mathematics

Jessica Purcell

Jessica Purcell 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 Jessica Purcell rather than just read about it. In short: Jessica A. Shepherd Purcell is an American mathematician specializing in low-dimensional topology whose research topics have included hyperbolic Dehn surgery and the Jones polynomial.

Key takeaways

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

Reference excerpt

Jessica A. Shepherd Purcell is an American mathematician specializing in low-dimensional topology whose research topics have included hyperbolic Dehn surgery and the Jones polynomial. She is a professor of mathematics at Monash University in Melbourne, Australia.

Education Purcell credits a high school mathematics teacher, Mr. Pehrson, for her interest in mathematics. She majored in mathematics as an undergraduate at the University of Utah, with a minor in computer science. She was a co-winner of the 1998 Alice T. Schafer Prize for Excellence in Mathematics by an Undergraduate Woman of the Association for Women in Mathematics, and graduated summa cum laude in 1998. After earning a master's degree in mathematics at the University of Michigan in 1999, Purcell completed her Ph.D. at Stanford University in 2004. Her dissertation, Cusp Shapes of Hyperbolic Link Complements and Dehn Filling, was supervised by Steven Kerckhoff.

Career After postdoctoral research at the University of Texas at Austin and University of Oxford, Purcell became an assistant professor at Brigham Young University in 2007. She was named a Sloan Research Fellow in 2011, and earned tenure at Brigham Young in 2013. After visits to Monash University and at the Institute for Advanced Study as a Von Neumann Fellow, she moved to Monash as an associate professor in 2015, became an ARC Future Fellow in 2017, and was named full professor in 2019. She chaired the Women in Mathematics Special Interest Group of the Australian Mathematical Society for 2018–2019 and 2019–2020.

Recognition Purcell's work has earned international recognition for advancing understanding of geometric structures in three-dimensional spaces, including applications to theoretical physics and pure mathematics. She has received prestigious awards, such as the Alfred P. Sloan Research Fellowship in 2011, the National Science Foundation CAREER Award from 2013 to 2016, and the Von Neumann Fellowship at the Institute for Advanced Study in 2015. Purcell was elected a Fellow of the Australian Academy of Science in May 2025. She was elected to the 2026 class of Fellows of the American Mathematical Society.

Books Purcell is the author of the book Hyperbolic Knot Theory (Graduate Studies in Mathematics 209, American Mathematical Society, 2020). With David Futer and Efstratia Kalfagianni she is a coauthor of Guts of Surfaces and the Colored Jones Polynomial (Lecture Notes in Mathematics 2069, Springer, 2012).

References

External links Home page Jessica Purcell publications indexed by Google Scholar Meet Professor Jessica Purcell, Monash University

Illustrations

Worked examples

Example 1 — a first encounter with Jessica Purcell

Start with the simplest possible case. Write down what Jessica Purcell 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 Jessica Purcell 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 Jessica Purcell 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 Jessica Purcell

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

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

Frequently asked questions

What is Jessica Purcell in simple terms?

Jessica A. Shepherd Purcell is an American mathematician specializing in low-dimensional topology whose research topics have included hyperbolic Dehn surgery and the Jones polynomial.

Why does Jessica Purcell 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 Jessica Purcell?

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 Jessica Purcell.