mathematics

Gustavo Ponce

Gustavo Ponce 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 Gustavo Ponce rather than just read about it. In short: Gustavo A. Ponce (born 20 April 1952 in Venezuela) is a Venezuelan mathematician.

Key takeaways

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

Reference excerpt

Gustavo A. Ponce (born 20 April 1952 in Venezuela) is a Venezuelan mathematician.

Education and career Ponce graduated from the Central University of Venezuela with a bachelor's degree in 1976. At the Courant Institute of Mathematical Sciences of New York University he graduated with a master's degree in 1980 and a Ph.D. in 1982 with thesis Long time stability of solutions of nonlinear evolution equations under the supervision of Sergiu Klainerman (and Louis Nirenberg). Ponce was a visiting lecturer at the University of California, Berkeley from 1982 to 1984, an assistant professor at the Central University of Venezuela from 1984 to 1986, and an assistant professor at the University of Chicago from 1986 to 1989. He was from 1989 to 1991 an associate professor at Pennsylvania State University and is since 1991 a full professor at the University of California, Santa Barbara. He was a visiting professor for brief periods at many academic institutions, including the University of Bonn in 1989, the University of Paris-Sud in 1997 (and again in 2003 and 2012), MSRI in 2001, the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in 2002 (and again in 2010), the Institute for Advanced Study in 2004, the Institute Henri Poincaré in 2009, the Autonomous University of Madrid in 2011, the University of the Basque Country in 2015, and IHES in 2016. Ponce does research on nonlinear partial differential equations (PDEs) using PDE solutions to equations in mathematical physics, such as the Euler and Navier-Stokes equations of hydrodynamics. He was on the editorial boards of Transactions of the AMS from 2006 to 2014 and the Memoirs of the AMS from 2006 to 2014. In 1998 he was an Invited Speaker with talk On nonlinear dispersive equations at the International Congress of Mathematicians in Berlin. In 2012 he was elected a Fellow of the American Mathematical Society.

Selected publications with Felipe Linares: Introduction to nonlinear dispersive equations, Universitext (2nd ed.), Springer, 2015, doi:10.1007/978-1-4939-2181-2, ISBN 978-1-4939-2180-5 with Sergiu Klainerman: Klainerman, S.; Ponce, Gustavo (1983), "Global, small amplitude solutions to nonlinear evolution equations", Communications on Pure and Applied Mathematics, 63: 133–141, doi:10.1002/cpa.3160360106 with Tosio Kato: Kato, Tosio; Ponce, Gustavo (1988), "Commutators estimates and the Euler and Navier-Stokes equations", Communications on Pure and Applied Mathematics, 41 (7): 891–907, doi:10.1002/cpa.3160410704 with Felipe Linares: Linares, Felipe; Ponce, Gustavo (1993), "On the Davey-Stewartson systems", Annales de l'Institut Henri Poincaré C, 10 (5): 523–548, doi:10.1016/S0294-1449(16)30203-7 with Carlos Kenig and Luis Vega: Kenig, Carlos; Ponce, Gustavo; Vega, Luis (1996), "A bilinear estimate with applications to KdV equation", Journal of the American Mathematical Society, 9 (2): 573–603, doi:10.1090/S0894-0347-96-00200-7, JSTOR 2152869 with Carlos Kenig and Luis Vega: "Smoothing effects and local theory theory for generalized nonlinear Schrödinger equations", Inventiones Mathematicae, 134: 489–545, 1998, doi:10.1007/s002220050272 with Carlos Kenig and Luis Vega: Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis (2004), "The Cauchy problem for quasi-linear Schrödinger equations", Inventiones Mathematicae, 158 (2): 343–388, doi:10.1007/s00222-004-0373-4 with Carlos Kenig, Christian Rolvung, and Luis Vega: Kenig, C.E.; Ponce, G.; Rolvung, C.; Vega, L. (2005), "Variable Coefficient Schrödinger flows for ultrahyperbolic operators", Advances in Mathematics, 196 (2): 373–486, arXiv:math/0503205, doi:10.1016/j.aim.2004.02.002 with A. Alexandrou Himonas, Gerard Misiolek, and Yong Zhou: Himonas, A. Alexandrou; Misiołek, Gerard; Ponce, Gustavo; Zhou, Yong (2007), "Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm equation", Communications in Mathematical Physics, 271 (2): 511–522, arXiv:math/0604192, doi:10.1007/s00220-006-0172-4 with Luis Escauriaza, Carlos Kenig, and Luis Vega: Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. (2006), "On uniqueness properties of solutions of Schrödinger equations", Communications in Partial Differential Equations, 31 (12): 1811–1823, arXiv:1110.4873, doi:10.1080/03605300500530446, S2CID 121929231

References

Illustrations

Worked examples

Example 1 — a first encounter with Gustavo Ponce

Start with the simplest possible case. Write down what Gustavo Ponce 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 Gustavo Ponce 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 Gustavo Ponce 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 Gustavo Ponce

In research: Gustavo Ponce 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 Gustavo Ponce 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: Gustavo Ponce is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1952 births, Central University of Venezuela alumni, Courant Institute of Mathematical Sciences alumni, so understanding it makes those chapters shorter.
In everyday life: Look for Gustavo Ponce 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 Gustavo Ponce in 20 minutes

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

Frequently asked questions

What is Gustavo Ponce in simple terms?

Gustavo A. Ponce (born 20 April 1952 in Venezuela) is a Venezuelan mathematician.

Why does Gustavo Ponce 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 Gustavo Ponce?

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 Gustavo Ponce.