mathematics

Ivan Panin (mathematician)

Ivan Panin (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 Panin (mathematician) rather than just read about it. In short: Ivan Aleksandrovich Panin (Иван Александрович Панин, born 2 July 1959 in Apatity, Russia) is a Russian mathematician, specializing in algebra, algebraic geometry, and algebraic K-theory. Education and career In 1973 he entered boarding school at D.

Key takeaways

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Reference excerpt

Ivan Aleksandrovich Panin (Иван Александрович Панин, born 2 July 1959 in Apatity, Russia) is a Russian mathematician, specializing in algebra, algebraic geometry, and algebraic K-theory.

Education and career In 1973 he entered boarding school at D. K. Faddeev Academic Gymnasium and graduated there in 1976 There he graduated in 1981 from the Faculty of Mathematics and Mechanics of Saint Petersburg State University. At the St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences (abbreviated ПОМИ им. В. А. Стеклова РАН in Russian), he defended in 1984 his thesis for the degree of candidate of physical and mathematical sciences (Ph.D.) with supervisor Andrei Suslin and then became employed there as a staff member. Panin received in 1996 the degree of Doctor nauk from the St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences. There in 1999 he became the head of the laboratory of algebra and number theory. In 2003 he was elected a corresponding member of the Russian Academy of Sciences in the Department of Mathematical Sciences. In 2018 in Rio de Janeiro he was an invited speaker at the International Congress of Mathematicians.

Research The main directions of I. A. Panin's work are the theory of oriented cohomology on algebraic varieties, algebraic K-theory of homogeneous varieties, Gersten's conjecture, the Grothendieck-Serre conjecture on principal G-bundles, and purity in algebraic geometry. I. A. Panin proved (together with A. L. Smirnov) theorems of the Riemann-Roch type for oriented cohomology theories and Riemann-Roch type theorems for the Adams operation. Panin found a proof of Gersten's conjecture in the case of equal characteristic and an affirmative solution (jointly with Manuel Ojanguren) of the "purity" problem for quadratic forms. Panin computed the algebraic K-groups of all twisted forms of flag varieties and all principal homogeneous spaces over the inner forms of semisimple algebraic groups. He, jointly with A. S. Merkurjev and A. R. Wadsworth, generalized, to arbitrary Borel varieties, results proved by David Tao concerning index reduction formulas for the function fields of involution varieties.

Selected publications Panin I. A. (1994). "On the algebraic K-theory of twisted flag varieties". K-Theory. 8 (6): 541–585. doi:10.1007/BF00961020. Merkurjev A. S., Panin I. A., Wadsworth A. R. (1996). "Index reduction formulas for twisted flag varieties". K-Theory. 10 (6): 517–596. doi:10.1007/BF00537543.{{cite journal}}: CS1 maint: multiple names: authors list (link) Панин И. А. (1998). "Принцип расщепления и K-теория односвязных полупростых алгебраических групп (The splitting principle and the K-theory of simply connected semisimple algebraic groups)" (PDF). Алгебра и анализ. 10 (1): 88–131. Ojanguren M., Panin I. (1999). "A purity theorem for the Witt group" (PDF). Ann. Sci. École Norm. Sup. 32 (1): 71–86. doi:10.1016/s0012-9593(99)80009-3. Panin, Ivan; Pimenov, Konstantin; Röndigs, Oliver (2009). "On Voevodsky's Algebraic K-Theory Spectrum". In Baas, N.; Friedlander, E.; Jahren, B.; Østvær, P. (eds.). Algebraic Topology. Abel Symposia, Vol. 4. Springer. pp. 279–330. doi:10.1007/978-3-642-01200-6_10. ISBN 978-3-642-01199-3. S2CID 15407424.

References

External links "Framed motives of algebraic varieties - Ivan Panin (talk on March 25, 2015)". YouTube. Institute for Advanced Study. July 27, 2016.

Worked examples

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

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

In research: Ivan Panin (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 Panin (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 Panin (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1959 births, 20th-century Russian mathematicians, 21st-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Ivan Panin (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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Frequently asked questions

What is Ivan Panin (mathematician) in simple terms?

Why does Ivan Panin (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.

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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 Panin (mathematician).