mathematics

Stephen S. Kudla

Stephen S. Kudla 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 Stephen S. Kudla rather than just read about it. In short: Stephen S. Kudla (born 1950 Caracas, Venezuela) is an American mathematician working in arithmetic geometry and automorphic forms.

Key takeaways

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

Reference excerpt

Stephen S. Kudla (born 1950 Caracas, Venezuela) is an American mathematician working in arithmetic geometry and automorphic forms. He is a professor in the Department of Mathematics at the University of Toronto.

Life

After receiving his doctorate, Kudla spent a year at the Institute for Advanced Study in Princeton, following which he joined the faculty at the University of Maryland, College Park. Since 2006, he has been a professor at the University of Toronto where he held a Canada Research Chair for the period 2006–2020. In 1997, he discovered relationships between the Fourier coefficients of derivatives of Siegel Eisenstein series and arithmetic invariants of Shimura varieties (heights pairings of arithmetic cycles). He was a Sloan Fellow in 1981, received the Max-Planck Research Award in 2000, and the Jeffery–Williams Prize of the Canadian Mathematical Society in 2009. He was an Invited Speaker at the 2002 International Congress of Mathematicians in Beijing, where he gave a lecture on "Derivatives of Eisenstein series and arithmetic geometry". He was on the Scientific Review Panel of the Pacific Institute for the Mathematical Sciences (PIMS) for the period 2009–2013. For 2004 - 2010, he was a co-editor of the Canadian Journal of Mathematics, and has been co-organizer of several conferences at the Mathematical Research Institute of Oberwolfach.

Education Ph.D. State University of New York at Stony Brook 1975; Dissertation: Real Points on Algebraic Varieties Defined by Quaternion Algebras. Advisor: Michio Kuga.

Selected publications with Michael Rapoport, T. Yang: Modular forms and special cycles on Shimura curves. In: Annals of Mathematics Studies. 161. Princeton University Press, Princeton, NJ, 2006. x+373 pages ISBN 0-691-12551-1 MR 2220359

References

Illustrations

Worked examples

Example 1 — a first encounter with Stephen S. Kudla

Start with the simplest possible case. Write down what Stephen S. Kudla 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 Stephen S. Kudla 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 Stephen S. Kudla 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 Stephen S. Kudla

In research: Stephen S. Kudla 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 Stephen S. Kudla 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: Stephen S. Kudla is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1950 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Stephen S. Kudla 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 Stephen S. Kudla in 20 minutes

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

Frequently asked questions

What is Stephen S. Kudla in simple terms?

Stephen S. Kudla (born 1950 Caracas, Venezuela) is an American mathematician working in arithmetic geometry and automorphic forms.

Why does Stephen S. Kudla 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 Stephen S. Kudla?

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 Stephen S. Kudla.