mathematics

Mathieu Lewin

Mathieu Lewin 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 Mathieu Lewin rather than just read about it. In short: Mathieu Lewin (born 14 November 1977 in Senlis, Oise, France) is a French mathematician and mathematical physicist who deals with partial differential equations, mathematical quantum field theory, and mathematics of quantum mechanical many-body systems. Biography Lewin studied mathematics at the École normale supérieure de Cachan, receiving his master's degree in 2000.

Key takeaways

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

Reference excerpt

Mathieu Lewin (born 14 November 1977 in Senlis, Oise, France) is a French mathematician and mathematical physicist who deals with partial differential equations, mathematical quantum field theory, and mathematics of quantum mechanical many-body systems.

Biography Lewin studied mathematics at the École normale supérieure de Cachan, receiving his master's degree in 2000. He then received his PhD in 2004 at the Paris Dauphine University (Dauphine-Paris) PhD under the direction of Éric Séré. His dissertation was titled Some Nonlinear Models in quantum mechanics. From 2004 to 2005 he was a postdoctoral fellow at the University of Copenhagen under Jan Philip Solovej. From 2005, he conducted research for the Centre national de la recherche scientifique (CNRS) at the University of Cergy-Pontoise, then at the Paris-Dauphine university. In July 2012, he was awarded an EMS Prize "for his ground breaking work in rigorous aspects of quantum chemistry, mean field approximations to relativistic quantum field theory and statistical mechanics".

Works His works concern the mathematical properties of matter at the microscopic scale, and they are mostly based on quantum mechanics. He uses tools from the calculus of variations, nonlinear functional analysis, partial differential equations, and spectral theory. For instance, he studied several nonlinear models for atoms and molecules (e.g. the Multi-configurational self-consistent field and Hartree–Fock methods), or for infinite quantum systems (e.g. in quantum field theory and condensed matter).

Selection of papers Lewin, Mathieu (2004). "Solutions of the Multiconfiguration Equations in Quantum Chemistry". Archive for Rational Mechanics and Analysis. 171 (1). Springer: 83–114. Bibcode:2004ArRMA.171...83L. doi:10.1007/s00205-003-0281-6. S2CID 16366393. Hainzl, Christian; Lewin, Mathieu; Solovej, Jan Philip (2007). "The mean-field approximation in quantum electrodynamics: the no-photon case". Communications on Pure and Applied Mathematics. 60 (4). Wiley: 150402. arXiv:math-ph/0503075. doi:10.1002/cpa.20145. S2CID 14193609. Esteban, Maria J.; Lewin, Mathieu; Séré, Eric (2008). "Variational methods in relativistic quantum mechanics". Bulletin of the American Mathematical Society. 45 (4). American Mathematical Society (AMS): 535. arXiv:0706.3309. doi:10.1090/s0273-0979-08-01212-3. Lenzmann, Enno; Lewin, Mathieu (2010). "Minimizers for the Hartree-Fock-Bogoliubov theory of neutron stars and white dwarfs". Duke Mathematical Journal. 152 (2). Duke University Press: 257–315. arXiv:0809.2560. doi:10.1215/00127094-2010-013. S2CID 15321236. Lewin, Mathieu (2011). "Geometric methods for nonlinear many-body quantum systems". Journal of Functional Analysis. 260 (12). Elsevier: 3535–3595. arXiv:1009.2836. doi:10.1016/j.jfa.2010.11.017. Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert (2011). "Energy Cost to Make a Hole in the Fermi Sea". Physical Review Letters. 106 (15) 150402. American Physical Society (APS). arXiv:1102.1414. Bibcode:2011PhRvL.106o0402F. doi:10.1103/physrevlett.106.150402. PMID 21568533. Lewin, Mathieu; Nam, Phan Thành; Solovej, Jan Philip; Serfaty, Sylvia (2014). "Bogoliubov spectrum of interacting Bose gases". Communications on Pure and Applied Mathematics. 68 (3). Wiley: 413–471. arXiv:1211.2778. doi:10.1002/cpa.21519. S2CID 53480317. Lewin, Mathieu; Nam, Phan Thành; Rougerie, Nicolas (2014). "Derivation of Hartreeʼs theory for generic mean-field Bose systems". Advances in Mathematics. 254. Elsevier: 570–621. arXiv:1303.0981. doi:10.1016/j.aim.2013.12.010. Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert (2014). "Strichartz inequality for orthonormal functions". Journal of the European Mathematical Society. 16 (7). European Mathematical Society (EMS): 1507–1526. arXiv:1306.1309. doi:10.4171/JEMS/467. Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert (2018). "Statistical mechanics of the Uniform Electron Gas". Journal de l'École Polytechnique — Mathématiques. 5. Ecole Polytechnique: 79–116. arXiv:1705.10676. doi:10.5802/jep.64. Lewin, Mathieu; Nam, Phan Thành; Rougerie, Nicolas (2021). "Classical field theory limit of many-body quantum Gibbs states in 2D and 3D". Inventiones Mathematicae. 224 (2). Springer: 315–444. arXiv:1810.08370. Bibcode:2021InMat.224..315L. doi:10.1007/s00222-020-01010-4. S2CID 253745623.

References

Bibliography Web page

Worked examples

Example 1 — a first encounter with Mathieu Lewin

Start with the simplest possible case. Write down what Mathieu Lewin 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 Mathieu Lewin 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 Mathieu Lewin 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 Mathieu Lewin

In research: Mathieu Lewin 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 Mathieu Lewin 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: Mathieu Lewin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1977 births, Academic staff of Paris Dauphine University, French mathematician stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Mathieu Lewin 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 Mathieu Lewin in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Mathieu Lewin 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 Mathieu Lewin out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Mathieu Lewin in simple terms?

Why does Mathieu Lewin 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 Mathieu Lewin?

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 Mathieu Lewin.