mathematics

Jan Trlifaj

Jan Trlifaj 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 Jan Trlifaj rather than just read about it. In short: Jan Trlifaj (born 30 December 1954) is a Czech mathematician. He is a professor of mathematics at Charles University whose research interests include commutative algebra, homological algebra and representation theory.

Key takeaways

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

Reference excerpt

Jan Trlifaj (born 30 December 1954) is a Czech mathematician. He is a professor of mathematics at Charles University whose research interests include commutative algebra, homological algebra and representation theory.

Career and research Jan Trlifaj studied mathematics at the Faculty of Mathematics and Physics, Charles University, from which he received MSc. in 1979, Ph.D. in 1989 under Ladislav Bican. and Prof. of Mathematics in the field Algebra and number theory in 2009. In the academic year 1994/95 he had the position as Postdoctoral Fellow of the Royal Society at Department of Mathematics at University of Manchester. In Fall 1998 he received the J.W.Fulbright Scholarship at the Department of Mathematics, University California at Irvine. During Fall 2002 and 2006 he was a visiting professor at Centre de Recerca Matemàtica, Barcelona. Since 1990, he has completed numerous short term visiting appointments and given over 100 invited lectures at conferences and seminars worldwide. Since 2017, he is Fellow of Learned Society of the Czech Republic. He served in the organizing committee of 18th International Conference on Representations of Algebras (ICRA 2018), held for 250 participants from 34 countries in August 2018 in Prague, Czech Republic. He has been elected Fellow of the American Mathematical Society (AMS) in 2020, for contributions to homological algebra and tilting theory for non finitely generated modules. He serves as Member of the Science board for Neuron prize that is awarded to best Czech scientists by Neuron Endowment Fund.

Selected publications

Papers 1994: "Every *-module is finitely generated", Journal of Algebra, 169 (2): 392–398, doi:10.1006/jabr.1994.1291 1996: Trlifaj, Jan (1996), "Whitehead test modules", Transactions of the American Mathematical Society, 348 (4): 1521–1554, doi:10.1090/S0002-9947-96-01494-8 2001: Eklof, Paul C.; Trlifaj, Jan (2001), "How to make Ext vanish", Bulletin of the London Mathematical Society, 33 (1): 41–51, doi:10.1112/blms/33.1.41, S2CID 11541149 (with Paul C. Eklof), Shelah, Saharon; Trlifaj, Jan (2001), "Spectra of the Γ-invariant of uniform modules", Journal of Pure and Applied Algebra, 162 (2–3): 367–379, doi:10.1016/S0022-4049(00)00118-3 (with Saharon Shelah) 2007: Šťovíček, Jan; Trlifaj, Jan (2007), "All tilting modules are of countable type", Bulletin of the London Mathematical Society, 39 (1): 121–132, doi:10.1112/blms/bdl019 (with Jan Šťovíček) 2012: Herbera, Dolors; Trlifaj, Jan (2012), "Almost free modules and Mittag-Leffler conditions", Advances in Mathematics, 229 (6): 3436–3467, arXiv:0910.4277, doi:10.1016/j.aim.2012.02.013 (with Dolors Herbera), Estrada, Sergio; Guil Asensio, Pedro A.; Prest, Mike; Trlifaj, Jan (2012), "Model category structures arising from Drinfeld vector bundles" (PDF), Advances in Mathematics, 231 (3–4): 1417–1438, doi:10.1016/j.aim.2012.06.011 (with Sergio Estrada, Pedro A. Guil Asensio, and Mike Prest) 2014: Angeleri Hügel, Lidia; Pospíšil, David; Šťovíček, Jan; Trlifaj, Jan (2014), "Tilting, cotilting, and spectra of commutative noetherian rings", Transactions of the American Mathematical Society, 366 (7): 3487–3517, arXiv:1203.0907, doi:10.1090/S0002-9947-2014-05904-7 (with Lidia Angeleri Hügel, David Pospíšil, and Jan Šťovíček) 2016: Slávik, Alexander; Trlifaj, Jan (2016), "Very flat, locally very flat, and contraadjusted modules", Journal of Pure and Applied Algebra, 220 (12): 3910–3926, arXiv:1601.00783, doi:10.1016/j.jpaa.2016.05.020, S2CID 119176440 (with Alexander Slávik)

Books 2006, 2012: Approximations and Endomorphism Algebras of Modules, de Gruyter Expositions in Mathematics 41, Vol. 1 - Approximations, Vol. 2 - Predictions, W. de Gruyter Berlin - Boston, xxviii + 972 pp. (with Rüdiger Göbel)

Awards and distinctions Prize of the Dean of MFF for the best monograph 2006 MFF UK Silver medal at the Sexagennial anniversary Fellow of the American Mathematical Society, 2020

References

External links Jan Trlifaj at the Mathematics Genealogy Project Personal website

Worked examples

Example 1 — a first encounter with Jan Trlifaj

Start with the simplest possible case. Write down what Jan Trlifaj 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 Jan Trlifaj 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 Jan Trlifaj 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 Jan Trlifaj

In research: Jan Trlifaj 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 Jan Trlifaj 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: Jan Trlifaj is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1954 births, 20th-century Czech mathematicians, 21st-century Czech mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jan Trlifaj 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 Jan Trlifaj in 20 minutes

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

Frequently asked questions

What is Jan Trlifaj in simple terms?

Why does Jan Trlifaj 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 Jan Trlifaj?

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 Jan Trlifaj.