mathematics

Roman Mikhaylov

Roman Mikhaylov 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 Roman Mikhaylov rather than just read about it. In short: Roman Valeryevich Mikhailov (Russian: Роман Валерьевич Михайлов; born 2 October 1978) is a Russian mathematician, writer, and film and theatre director. He holds a Doctor of Sciences degree in physics and mathematics and is a professor of the Russian Academy of Sciences.

Key takeaways

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

Reference excerpt

Roman Valeryevich Mikhailov (Russian: Роман Валерьевич Михайлов; born 2 October 1978) is a Russian mathematician, writer, and film and theatre director. He holds a Doctor of Sciences degree in physics and mathematics and is a professor of the Russian Academy of Sciences. Mikhailov is the author of more than 60 scientific publications and a monograph in algebra and topology, and is also a novelist and independent filmmaker. He is a specialist in homological algebra, homotopy theory, and group theory. He was an invited speaker at the 7th European Congress of Mathematics (2016) and at the International Congress of Mathematicians (2022). In 2021, he received the Andrei Bely Prize for prose.

Education

Mikhailov graduated from the Faculty of Mechanics and Mathematics of Moscow State University in 2001. In 2003, he defended his PhD dissertation at the Steklov Mathematical Institute of the Russian Academy of Sciences, and in 2010 defended his doctoral dissertation entitled Homotopy Theory of Normal Series in Groups. He later worked at the Steklov Institute and held research positions at Saint Petersburg State University, the Institute for Advanced Study (Princeton), and the University of Latvia.

Scientific work Mikhailov's research interests include homological and homotopical algebra, algebraic K-theory, group theory, group rings, and category theory. He solved or substantially advanced several long-standing problems in algebra, including problems posed by Aldridge Bousfield, Gilbert Baumslag, Levine, and Plotkin. Together with Laurent Bartholdi, Mikhailov solved the dimension subgroup problem, open for more than 80 years, showing that arbitrary finite abelian groups may occur as subgroups of dimension quotients. Their proof relies on homotopy groups of spheres. The work was recognized by the London Mathematical Society as one of the best papers published in 2020–2023. Mikhailov introduced several concepts in group theory and homotopy theory, including homotopy patterns, pattern inflations, FR-languages, transfinite parafreeness, and metabelian telescopes. At the ICM 2022 he presented a research program applying homotopy patterns to problems in group rings. In 2022, Mikhailov announced his withdrawal from active academic research.

Literature Mikhailov is the author of several experimental novels and short-story collections, including Ravinagar (2016), The Beautiful Night of All People (2017), Berries (2020), and Wait for Summer and See What Happens (2021). His prose has been praised by writer Mikhail Elizarov and philosopher Yoel Regev. In 2021, he received the Andrei Bely Prize for his novel Wait for Summer and See What Happens.

Film Mikhailov made his directorial film debut with A Fairy Tale for the Old (2022), co-directed with actor Fyodor Lavrov; the film won the main prize at the Spirit of Fire Film Festival. His subsequent films include Snow, Sister, and Wolverine (2023), Heritage (2023), October Vacation (2023), Let’s Go to Macau (2023), We Need to Make Films about Love (2024), and Firebird (2024). In 2024 he completed his first multi-episode project, Journey to the Sun and Back, based on his novel Wait for Summer and See What Happens.

Public stance Since December 2020, Mikhailov has been listed in the database of the Ukrainian website Myrotvorets due to his visit to the self-proclaimed Donetsk and Luhansk People's Republics in 2016.

Selected awards

Science Prize and Medal of the Russian Academy of Sciences for Young Scientists (2005) Moscow Mathematical Society Prize (2006) Von Neumann Fellowship, Institute for Advanced Study (2011)

Literature Andrei Bely Prize for Prose (2021)

Film Spirit of Fire Film Festival – Grand Prize (2022) Gorky Fest – Grand Prize (2023)

Filmography We Need to Make Films about Love (2024) Firebird (2024) Snow, Sister, and Wolverine (2023) Heritage (2023) October Vacation (2023) Let’s Go to Macau (2023) A Fairy Tale for the Old (2022)

References

External links Roman Mikhaylov at IMDb

Worked examples

Example 1 — a first encounter with Roman Mikhaylov

Start with the simplest possible case. Write down what Roman Mikhaylov 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 Roman Mikhaylov 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 Roman Mikhaylov 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 Roman Mikhaylov

In research: Roman Mikhaylov 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 Roman Mikhaylov 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: Roman Mikhaylov is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1978 births, 21st-century Russian writers, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Roman Mikhaylov 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 Roman Mikhaylov in 20 minutes

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

Frequently asked questions

What is Roman Mikhaylov in simple terms?

Why does Roman Mikhaylov 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 Roman Mikhaylov?

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 Roman Mikhaylov.