astronomy

Monica Vișan

Monica Vișan is a astronomy 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 Monica Vișan rather than just read about it. In short: Monica Vișan (born August 5, 1979, in Drobeta-Turnu Severin, Romania) is a Romanian mathematician at the University of California, Los Angeles who specializes in partial differential equations and is well known for her work on the nonlinear Schrödinger equation. Education and career Vișan earned a bachelor's degree at the University of Bucharest in 2002.

Key takeaways

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

Reference excerpt

Monica Vișan (born August 5, 1979, in Drobeta-Turnu Severin, Romania) is a Romanian mathematician at the University of California, Los Angeles who specializes in partial differential equations and is well known for her work on the nonlinear Schrödinger equation.

Education and career Vișan earned a bachelor's degree at the University of Bucharest in 2002. She became a student of Terence Tao at the University of California, Los Angeles (UCLA), where she completed her doctorate in 2006. Her dissertation was titled The Defocusing Energy-Critical Nonlinear Schrödinger Equation in Dimensions Five and Higher. After postdoctoral research at the Institute for Advanced Study, Vișan became an assistant professor in the mathematics department at the University of Chicago in 2008. She returned to UCLA as a faculty member in 2009 and (keeping her appointment at UCLA) spent 2010–2011 as Harrington Faculty Fellow at the University of Texas at Austin.

Recognition Vișan won a Sloan Research Fellowship in 2010. She was elected as a Fellow of the American Mathematical Society in the 2024 class of fellows.

Selected publications With Herbert Koch and Daniel Tătaru, Vișan is the author of the book Dispersive Equations and Nonlinear Waves: Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps. Her research papers include:

Ryckman, Eric; Vișan, Monica (2007), "Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1 + 4 {\displaystyle \mathbb {R} ^{1+4}} ", American Journal of Mathematics, 129 (1): 1–60, arXiv:math/0501462, doi:10.1353/ajm.2007.0004, MR 2288737, S2CID 19024265 Vișan, Monica (2007), "The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions", Duke Mathematical Journal, 138 (2): 281–374, arXiv:math/0508298, doi:10.1215/S0012-7094-07-13825-0, MR 2318286, S2CID 2427673 Tao, Terence; Vișan, Monica; Zhang, Xiaoyi (2007), "The nonlinear Schrödinger equation with combined power-type nonlinearities", Communications in Partial Differential Equations, 32 (7–9): 1281–1343, arXiv:math/0511070, doi:10.1080/03605300701588805, MR 2354495, S2CID 15109526 Killip, Rowan; Tao, Terence; Vișan, Monica (2009), "The cubic nonlinear Schrödinger equation in two dimensions with radial data", Journal of the European Mathematical Society, 11 (6): 1203–1258, arXiv:0707.3188, doi:10.4171/JEMS/180, MR 2557134 Killip, Rowan; Vişan, Monica (2010), "The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher", American Journal of Mathematics, 132 (2): 361–424, arXiv:0804.1018, doi:10.1353/ajm.0.0107, MR 2654778, S2CID 1068572 Killip, Rowan; Vişan, Monica (2013), "Nonlinear Schrödinger equations at critical regularity" (PDF), Evolution equations, Clay Math. Proc., vol. 17, Amer. Math. Soc., Providence, RI, pp. 325–437, MR 3098643

References

External links Home page

Worked examples

Example 1 — a first encounter with Monica Vișan

Start with the simplest possible case. Write down what Monica Vișan claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Monica Vișan 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 Monica Vișan 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 Monica Vișan

In research: Monica Vișan appears in astronomy 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 Monica Vișan 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: Monica Vișan is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1979 births, 21st-century Romanian mathematicians, Fellows of the American Mathematical Society, so understanding it makes those chapters shorter.
In everyday life: Look for Monica Vișan 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 “Monica Vișan” →

Affiliate

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

How to study Monica Vișan in 20 minutes

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

Frequently asked questions

What is Monica Vișan in simple terms?

Why does Monica Vișan matter?

Because it connects several astronomy 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 Monica Vișan?

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 Monica Vișan.