mathematics

Peter Ozsváth

Peter Ozsváth 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 Peter Ozsváth rather than just read about it. In short: Peter Steven Ozsváth (born October 20, 1967) is a professor of mathematics at Princeton University. He created, along with Zoltán Szabó, Heegaard Floer homology, a homology theory for 3-manifolds.

Key takeaways

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

Reference excerpt

Peter Steven Ozsváth (born October 20, 1967) is a professor of mathematics at Princeton University. He created, along with Zoltán Szabó, Heegaard Floer homology, a homology theory for 3-manifolds.

Education Ozsváth received his PhD from Princeton in 1994 under the supervision of John Morgan; his dissertation was entitled On Blowup Formulas For SU(2) Donaldson Polynomials.

Awards In 2007, Ozsváth was one of the recipients of the Oswald Veblen Prize in Geometry. In 2008 he was named a Guggenheim Fellow. In July 2017, he was a plenary lecturer in the Mathematical Congress of the Americas. He was elected a member of the National Academy of Sciences in 2018. He was elected to the 2026 class of Fellows of the American Mathematical Society.

Selected publications Ozsváth, Peter; Szabó, Zoltán (2004). "Holomorphic disks and topological invariants for closed three-manifolds". Ann. of Math. 159 (3): 1027–1158. arXiv:math/0101206. doi:10.4007/annals.2004.159.1027. S2CID 119143219. Ozsváth, Peter; Szabó, Zoltán (2004). "Holomorphic disks and three-manifold invariants: properties and applications". Ann. of Math. 159 (3): 1159–1245. doi:10.4007/annals.2004.159.1159. Grid Homology for Knots and Links, American Math Society, (2015)

References

External links Personal homepage Peter Ozsváth at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Peter Ozsváth

Start with the simplest possible case. Write down what Peter Ozsváth 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 Peter Ozsváth 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 Peter Ozsváth 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 Peter Ozsváth

In research: Peter Ozsváth 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 Peter Ozsváth 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: Peter Ozsváth is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1967 births, 20th-century American mathematicians, 20th-century Hungarian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Peter Ozsváth 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 Peter Ozsváth in 20 minutes

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

Frequently asked questions

What is Peter Ozsváth in simple terms?

Peter Steven Ozsváth (born October 20, 1967) is a professor of mathematics at Princeton University. He created, along with Zoltán Szabó, Heegaard Floer homology, a homology theory for 3-manifolds.

Why does Peter Ozsváth 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 Peter Ozsváth?

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 Peter Ozsváth.