Margaret Bilu
I am a CNRS researcher (chargée de recherche) at the Institut de Mathématiques de Bordeaux. Before that, I was a Marie Skłodowska-Curie fellow at IST Austria, working with Tim Browning.
Contact
Institut de Mathématiques de Bordeaux351, cours de la Libération
33405 Talence
FRANCE
firstname.lastname@math.u-bordeaux.fr
Curriculum vitae
Research
My research interests lie in number theory and algebraic geometry. I am particularly interested in developing and proving motivic analogues of number-theoretic tools and results in the Grothendieck ring of varieties. In my thesis, I developed a notion of motivic Euler product which has since found several applications.Organization
I helped organize an online seminar on rational points and related
topics: Zoom
on Rational Points Past and future talks and travel (real or virtual)
- Séminaire Mathematic
Park, Institut Henri Poincaré, April 27th, 2024
- Workshop Enumerative Geometry and Arithmetic, Lorentz Center, Leiden, March 11-15, 2024
- WAARP,
University of Bristol, September 11-15, 2023
- SAGA, Laboratoire de Mathématiques d'Orsay, April 25th, 2023
- Séminaire Géométrie et Théorie des Modèles, IHP, April 21st, 2023
- Séminaire Algèbre et Géometries, Institut Fourier, Grenoble, April 3rd, 2023
- Séminaire
de Géométrie Arithmétique et Motivique, LAGA, Sorbonne
Paris Nord, March 17th, 2023
- Rencontre
ANR Fracasso, Bordeaux, March 9-10, 2023
- Non-archimedean methods in arithmetic and geometry, Les Diablerets, Switzerland, February 12-17, 2023
- Séminaire
d'Arithmétique, UMPA, Lyon, January 26th, 2023
- Séminaire de théorie des nombres, Bordeaux, December 2nd, 2022
- Women in Numbers Europe (Project group leader), Utrecht, August 29th-September 2nd 2022
- Rational
Points on Higher-Dimensional Varieties, ICMS, Edinburgh,
April 25-29, 2022
- Séminaire de
théorie des nombres de l'IMJ-PRG, March 21st, 2022
- Algebra,
Geometry and Physics seminar (MPIM Bonn/HU Berlin), July
20th, 2021
- BIRS workshop "Geometry via arithmetic", July 11-16, 2021
- Browning group working seminar, IST Austria, July 2nd, 2021
- Around
Frobenius distributions and related topics II, June
28-29, 2021
- Séminaire
de théorie des nombres, Université de Bordeaux, May
21st, 2021
- Séminaire de théorie des nombres, Institut Fourier, April 13th, 2021
- Browning group
working seminar, IST Austria, January 27th, 2021
- Séminaire
de géométrie, Université Savoie Mont Blanc, Chambéry,
January 21st, 2021
- Oberseminar
Zahlentheorie und Arithmetische Geometrie, Hannover,
November 27th, 2020
- Duke Algebraic Geometry Seminar, November 20th, 2020
- Browning
group working seminar, IST Austria, October 7th, 14th,
21st, 2020
- Arithmetic Statistics and Local-Global Principles, Erwin Schrödinger Institute, Vienna, Austria, July 20-24, 2020. (cancelled)
- Stanford
Algebraic Geometry Seminar online, June 12th, 2020
- Fifth
International Workshop on Zeta Functions in Algebra and
Geometry, Nice, France, May 25-28th, 2020 (postponed)
- Simons
Symposium on the Geometry of Arithmetic Statistics,
Schloss Elmau, Krün, Germany, May 3-9, 2020 (postponed)
- Georgia
Algebraic Geometry Symposium, Emory University, Atlanta,
April 17-19, 2020 (postponed)
- Number
Theory Seminar, Duke University, March 18th, 2020 (cancelled)
- Quebec-Vermont
Number Theory Seminar, Mc Gill University, Montreal,
March 12th, 2020 (cancelled)
- PU/IAS
Number Theory Seminar, Princeton University, January 23,
2020
- Number Theory seminar, Boston University, November 4th, 2019
- Geometry/Topology
seminar, University of Chicago, October 21st, 2019
- Algebraic Geometry seminar, University of Michigan, October 16th, 2019
- Algebraic
Geometry seminar, University of Stony Brook, September
18th, 2019
- Conference
"Rational points on Fano and similar varieties",
Institut Henri Poincaré, Paris, May 20-24, 2019 Video
- Algebraic
Geometry seminar, Princeton University, April 1st, 2019
- Algebra Seminar, Brown University, March 11, 2019
- Number Theory seminar,
MIT, November 20, 2018
- CANT 2018,
Graduate Center at the City University of New York, May 23,
2018
- Algebra
seminar, University of Pennsylvania, October 23, 2017
- Atkin Memorial Workshop on Height zeta functions, University of Illinois at Chicago, April 28-30, 2017
- Séminaire de théorie des nombres de l'IMJ-PRG, Paris, March 20th 2017
- Algebraic Geometry Seminar, Courant Institute of Mathematical Sciences, New York University, October 25, 2016
- Special day on motivic integration and non-archimedean geometry, Université Lille 1, October 10, 2016
- Intercity Number Theory Seminar, Leuven, Belgium, June 10, 2016
- Number Theory Seminar, ETH Zürich, March 4, 2016
- Séminaire Géométrie et Singularités, IRMAR, Université
Rennes 1, February 10, 2016
Publications and preprints
- A motivic circle method (joint with T. Browning). Link to arXiv
- A quadratic enrichment of the logarithmic derivative of the
zeta function (joint with W. Ho, P. Srinivasan, I. Vogt and K.
Wickelgren). Link to arXiv
- Zeta statistics and Hadamard functions (joint with R. Das and S. Howe), Adv.
Math. 407 (2022), 108556. Link to arXiv.
- Motivic Euler products in motivic statistics (joint with S. Howe), Algebra Number Theory 15 (2021), no. 9, 2195–2259.Link to arXiv.
- Motivic Euler products and Motivic Height Zeta Functions,
Mem. Amer. Math. Soc. 282 (2023), no. 1396. Link to arxiv.
This is an updated version of my PhD Thesis.
- Rational points on analytic varieties (joint with A. Beshenov, Yu. Bilu and P. Rath), EMS Surv. Math. Sci. 2 (2015), p. 109-130. Link to arXiv. These are notes I wrote up following a mini-course by Yuri Bilu. It starts with some elementary results by Jarník and Dörge, continues with the theorem of Bombieri and Pila about rational points with given denominator on analytic curves, and then presents the powerful theorem of Pila and Wilkie about rational points of bounded height on sets definable in an o-minimal structure. Finally, applications to the Manin-Mumford and André-Oort conjectures are given.
Theses and essays
- My PhD thesis.Here are notes from talks I have given on the subject.
- My Introduction à un domaine
de recherche: this is a short thesis written towards the
end of one's studies at the ENS. Its aim is to present, in a
way accessible to non-specialists, the research area one wants
to specialise in and the questions one intends to address
during one's PhD. It summarises in particular the
contents of my Master's thesis.
- My Master's thesis was about Hrushovski
and Kazhdan's motivic Poisson summation formula. It is a
motivic analogue of the classical Poisson summation formula
for functions over the adele group of a global field, which is
proved in the first part of the text, following Tate's thesis.
- MyPart III essay
written during my year at Cambridge: this is an account of the
theory of complex multiplication of abelian varieties.
- My Mémoire de maîtrise: this is a thesis written in my first year at the ENS, together with Guillaume Dubach. The u-invariant of a field is the maximal dimension of an anisotropic quadratic form over this field. A conjecture by Kaplansky states that the u-invariant of a field should always be a power of 2. This text presents the construction, due to Merkurjev, of a field with u-invariant 2n for every positive integer n, which thereby disproves Kaplansky's conjecture. This beautiful argument uses division algebras and Clifford algebras. Our text also contains the proof, by Pfister, of another conjecture by Kaplansky, stating that the level of a field, that is, the minimal integer n such that -1 is a sum of n squares, is always a power of 2.
Teaching
Outreach/Mathématiques périscolaires
Les activités suivantes peuvent intéresser tout collégien ou lycéen aimant les mathématiques.- L'association Animath et l'Préparation Olympique Française de Mathématiques (POFM) fournissent une préparation à diverses compétitions internationales de mathématiques, appelées olympiades. Il s'agit de s'entraîner à résoudre en temps limité des problèmes assez courts provenant de plusieurs domaines des mathématiques. Plus d'informations ici.
- Le Tournoi Français des Jeunes Mathématiciens est un tournoi où il s'agit de réfléchir par équipes pendant quelques mois à des problèmes comprenant des questions de difficulté variable, dont certaines ouvertes, puis de présenter ce qu'on a trouvé sous forme écrite et orale.
- Le club Parimaths est un club de mathématiques ayant lieu à l'ENS tous les samedis en période scolaire. Sur le site on peut consulter les feuilles distribuées lors de certaines séances.
- Séries génératrices
- Graphes
- Théorie extrémale des graphes
- Polynômes et nombres entiers
- Fractions continues
- Polygones équidécomposables
Last updated: December 18th, 2023