mathematics

Tristan Rivière

Tristan Rivière 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 Tristan Rivière rather than just read about it. In short: Tristan Rivière (born 1967) is a French mathematician, working on partial differential equations and the calculus of variations. Biography Rivière studied at the École Polytechnique and obtained his PhD in 1993 at the Pierre and Marie Curie University, under the supervision of Fabrice Bethuel, with a thesis on harmonic maps between manifolds.

Key takeaways

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

Reference excerpt

Tristan Rivière (born 1967) is a French mathematician, working on partial differential equations and the calculus of variations.

Biography Rivière studied at the École Polytechnique and obtained his PhD in 1993 at the Pierre and Marie Curie University, under the supervision of Fabrice Bethuel, with a thesis on harmonic maps between manifolds. In 1992 he was appointed chargé de recherche at CNRS. In 1997 he received his habilitation at the University of Paris-Sud in Orsay. From 1999 to 2000 he was a visiting associate professor at the Courant Institute of Mathematical Sciences (New York University). Since 2003 he is full professor at ETH Zurich and since 2009 he is the Director of the Institute for Mathematical Research at ETH.

Research activity His research interests include partial differential equations in physics (liquid crystals, Bose–Einstein condensates, micromagnetics, Ginzburg–Landau theory of superconductivity, gauge theory) and differential geometry (harmonic maps between manifolds, geometric flows, minimal surfaces, the Willmore functional and Yang–Mills fields). His work focuses in particular on non-linear phenomena, formation of vortices, energy quantization and regularity issues.

Awards and recognition In 1996 he received the Bronze Medal of the CNRS, while in 2003 he was awarded the first Stampacchia Medal. In 2002 he was an invited speaker at the International Congress of Mathematicians in Beijing, where he gave a talk on bubbling, quantization and regularity issues in geometric non-linear analysis.

Selected publications "Everywhere discontinuous Harmonic Maps into Spheres." Acta Mathematica, 175 (1995), 197-226 with F. Pacard: Linear and Nonlinear Aspects of Vortices. Birkhäuser 2000 "Conservation laws for conformally invariant variational problems". Inventiones Math., 168 (2007), 1-22 with R. Hardt: "Connecting rational homotopy type singularities of maps between manifolds". Acta Mathematica, 200 (2008), 15-83 "Analysis Aspects of Willmore Surfaces". Inventiones Math., 174 (2008), no. 1, 1-45 with G. Tian: "The singular set of 1-1 Integral currents". Annals of Mathematics, 169 (2009), no. 3, 741-794 with Y. Bernard: "Energy Quantization for Willmore Surfaces and Applications". Annals of Mathematics, 180 (2014), no. 1, 87-136 "A viscosity method in the min-max theory of minimal surfaces". Publications mathématiques de l'IHÉS, 126 (2017), no. 1, 177-246

References

External links Homepage, ETH Zürich

Illustrations

Worked examples

Example 1 — a first encounter with Tristan Rivière

Start with the simplest possible case. Write down what Tristan Rivière 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 Tristan Rivière 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 Tristan Rivière 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 Tristan Rivière

In research: Tristan Rivière 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 Tristan Rivière 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: Tristan Rivière is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1967 births, Academic staff of ETH Zurich, Academic staff of the University of Paris, so understanding it makes those chapters shorter.
In everyday life: Look for Tristan Rivière 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 Tristan Rivière in 20 minutes

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

Frequently asked questions

What is Tristan Rivière in simple terms?

Tristan Rivière (born 1967) is a French mathematician, working on partial differential equations and the calculus of variations. Biography Rivière studied at the École Polytechnique and obtained his PhD in 1993 at the Pierre and Marie Curie University, under the supervision of Fabrice Bethuel, with…

Why does Tristan Rivière 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 Tristan Rivière?

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 Tristan Rivière.