mathematics

Vincent Pilloni

Vincent Pilloni is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Vincent Pilloni rather than just read about it. In short: Vincent Pilloni is a French mathematician, specializing in arithmetic geometry and the Langlands program. Career Pilloni studied at the École Normale Supérieure and received his doctorate in 2009 from Université Sorbonne Paris Nord with thesis advisor Jacques Tilouine and thesis Arithmétique des variétés de Siegel.

Key takeaways

Vincent Pilloni belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Vincent Pilloni to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Vincent Pilloni from memory before moving on to harder problems.

Reference excerpt

Vincent Pilloni is a French mathematician, specializing in arithmetic geometry and the Langlands program.

Career Pilloni studied at the École Normale Supérieure and received his doctorate in 2009 from Université Sorbonne Paris Nord with thesis advisor Jacques Tilouine and thesis Arithmétique des variétés de Siegel. His research deals with, among other topics, the question of how the modularity theorem for elliptic curves over the rational numbers (which led to the proof of Fermat's Last Theorem) can be extended to abelian varieties. With George Boxer, Frank Calegari and Toby Gee, he proved that all abelian surfaces and genus two curves over totally real fields are potentially modular and satisfy the Hasse-Weil conjecture. Pilloni is a Chargé de recherche of CNRS at Paris-Saclay University based at the Institut de mathématique d'Orsay. In 2018 he was an invited speaker, with Fabrizio Andreatta and Adrian Iovita, at the International Congress of Mathematicians in Rio de Janeiro. In 2018 Pilloni received the Prix Élie Cartan. In 2021 he was awarded the Fermat Prize.

Selected publications Pilloni, Vincent (2012). "Sur la théorie de Hida pour le groupe GSp 2 g {\displaystyle {\textrm {GSp}}_{2g}} ". Bulletin de la Société mathématique de France. 140 (3). Societe Mathematique de France: 335–400. doi:10.24033/bsmf.2630. ISSN 0037-9484. Pilloni, Vincent (2012). "Modularité, formes de Siegel et surfaces abéliennes". Journal für die reine und angewandte Mathematik (Crelle's Journal). 2012 (666). Walter de Gruyter GmbH. doi:10.1515/crelle.2011.123. ISSN 1435-5345. S2CID 121162699. Pilloni, Vincent (15 March 2011). "Prolongement analytique sur les variétés de Siegel". Duke Mathematical Journal. 157 (1). Duke University Press. doi:10.1215/00127094-2011-004. ISSN 0012-7094. Bijakowski, Stéphane; Pilloni, Vincent; Stroh, Benoît (1 May 2016). "Classicité de formes modulaires surconvergentes". Annals of Mathematics. 183 (3): 975–1014. arXiv:1212.2035. doi:10.4007/annals.2016.183.3.5. ISSN 0003-486X. S2CID 55728265. Andreatta, Fabrizio; Iovita, Adrian; Pilloni, Vincent (1 March 2015). "p-adic families of Siegel modular cuspforms". Annals of Mathematics: 623–697. arXiv:1212.3812. doi:10.4007/annals.2015.181.2.5. ISSN 0003-486X. S2CID 54623621. Vincent Pilloni; Adrian Iovita; Fabrizio Andreatta (2018). "Le halo spectral". Annales scientifiques de l'École normale supérieure. 51 (3). Societe Mathematique de France: 603–655. doi:10.24033/asens.2362. hdl:11577/3287053. ISSN 0012-9593. Andreatta, Fabrizio; Iovita, Adrian; Pilloni, Vincent (2016). "On overconvergent Hilbert modular cusp forms" (PDF). Astérisque. 382: 163–193. MR 3581177. with Benoit Stroh: Surconvergence, ramification et modularité, Astérisque, vol. 382, 2016, pp. 195–266. MR Pilloni, Vincent (9 November 2016). "Formes modulaires p-adiques de Hilbert de poids 1". Inventiones Mathematicae. 208 (2). Springer Science and Business Media LLC: 633–676. doi:10.1007/s00222-016-0697-x. ISSN 0020-9910. S2CID 125123116.

References

External links website at ENS Lyon Interview 2018, CNRS (in French) "Construction of eigenvarieties and coherent cohomology – Vincent Pilloni". YouTube. 25 August 2016. "Higher Hida theory – Vincent Pilloni". YouTube. 10 November 2017. "p-adic variation of automorphic sheaves – A. Iovita & F. Andreatta & V. Pillion – ICM2018". YouTube. Rio ICM2018. 27 September 2018.

Worked examples

Example 1 — a first encounter with Vincent Pilloni

Start with the simplest possible case. Write down what Vincent Pilloni claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Vincent Pilloni before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Vincent Pilloni ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Vincent Pilloni

In research: Vincent Pilloni appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Vincent Pilloni in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Vincent Pilloni is common in secondary-school and first-year university syllabi. It links to neighbouring topics 21st-century French mathematicians, Algebraic geometers, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Vincent Pilloni outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Vincent Pilloni in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Vincent Pilloni means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Vincent Pilloni out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Vincent Pilloni in simple terms?

Vincent Pilloni is a French mathematician, specializing in arithmetic geometry and the Langlands program. Career Pilloni studied at the École Normale Supérieure and received his doctorate in 2009 from Université Sorbonne Paris Nord with thesis advisor Jacques Tilouine and thesis Arithmétique des va…

Why does Vincent Pilloni matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Vincent Pilloni?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Vincent Pilloni.