Mon, 02 Dec 2019

17:30 - 18:30
L1

### Carlo Rovelli - Spin networks: the quantum structure of spacetime from Penrose's intuition to Loop Quantum Gravity

Carlo Rovelli
(Université d'Aix-Marseille)
Further Information

Oxford Mathematics Public Lectures- The Roger Penrose Lecture

Carlo Rovelli  - Spin networks: the quantum structure of spacetime from Penrose's intuition to Loop Quantum Gravity

Monday 2 December 2019

In developing the mathematical description of quantum spacetime, Loop Quantum Gravity stumbled upon a curious mathematical structure: graphs labelled by spins. This turned out to be precisely the structure of quantum space suggested by Roger Penrose two decades earlier, just on the basis of his intuition. Today these graphs with spin, called "spin networks" have become a common tool to explore the quantum properties of gravity. In this talk Carlo will tell this beautiful story and illustrate the current role of spin networks in the efforts to understand quantum gravity.

Carlo Rovelli is a Professor in the Centre de Physique Théorique de Luminy of Aix-Marseille Université where he works mainly in the field of quantum gravity and  is a founder of loop quantum gravity theory. His popular-science book 'Seven Brief Lessons on Physics' has been translated into 41 languages and has sold over a million copies worldwide.

5.30pm-6.30pm, Mathematical Institute, Oxford

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

Thu, 13 Jun 2019
14:00
L3

### Affine Hecke Algebras for p-adic classical groups, local Langlands correspondence and unipotent representations

Volker Heiermann
(Université d'Aix-Marseille)
Abstract

I will review the equivalence of categories of a Bernstein component of a p-adic classical group with the category of right modules over a certain affine Hecke algebra (with parameters) that I obtained previously. The parameters can be made explicit by the parametrization of supercuspidal representations of classical groups obtained by C. Moeglin, using methods of J. Arthur. Via this equivalence, I can show that the category of smooth complex representations of a quasisplit $p$-adic classical group and its pure inner forms is naturally decomposed into subcategories that are equivalent to the tensor product of categories of unipotent representations of classical groups (in the sense of G. Lusztig). All classical groups (general linear, orthogonal, symplectic and unitary groups) appear in this context.

Thu, 01 Nov 2018

14:30 - 17:00
L5

### Potential operators, analyticity and bounded holomorphic functional calculus for the Stokes operator

Sylvie Monniaux
(Université d'Aix-Marseille)
Abstract

This is part of a meeting of the North British Functional Aanlysis Seminar.  There will be a tea break (15:30-16:00)

In a first talk, I shall recall the basic definitions and properties of ${\mathcal{H}}^\infty}$ functional calculus. I shall show how a second order problem can be reduced to a first order system and how to construct potential operators.
In a second talk, we will see how to use potential operators for the specific problem of the Stokes operator with the so-called “natural” boundary conditions in non smooth domains.
Most parts which will be presented are taken from a joint work with Alan McIntosh (to be published soon in the journal "Revista Matematica Iberoamericana”)

Wed, 26 Oct 2016
15:00
L5

### The geometry of efficient arithmetic on elliptic curves

David Kohel
(Université d'Aix-Marseille)
Abstract

The introduction of Edwards' curves in 2007 relaunched a
deeper study of the arithmetic of elliptic curves with a
view to cryptographic applications.  In particular, this
research focused on the role of the model of the curve ---
a triple consisting of a curve, base point, and projective
(or affine) embedding. From the computational perspective,
a projective (as opposed to affine) model allows one to
avoid inversions in the base field, while from the
mathematical perspective, it permits one to reduce various
arithmetical operations to linear algebra (passing through
the language of sheaves). We describe the role of the model,
particularly its classification up to linear isomorphism
and its role in the linearization of the operations of addition,
doubling, and scalar multiplication.

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