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Ivan Smith (mathematician)

Ivan Smith (mathematician) 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 Ivan Smith (mathematician) rather than just read about it. In short: Ivan Smith (born 1973) is a British mathematician who deals with symplectic manifolds and their interaction with algebraic geometry, low-dimensional topology, and dynamics. He is a professor at the University of Cambridge.

Key takeaways

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

Reference excerpt

Ivan Smith (born 1973) is a British mathematician who deals with symplectic manifolds and their interaction with algebraic geometry, low-dimensional topology, and dynamics. He is a professor at the University of Cambridge.

Education and career Smith was born in 1973 as the second child of Neil Smith, a professor of linguistics at University College London, and Saras Smith. He studied at the University of Oxford, where he received his doctorate in 1999 under the supervision of Simon Donaldson with thesis Symplectic Geometry of Lefschetz Fibrations. Smith is now a professor in Cambridge at Gonville & Caius College. Among other things, Smith derived nodal invariants from symplectic geometry. He received in 2007 the Whitehead Prize for his work in symplectic topology (highlighting the breadth of applied techniques from algebraic geometry and topology) and in 2013 the Adams Prize. In 2018 he was an invited speaker at the International Congress of Mathematicians in Rio de Janeiro. Smith was elected a Fellow of the Royal Society in 2023.

Selected publications Smith, Ivan; Thomas, Richard P.; Yau, Shing-Tung (2002). "Symplectic conifold transitions". Journal of Differential Geometry. 62 (2): 209–242. arXiv:math/0209319. doi:10.4310/jdg/1090950192. hdl:10044/1/231. MR 1988503. Fukaya, Kenji; Seidel, Paul; Smith, Ivan (2007). "Exact Lagrangian submanifolds in simply-connected cotangent bundles". Inventiones Mathematicae. 172 (1): 1–27. arXiv:math/0701783. Bibcode:2007InMat.172....1F. doi:10.1007/s00222-007-0092-8. MR 2385665. S2CID 647814. with Denis Auroux: Lefschetz pencils, branched covers and symplectic invariants . In: Symplectic 4-manifolds and algebraic surfaces (Cetraro, 2003), Lect. Notes in Math. 1938, Springer, 2008, 1–53, Arxiv with Mohammed Abouzaid: "Homological mirror symmetry for the 4-torus", Duke Math. J., Vol. 152, 2010, pp. 373–440, Arxiv Floer cohomology and pencils of quadrics , Inventiones Mathematicae, Vol. 189, 2012, pp. 149–250, Arxiv "A symplectic prolegomenon", Bulletin AMS, Vol. 52, 2015, pp. 415–464, doi:10.1090/S0273-0979-2015-01477-1 Quiver algebras as Fukaya categories , Geom. Topol., Vol. 19, 2015, 2557–2617, Arxiv with Mohammed Abouzaid: Khovanov homology from Floer cohomology , Arxiv 2015 with Mohammed Abouzaid: The symplectic arc algebra is formal , Duke Math. J., Vol. 165, 2016, pp. 985–1060, Arxiv

References

External links Homepage in Cambridge "Lagrangian Whitney sphere links - Ivan Smith". YouTube. 1 November 2016. "An interview with Ivan Smith". YouTube. 8 August 2018. "Stability conditions in symplectic topology – Ivan Smith – ICM2018". YouTube. 3 October 2018.

Worked examples

Example 1 — a first encounter with Ivan Smith (mathematician)

Start with the simplest possible case. Write down what Ivan Smith (mathematician) 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 Ivan Smith (mathematician) 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 Ivan Smith (mathematician) 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 Ivan Smith (mathematician)

In research
Ivan Smith (mathematician) 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 Ivan Smith (mathematician) 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
Ivan Smith (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1973 births, 20th-century British mathematicians, 21st-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Ivan Smith (mathematician) 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 Ivan Smith (mathematician) in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Ivan Smith (mathematician) means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Ivan Smith (mathematician) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ivan Smith (mathematician) in simple terms?

Ivan Smith (born 1973) is a British mathematician who deals with symplectic manifolds and their interaction with algebraic geometry, low-dimensional topology, and dynamics. He is a professor at the University of Cambridge.

Why does Ivan Smith (mathematician) 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 Ivan Smith (mathematician)?

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 Ivan Smith (mathematician).

Tags

  • 1973 births
  • 20th-century British mathematicians
  • 21st-century British mathematicians
  • Alumni of the University of Oxford
  • British fellows of the Royal Society
  • British topologists
  • Differential geometers
  • Fellows of Gonville and Caius College, Cambridge
  • Living people
  • Whitehead Prize winners

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