mathematics

Mikhail Khovanov

Mikhail Khovanov 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 Mikhail Khovanov rather than just read about it. In short: Mikhail Khovanov (Russian: Михаил Гелиевич Хованов; born 13 January 1972) is a Russian professor of mathematics at Johns Hopkins University who works on representation theory, knot theory, and algebraic topology. He is known for introducing Khovanov homology for links, which was one of the first examples of categorification.

Key takeaways

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

Reference excerpt

Mikhail Khovanov (Russian: Михаил Гелиевич Хованов; born 13 January 1972) is a Russian professor of mathematics at Johns Hopkins University who works on representation theory, knot theory, and algebraic topology. He is known for introducing Khovanov homology for links, which was one of the first examples of categorification.

Education and career Khovanov graduated from Moscow State School 57 mathematical class in 1988. He earned a PhD in mathematics from Yale University in 1997, where he studied under Igor Frenkel. Khovanov was a faculty member at UC Davis before moving to Columbia University. He is a half-brother of Tanya Khovanova.

References

External links Khovanov's faculty page at Columbia List of Khovanov's publications

Worked examples

Example 1 — a first encounter with Mikhail Khovanov

Start with the simplest possible case. Write down what Mikhail Khovanov 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 Mikhail Khovanov 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 Mikhail Khovanov 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 Mikhail Khovanov

In research: Mikhail Khovanov 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 Mikhail Khovanov 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: Mikhail Khovanov is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1972 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Mikhail Khovanov 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 Mikhail Khovanov in 20 minutes

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

Frequently asked questions

What is Mikhail Khovanov in simple terms?

Why does Mikhail Khovanov 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 Mikhail Khovanov?

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 Mikhail Khovanov.