mathematics

Volodymyr Mazorchuk

Volodymyr Mazorchuk 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 Volodymyr Mazorchuk rather than just read about it. In short: Volodymyr Mazorchuk (born 1972) is a Ukrainian-Swedish mathematician at Uppsala University and was awarded the Göran Gustafsson Prize in 2016. He received his PhD in mathematics from Taras Shevchenko National University of Kyiv in 1996 with advisor Yuriy Drozd.

Key takeaways

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

Reference excerpt

Volodymyr Mazorchuk (born 1972) is a Ukrainian-Swedish mathematician at Uppsala University and was awarded the Göran Gustafsson Prize in 2016. He received his PhD in mathematics from Taras Shevchenko National University of Kyiv in 1996 with advisor Yuriy Drozd.

Selected publications

Articles König, Steffen; Mazorchuk, Volodymyr (2002). "Enright's completions and injectively copresented modules". Transactions of the American Mathematical Society. 354 (7): 2725–2743. doi:10.1090/S0002-9947-02-02958-6. Mazorchuk, Volodymyr; Stroppel, Catharina (2004). "Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module". Transactions of the American Mathematical Society. 357 (7): 2939–2973. doi:10.1090/S0002-9947-04-03650-5. Khovanov, Mikhail; Mazorchuk, Volodymyr; Stroppel, Catharina (2007). "A categorification of integral Specht modules" (PDF). Proceedings of the American Mathematical Society. 136 (4): 1163–1169. doi:10.1090/S0002-9939-07-09124-1. S2CID 7656634. Mazorchuk, Volodymyr; Ovsienko, Serge; Stroppel, Catharina (2008). "Quadratic duals, Koszul dual functors, and applications". Transactions of the American Mathematical Society. 361 (3): 1129–1172. arXiv:math/0603475. doi:10.1090/S0002-9947-08-04539-X. S2CID 779678. Ganyushkin, Olexandr; Mazorchuk, Volodymyr; Steinberg, Benjamin (2009). "On the irreducible representations of a finite semigroup". Proceedings of the American Mathematical Society. 137 (11): 3585. arXiv:0712.2076. doi:10.1090/S0002-9939-09-09857-8. S2CID 1805531. Mazorchuk, Volodymyr (2010). "Some homological properties of the category 𝒪, II". Representation Theory. 14 (6): 249–263. arXiv:0909.2729. doi:10.1090/S1088-4165-10-00368-7. S2CID 6089238. Mazorchuk, Volodymyr; Wiesner, Emilie (2014). "Simple Virasoro modules induced from codimension one subalgebras of the positive part". Proceedings of the American Mathematical Society. 142 (11): 3695–3703. arXiv:1209.1691. doi:10.1090/S0002-9939-2014-12098-3. S2CID 8112726. Futorny, Vyacheslav; Grantcharov, Dimitar; Mazorchuk, Volodymyr (2014). "Weight modules over infinite dimensional Weyl algebras". Proceedings of the American Mathematical Society. 142 (9): 3049–3057. arXiv:1207.5780. doi:10.1090/S0002-9939-2014-12071-5. S2CID 48992277. Mazorchuk, Volodymyr; Miemietz, Vanessa (2015). "Transitive 2 {\displaystyle 2} -representations of finitely 2 {\displaystyle 2} -categories" (PDF). Transactions of the American Mathematical Society. 368 (11): 7623–7644. doi:10.1090/tran/6583. S2CID 15404906. Kildetoft, Tobias; MacKaay, Marco; Mazorchuk, Volodymyr; Zimmermann, Jakob (2018). "Simple transitive 2 {\displaystyle 2} -representations of small quotients of Soergel bimodules". Transactions of the American Mathematical Society. 371 (8): 5551–5590. arXiv:1605.01373. doi:10.1090/tran/7456. S2CID 119314739. Chen, Chih-Whi; Mazorchuk, Volodymyr (2020). "Simple supermodules over Lie superalgebras". Transactions of the American Mathematical Society. 374 (2): 899–921. arXiv:1801.00654. doi:10.1090/tran/8303. S2CID 119307087.

Books Lectures on s l 2 ( C ) {\displaystyle {\mathfrak {sl}}_{2}(\mathbb {C} )} -modules. World Scientific Publishing Company. 4 December 2009. ISBN 9781911299448. Lectures on Algebraic Categorification. European Mathematical Society. 2012. ISBN 9783037191088.

References

Worked examples

Example 1 — a first encounter with Volodymyr Mazorchuk

Start with the simplest possible case. Write down what Volodymyr Mazorchuk 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 Volodymyr Mazorchuk 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 Volodymyr Mazorchuk 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 Volodymyr Mazorchuk

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

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

Frequently asked questions

What is Volodymyr Mazorchuk in simple terms?

Why does Volodymyr Mazorchuk 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 Volodymyr Mazorchuk?

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 Volodymyr Mazorchuk.