mathematics

Igor Frenkel

Igor Frenkel 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 Igor Frenkel rather than just read about it. In short: Igor Borisovich Frenkel (Russian: Игорь Борисович Френкель; born 22 April 1952) is a Russian-American mathematician at Yale University working in representation theory and mathematical physics. Frenkel emigrated to the United States in 1979.

Key takeaways

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

Reference excerpt

Igor Borisovich Frenkel (Russian: Игорь Борисович Френкель; born 22 April 1952) is a Russian-American mathematician at Yale University working in representation theory and mathematical physics. Frenkel emigrated to the United States in 1979. He received his PhD from Yale University in 1980 with a dissertation on the "Orbital Theory for Affine Lie Algebras". He held positions at the IAS and MSRI, and a tenured professorship at Rutgers University, before taking his current job of tenured professor at Yale University. He was elected to the National Academy of Sciences in 2018. He is also a Fellow of the American Academy of Arts and Sciences.

Mathematical work In collaboration with James Lepowsky and Arne Meurman, he constructed the monster vertex algebra, a vertex algebra which provides a representation of the monster group. Around 1990, as a member of the School of Mathematics at the Institute for Advanced Study, Frenkel worked on the mathematical theory of knots, hoping to develop a theory in which the knot would be seen as a physical object. He continued to develop the idea with his student Mikhail Khovanov, and their collaboration ultimately led to the discovery of Khovanov homology, a refinement of the Jones polynomial, in 2002. A detailed description of Igor Frenkel's research over the years can be found in "Perspectives in Representation Theory".

References

External links Home page Igor Frenkel at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Igor Frenkel

Start with the simplest possible case. Write down what Igor Frenkel 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 Igor Frenkel 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 Igor Frenkel 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 Igor Frenkel

In research: Igor Frenkel 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 Igor Frenkel 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: Igor Frenkel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1952 births, 20th-century American mathematicians, American mathematician stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Igor Frenkel 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 Igor Frenkel in 20 minutes

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

Frequently asked questions

What is Igor Frenkel in simple terms?

Why does Igor Frenkel 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 Igor Frenkel?

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 Igor Frenkel.