has been looking at the ECC ever since it was introduced.

The presentation will focus primarily on the ecology and management of wolves in Washington State, with an emphasis on the North Cascades and the recent establishment of the Lookout Pack in the

There is a vast amount of data available today and data is now being collected and stored at a rate never seen before.

After describing some joint work with Menezes in which isogenies are used to show that conventional wisdom about parameter selection might sometimes be wrong, I'll shift gears and make some comments

In 2000, Galbraith and McKee conjectured a formula estimating the probability of primality of the number of rational points on an elliptic curve over a finite field.

The talk is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law.

This talk is about efficient pairing computation on elliptic curves.

Sage ( sagemath.org) is the most feature rich general purpose free open source software for computing with elliptic curves.

After describing some joint work with Menezes in which isogenies are used to show that conventional wisdom about parameter selection might sometimes be wrong, I'll shift gears and make some comments

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As a culture, we have the capacity to lead creative lives. Part of that capacity lies in how something like music can touch on just about every aspect of human thinking and experience.

Elliptic curves with complex multiplication: history and perspectives The theory of complex multiplication on curves is very old and rich, going back at least to Klein.

Elliptic curves E can be given by plane projective cubic curves and so seem to be very simple objects.

This will be a swift and informal introduction to cluster algebras, with hints on their applications to canonical bases and Teichmuller theory. Total positivity serves as the main motivation.

Much of the research in number theory, like mathematics as a whole, has been inspired by hard problems which are easy to state. A famous example is 'Fermat's Last Theorem'.

Scaling the Science Garrison Sposito, U.C. Berkeley; Mark Stacey, U.C. Berkeley; Stephanie Carlson, U.C. Berkeley; Charlotte Ambrose, NOAA's National Marine Fisheries Service; James Hunt, U.C.

CoSBiLab is a software platform implementing the new conceptual framework of algorithmic systems biology.