Viewing archives for Clay Research Conference

Enumerative geometry and representation theory

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Speaker: Andrei Okounkov (Columbia)

Formation of singularities in fluid interfaces

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Speaker: Charles Fefferman (Princeton)

Cohomology of algebraic varieties

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Speaker: Peter Scholze (Bonn)

Algebraic and motivic vector bundles

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Speaker: Mike Hopkins (Harvard)

The work of Peter Scholze

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Speaker: Michael Rapoport (Bonn)

Higher-order Fourier analysis and applications

Abstract: Higher-order Fourier analysis is a tool developed by several mathematicians over the last couple of decades in order to solve, primarily, systems of linear equations in sets of integers. I will talk about the state of the theory now, what applications it has, and what open questions remain. As a particular application I hope to discuss recent joint work with Ford, Konyagin and Tao on large gaps between primes.

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Speaker: Ben Green (Oxford)

Chinese dragons and mating trees

Abstract: What is the right way to think of a “random surface” or a “random planar graph”?  How can one explain the dendritic patterns that appear in snowflakes, coral reefs, lightning bolts, and other physical systems, as well as in toy mathematical models inspired by these systems?  How are these questions related to random walks and random fractal curves (in particular the famous SLE curves)?  How are they related to conformal matings of Julia sets?  To string theory?  To statistical mechanics?

To begin to address these questions, I will introduce and explain the “quantum Loewner evolution” (QLE), which is a family of growth processes closely related to SLE.

Joint work with Bertrand Duplantier and Jason Miller.

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Speaker: Scott Sheffield (MIT)

The Schanuel paradigm

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Speaker: Jonathan Pila (Oxford)

Animation, teeth and skeletons

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Speaker: Ingrid Daubechies (Duke)

The work of Rahul Pandharipande

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Speaker: Richard Thomas (Imperial)

A new look at the Jones polynomial of a knot

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Speaker: Edward Witten (IAS)

The Birch–Swinnerton-Dyer conjecture: a status report

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Speaker: Fernando Rodriguez Villegas (UT Austin)