Frances Brown | |
|---|---|
| Born | 5 November 1977 |
| Nationality | Franco-British |
| Education | Eton College University of Cambridge École normale supérieure (Paris) / University of Bordeaux |
| Awards | Élie Cartan Prize |
| Scientific career | |
| Fields | Mathematics |
| Institutions | All Souls College, Oxford |
| Academic advisors | Pierre Cartier |
| Website | https://www.asc.ox.ac.uk/person/professor-francis-brown |
Francis Brown is a Franco-British mathematician who works on Arithmetic geometry and Quantum Field Theory.
Brown studied at the University of Cambridge and the École normale supérieure (Paris) and University of Bordeaux, [1] with Pierre Cartier, graduating in 2006 with a Ph.D. [2] He then spent time at the Max Planck Institute for Mathematics and Mittag-Leffler Institute. In 2007 he moved to Institut de mathématiques de Jussieu – Paris Rive Gauche where he won a European Research Council starter grant in 2010. In 2012, he moved to the Institut des Hautes Études Scientifiques and was awarded a CNRS Bronze Medal and Élie Cartan Prize for his proof of two conjectures related to multiple zeta functions. [3] [4] He had a Von Neumann Fellowship at the Institute for Advanced Study from 2014 to 2015 and is currently a senior research fellow at All Souls College, at the University of Oxford.
Brown's work is on the intersection of algebraic geometry and number theory. He has published on Tate Motives. [5] He also works on Zeta functions in quantum field theory.
In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a widely studied branch of theoretical and mathematical physics. Penrose's idea was that twistor space should be the basic arena for physics from which space-time itself should emerge. It has led to powerful mathematical tools that have applications to differential and integral geometry, nonlinear differential equations and representation theory, and in physics to general relativity, quantum field theory, and the theory of scattering amplitudes. Twistor theory arose in the context of the rapidly expanding mathematical developments in Einstein's theory of general relativity in the late 1950s and in the 1960s and carries a number of influences from that period. In particular, Roger Penrose has credited Ivor Robinson as an important early influence in the development of twistor theory, through his construction of so-called Robinson congruences.
In algebraic geometry, motives is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast array of similarly behaved cohomology theories such as singular cohomology, de Rham cohomology, etale cohomology, and crystalline cohomology. Philosophically, a "motif" is the "cohomology essence" of a variety.
In mathematics, the Milnor conjecture was a proposal by John Milnor (1970) of a description of the Milnor K-theory (mod 2) of a general field F with characteristic different from 2, by means of the Galois cohomology of F with coefficients in Z/2Z. It was proved by Vladimir Voevodsky.
In probability theory, the Schramm–Loewner evolution with parameter κ, also known as stochastic Loewner evolution (SLEκ), is a family of random planar curves that have been proven to be the scaling limit of a variety of two-dimensional lattice models in statistical mechanics. Given a parameter κ and a domain in the complex plane U, it gives a family of random curves in U, with κ controlling how much the curve turns. There are two main variants of SLE, chordal SLE which gives a family of random curves from two fixed boundary points, and radial SLE, which gives a family of random curves from a fixed boundary point to a fixed interior point. These curves are defined to satisfy conformal invariance and a domain Markov property.
François Loeser is a French mathematician. He is Professor of Mathematics at the Pierre-and-Marie-Curie University in Paris. From 2000 to 2010 he was Professor at École Normale Supérieure. Since 2015, he is a senior member of the Institut Universitaire de France.
In algebraic geometry, a period is a number that can be expressed as an integral of an algebraic function over an algebraic domain. Sums and products of periods remain periods, such that the periods form a ring.
In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist. This object is denoted F1, or, in a French–English pun, Fun. The name "field with one element" and the notation F1 are only suggestive, as there is no field with one element in classical abstract algebra. Instead, F1 refers to the idea that there should be a way to replace sets and operations, the traditional building blocks for abstract algebra, with other, more flexible objects. Many theories of F1 have been proposed, but it is not clear which, if any, of them give F1 all the desired properties. While there is still no field with a single element in these theories, there is a field-like object whose characteristic is one.
Lothar Göttsche is a German mathematician, known for his work in algebraic geometry.
Nikita Alexandrovich Nekrasov is a mathematical and theoretical physicist at the Simons Center for Geometry and Physics and C.N.Yang Institute for Theoretical Physics at Stony Brook University in New York, and a Professor of the Russian Academy of Sciences.
Alexander B. Goncharov is a Soviet American mathematician and the Philip Schuyler Beebe Professor of Mathematics at Yale University. He won the EMS Prize in 1992.
Christopher Deninger is a German mathematician at the University of Münster. Deninger's research focuses on arithmetic geometry, including applications to L-functions.
Éric Leichtnam is director of research at the CNRS at the Institut de Mathématiques de Jussieu in Paris. His fields of interest are noncommutative geometry, ergodic theory, Dirichlet problem, non-commutative residue.
Nets Hawk Katz is the W.L. Moody Professor of Mathematics at Rice University. He was a professor of Mathematics at Indiana University Bloomington until March 2013 and the IBM Professor of Mathematics at the California Institute of Technology until 2023.
Prakash Belkale is an Indian-American mathematician, specializing in algebraic geometry and representation theory.
Jean-Pierre Demailly was a French mathematician who worked in complex geometry. He was a professor at Université Grenoble Alpes and a permanent member of the French Academy of Sciences.
Bertrand Toën is a mathematician who works as a director of research at the Centre national de la recherche scientifique (CNRS) at the Paul Sabatier University, Toulouse, France. He received his PhD in 1999 from the Paul Sabatier University, where he was supervised by Carlos Simpson and Joseph Tapia.
Yves André is a French mathematician, specializing in arithmetic geometry.
Vincent Pilloni is a French mathematician, specializing in arithmetic geometry and the Langlands program.
Jean-Benoît Bost is a French mathematician.
