astronomy

Vinayak Vatsal

Vinayak Vatsal 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 Vinayak Vatsal rather than just read about it. In short: Vinayak Vatsal is a Canadian mathematician working in number theory and arithmetic geometry. Education Vatsal received his B.Sc. degree in 1992 from Stanford University and a Ph.D.

Key takeaways

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

Reference excerpt

Vinayak Vatsal is a Canadian mathematician working in number theory and arithmetic geometry.

Education Vatsal received his B.Sc. degree in 1992 from Stanford University and a Ph.D. (thesis title: Iwasawa Theory, modular forms and Artin representations) in 1997 from Princeton University under the supervision of Andrew Wiles who had just completed his proof of Fermat's Last Theorem. He then became a post-doctoral fellow at the University of Toronto.

Career and research Vatsal joined the faculty at the University of British Columbia in 1999 where he still works today. Vatsal's contributions include his work on the Iwasawa theory of elliptic curves, a field which he approached using novel ideas from ergodic theory. Vatsal has received numerous accolades. He was a Sloan Fellow in 2002–2004 and a recipient of the André Aisenstadt Prize (2004), the Ribenboim Prize (2006) and the Coxeter–James Prize (2007). In 2008, he was an invited speaker at the 2008 International Congress of Mathematicians in Madrid.

Selected publications Uniform distribution of Heegner Points, Inventiones Mathematicae, Vol. 148, 2002, pp. 1–48 (Proof of a conjecture of Barry Mazur) with Ralph Greenberg Iwasawa Invariants of Elliptic Curves, Inventiones Mathematicae, vol 142, 2000, pp. 17–63 Special values of anticyclotomic L-functions, Duke Mathematical Journal, vol. 116, 2003, pp. 219–261 with C. Cornut Nontriviality of Rankin-Selberg L-functions and CM points, in Burns, Kevin Buzzard, Nekovar (eds), L-functions and Galois Representations, Cambridge University Press, 2007, pp. 121–186 with C. Cornut CM points and quaternion algebras, Documenta Mathematica, volume 10, 2005

Other Vatsal is also a published author. His short story Mosaic appared in the Summer 1995 edition of Story magazine.

References

External links Vinayak Vatsal Homepage at UBC

Worked examples

Example 1 — a first encounter with Vinayak Vatsal

Start with the simplest possible case. Write down what Vinayak Vatsal 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 Vinayak Vatsal 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 Vinayak Vatsal 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 Vinayak Vatsal

In research: Vinayak Vatsal 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 Vinayak Vatsal 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: Vinayak Vatsal is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1969 births, Academic staff of the University of British Columbia, Canadian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Vinayak Vatsal 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 Vinayak Vatsal in 20 minutes

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

Frequently asked questions

What is Vinayak Vatsal in simple terms?

Vinayak Vatsal is a Canadian mathematician working in number theory and arithmetic geometry. Education Vatsal received his B.Sc. degree in 1992 from Stanford University and a Ph.D.

Why does Vinayak Vatsal 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 Vinayak Vatsal?

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 Vinayak Vatsal.