mathematics

James McKernan

James McKernan 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 James McKernan rather than just read about it. In short: James McKernan (born 1964) is a mathematician, and a professor of mathematics at the University of California, San Diego. He was a professor at the Massachusetts Institute of Technology from 2007 until 2013.

Key takeaways

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

Reference excerpt

James McKernan (born 1964) is a mathematician, and a professor of mathematics at the University of California, San Diego. He was a professor at the Massachusetts Institute of Technology from 2007 until 2013.

Education McKernan was educated at The Campion School and Trinity College, Cambridge, before going on to earn his Ph.D. from Harvard University in 1991. His dissertation, On the Hyperplane Sections of a Variety in Projective Space, was supervised by Joe Harris.

Recognition McKernan was the joint winner of the Cole Prize in 2009, and joint recipient of the Clay Research Award in 2007. Both honors were received jointly with his colleague Christopher Hacon. He gave an invited talk at the International Congress of Mathematicians in 2010, on the topic of "Algebraic Geometry". He was the joint winner (with Christopher Hacon) of the 2018 Breakthrough Prize in Mathematics. He was elected as a Fellow of the American Mathematical Society in the 2020 Class, for "contributions to algebraic geometry, in particular his proof of the finite generation of the canonical ring, the existence of flips and the boundedness of varieties of log general type".

References

External links Official website Citation for 2009 Cole Prize in Algebra The work of Hacon and McKernan

Illustrations

Worked examples

Example 1 — a first encounter with James McKernan

Start with the simplest possible case. Write down what James McKernan 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 James McKernan 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 James McKernan 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 James McKernan

In research: James McKernan 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 James McKernan 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: James McKernan is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1964 births, 20th-century British mathematicians, 21st-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for James McKernan 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 James McKernan in 20 minutes

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

Frequently asked questions

What is James McKernan in simple terms?

Why does James McKernan 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 James McKernan?

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 James McKernan.