astronomy

Matthew Emerton

Matthew Emerton 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 Matthew Emerton rather than just read about it. In short: Matthew James Emerton (born 9 November 1971) is an Australian mathematician who is a professor of mathematics at the University of Chicago. His research interests include number theory, especially the theory of automorphic forms.

Key takeaways

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

Reference excerpt

Matthew James Emerton (born 9 November 1971) is an Australian mathematician who is a professor of mathematics at the University of Chicago. His research interests include number theory, especially the theory of automorphic forms.

Early life and education He earned his PhD in 1998 from Harvard University (where he studied under Barry Mazur and his PhD thesis was titled "2-Adic Modular Forms of Minimal Slope") and a BS (honors) from the University of Melbourne.

Career After postdoctoral positions at the University of Michigan and the University of Chicago, Emerton joined the Northwestern University mathematics department as an assistant professor in 2001. He became an associate professor in 2005 and a full professor in 2008. He joined the University of Chicago faculty in 2011. Emerton introduced the notion of completed cohomology, which has proved to be a useful tool in the study of the p-adic theory of automorphic forms. Using this theory, together with the work of Colmez on the p-adic Langlands program, he posted a preprint in 2011 proving many cases of the Fontaine--Mazur conjecture.

Awards Emerton was a Sloan fellow in 1997 and was an invited speaker at the 2014 ICM in Seoul where he gave a talk entitled "Completed cohomology and the p-adic Langlands program".

Social media Emerton formally ranked among the top 0.25% users of MathOverflow, where he used to be a frequent contributor, known for his expository pieces on the Langlands program, his posts on algebraic geometry, and his posts on number theory. He has also been noted for his helpful comments on math blogs.

References

Worked examples

Example 1 — a first encounter with Matthew Emerton

Start with the simplest possible case. Write down what Matthew Emerton 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 Matthew Emerton 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 Matthew Emerton 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 Matthew Emerton

In research: Matthew Emerton 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 Matthew Emerton 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: Matthew Emerton is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1971 births, Australian mathematicians, Harvard University alumni, so understanding it makes those chapters shorter.
In everyday life: Look for Matthew Emerton 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 Matthew Emerton in 20 minutes

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

Frequently asked questions

What is Matthew Emerton in simple terms?

Why does Matthew Emerton 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 Matthew Emerton?

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 Matthew Emerton.