mathematics

Xavier Ros-Oton

Xavier Ros-Oton 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 Xavier Ros-Oton rather than just read about it. In short: Xavier Ros Oton (Barcelona, 1988) is a Spanish mathematician who works on partial differential equations (PDEs). He is an ICREA Research Professor and a Full Professor at the University of Barcelona.

Key takeaways

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

Reference excerpt

Xavier Ros Oton (Barcelona, 1988) is a Spanish mathematician who works on partial differential equations (PDEs). He is an ICREA Research Professor and a Full Professor at the University of Barcelona.

Research His research is mainly focused on topics related to the regularity of solutions to nonlinear elliptic and parabolic PDE. Some of his main contributions have been in the context of free boundary problems, integro-differential equations, and the calculus of variations.

Career He earned his Bachelor's and master's degree at the Universitat Politècnica de Catalunya in 2010 and 2011, and completed his PhD in 2014 under the supervision of Xavier Cabré. He then moved to the University of Texas at Austin, where he was an R. H. Bing Instructor, and worked with Alessio Figalli and Luis Caffarelli. After that, he was an assistant professor at the University of Zurich. Since 2020, Ros-Oton is an ICREA Research Professor at the University of Barcelona. He is a member of the editorial board of scientific journals, including Calculus of Variations and Partial Differential Equations and Collectanea Mathematica. In October 2022 was elected Académico Correspondiente of the Spanish Royal Academy of Sciences. He is the youngest member of the academy.

Honors and awards In 2017, he received both the Rubio de Francia Prize from the Royal Spanish Mathematical Society and the Antonio Valle Prize from the Spanish Society of Applied Mathematics. In 2018, he was the youngest PI of an ERC Starting Grant. Then, in 2019, he received the Scientific Research Award from the Fundacion Princesa de Girona. In 2021 he was awarded the Stampacchia Gold Medal in recognition of outstanding contributions to the field of Calculus of Variations. In 2023 was awarded with the Ferran Sunyer i Balaguer Prize for the book "Integro-Differential Elliptic Equations", with X. Fernandez-Real. In 2023 the government of China at the International Congress of Basic Science give to him the Frontiers of Science Awards, international prize given to 86 papers in all areas of Mathematics published in 2018–2022. Awarded twice for the articles "Generic regularity of free boundaries for the obstacle problem" and "Stable solutions to semilinear elliptic equations are smooth up to dimension 9". In 2023 was awarded by the Spanish Government with the "Premio Nacional de Investigación para Jóvenes 2023 en Matemáticas y Tecnologías de la Información y las Comunicaciones". He has been the PI of an ERC Consolidator Grant (2024-2029). In 2025 was awarded by the Executive Council of Catalonia (Fundació Catalana per a la Recerca i la Innovació) with the "Premi Nacional de Recerca al Talent Jove 2024".

Selected publications Figalli, A.; Ros-Oton, X.; Serra, J. (2024). The singular set in the Stefan problem. J. Amer. Math. Soc. 37, 305-389. Figalli, A.; Ros-Oton, X.; Serra, J. (2020). Generic regularity of free boundaries for the obstacle problem. Publ. Math. Inst. Hautes Études Sci. 132, 181–292. Cabré, X.; Figalli, A.; Ros-Oton, X.; Serra, J. (2020). Stable solutions to semilinear elliptic equations are smooth up to dimension 9. Acta Math. 224, 187–252. Caffarelli, L.; Ros-Oton, X.; Serra, J. (2017). Obstacle problems for integro-differential operators: regularity of solutions and free boundaries. Invent. Math. 208, 1155–1211.

References

External links Xavier Ros-Oton at the University of Barcelona Xavier Ros-Oton at Google Scholar Xavier Ros-Oton at ICREA Community Xavier Ros-Oton at ORCID Community

Illustrations

Worked examples

Example 1 — a first encounter with Xavier Ros-Oton

Start with the simplest possible case. Write down what Xavier Ros-Oton 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 Xavier Ros-Oton 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 Xavier Ros-Oton 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 Xavier Ros-Oton

In research: Xavier Ros-Oton 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 Xavier Ros-Oton 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: Xavier Ros-Oton is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1988 births, 21st-century Spanish mathematicians, European Research Council grantees, so understanding it makes those chapters shorter.
In everyday life: Look for Xavier Ros-Oton 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 Xavier Ros-Oton in 20 minutes

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Frequently asked questions

What is Xavier Ros-Oton in simple terms?

Xavier Ros Oton (Barcelona, 1988) is a Spanish mathematician who works on partial differential equations (PDEs). He is an ICREA Research Professor and a Full Professor at the University of Barcelona.

Why does Xavier Ros-Oton 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 Xavier Ros-Oton?

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 Xavier Ros-Oton.