mathematics

Rui Loja Fernandes

Rui Loja Fernandes 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 Rui Loja Fernandes rather than just read about it. In short: Rui António Loja Fernandes (July 20, 1965, Coimbra) is a Portuguese mathematician working in the USA. Education and career Fernandes obtained a bachelor's degree in Physics Engineering at Instituto Superior Técnico (Lisbon, Portugal) in 1988.

Key takeaways

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

Reference excerpt

Rui António Loja Fernandes (July 20, 1965, Coimbra) is a Portuguese mathematician working in the USA.

Education and career Fernandes obtained a bachelor's degree in Physics Engineering at Instituto Superior Técnico (Lisbon, Portugal) in 1988. He then moved to the USA and earned a master's degree in Mathematics in 1991 and a PhD in Mathematics in 1994 from the University of Minnesota. His PhD thesis was entitled "Completely Integrable bi-Hamiltonian Systems" and has been written under the supervision of Peter J. Olver. In 1994 he returned to Instituto Superior Técnico, where he worked first as Assistant Professor (1994-2002), and then as Associated Professor (2003-2007) and Full Professor (2007-2012). In 2012 he moved back to the USA and since then he is the Lois M. Lackner Professor of Mathematics at University of Illinois at Urbana–Champaign. In 2016, he became a Fellow of the American Mathematical Society "for contributions to the study of Poisson geometry and Lie algebroids, and for service to the mathematical community."

Research Fernandes research focusses on differential geometry, more precisely on Poisson and symplectic geometry. Among his most well-known results are a solution to the long-standing problem of describing the obstructions to the integrability of Lie algebroids and a new geometric proof of Conn's linearization theorem, both written in collaboration with Marius Crainic. He is the author of more than 40 research papers in peer-reviewed journals and has supervised 6 PhD students as of 2021.

References

External links Rui Loja Fernandes publications indexed by Google Scholar "Rui Loja Fernandes". ulisboa.pt. Retrieved May 13, 2017. "Rui Loja Fernandes". illinois.edu. Retrieved March 27, 2021.

Illustrations

Worked examples

Example 1 — a first encounter with Rui Loja Fernandes

Start with the simplest possible case. Write down what Rui Loja Fernandes 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 Rui Loja Fernandes 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 Rui Loja Fernandes 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 Rui Loja Fernandes

In research: Rui Loja Fernandes 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 Rui Loja Fernandes 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: Rui Loja Fernandes is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1965 births, 20th-century Portuguese mathematicians, 21st-century Portuguese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Rui Loja Fernandes 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Rui Loja Fernandes” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Rui Loja Fernandes in 20 minutes

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

Frequently asked questions

What is Rui Loja Fernandes in simple terms?

Rui António Loja Fernandes (July 20, 1965, Coimbra) is a Portuguese mathematician working in the USA. Education and career Fernandes obtained a bachelor's degree in Physics Engineering at Instituto Superior Técnico (Lisbon, Portugal) in 1988.

Why does Rui Loja Fernandes 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 Rui Loja Fernandes?

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 Rui Loja Fernandes.