mathematics

Sara Billey

Sara Billey 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 Sara Billey rather than just read about it. In short: Sara Cosette Billey is an American mathematician working in algebraic combinatorics. She is known for her contributions on Schubert polynomials, singular loci of Schubert varieties, Kostant polynomials, and Kazhdan–Lusztig polynomials often using computer verified proofs.

Key takeaways

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

Reference excerpt

Sara Cosette Billey is an American mathematician working in algebraic combinatorics. She is known for her contributions on Schubert polynomials, singular loci of Schubert varieties, Kostant polynomials, and Kazhdan–Lusztig polynomials often using computer verified proofs. She is currently a professor of mathematics at the University of Washington.

Education and career Billey did her undergraduate studies at the Massachusetts Institute of Technology, graduating in 1990. She earned her Ph.D. in mathematics in 1994 from the University of California, San Diego, under the joint supervision of Adriano Garsia and Mark Haiman. She returned to MIT as a postdoctoral researcher with Richard P. Stanley, and continued there as an assistant and associate professor until 2003, when she moved to the University of Washington.

Recognition In 2000, Billey received the Presidential Early Career Award for Scientists and Engineers, the highest honor given by the United States government to mathematicians, scientists, and engineers near the start of their independent research careers. Billey became a fellow of the American Mathematical Society in 2012, in the inaugural class.

Selected publications

Books Sara, Billey; Lakshmibai, V. (2000). Singular loci of Schubert varieties. Boston: Birkhäuser. ISBN 9780817640927. OCLC 44750779.

Articles Billey, Sara; Haiman, Mark (1995). "Schubert polynomials for the classical groups". Journal of the American Mathematical Society. 8 (2): 443–482. doi:10.1090/s0894-0347-1995-1290232-1. ISSN 0894-0347. Billey, Sara; Warrington, Gregory (2003). "Maximal singular loci of Schubert varieties in 𝑆𝐿(𝑛)/𝐵". Transactions of the American Mathematical Society. 355 (10): 3915–3945. doi:10.1090/s0002-9947-03-03019-8. ISSN 0002-9947. Billey, Sara (1999). "Kostant polynomials and the cohomology ring for G/B". Duke Mathematical Journal. 96 (1): 205–224. doi:10.1215/S0012-7094-99-09606-0. ISSN 0012-7094. S2CID 16184223.

References

External links Sara Billey's Home Page "AWM 2013 Essay Contest Winner writes about Sara Billey". Sara Billey publications indexed by Google Scholar

Illustrations

Worked examples

Example 1 — a first encounter with Sara Billey

Start with the simplest possible case. Write down what Sara Billey 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 Sara Billey 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 Sara Billey 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 Sara Billey

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

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

Frequently asked questions

What is Sara Billey in simple terms?

Why does Sara Billey 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 Sara Billey?

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 Sara Billey.