ArticleslgStudy

mathematics

Paul Balmer

Paul Balmer 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 Paul Balmer rather than just read about it. In short: Paul Balmer (born 1970) is a Swiss mathematician working in tensor triangular geometry, algebraic geometry, modular representation theory, and homotopy theory. He is a professor of mathematics at the University of California, Los Angeles.

Key takeaways

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

Reference excerpt

Paul Balmer (born 1970) is a Swiss mathematician working in tensor triangular geometry, algebraic geometry, modular representation theory, and homotopy theory. He is a professor of mathematics at the University of California, Los Angeles. Balmer received his Ph.D. from the University of Lausanne in 1998, under the supervision of Manuel Ojanguren, with the thesis Groupes de Witt dérivés des Schémas (in French). His research centers around triangulated categories. More specifically, he is a proponent of tensor-triangular geometry, an umbrella topic that covers geometric aspects of algebraic geometry, modular representation theory, stable homotopy theory, and other areas, by means of relevant tensor-triangulated categories. Balmer was an Invited Speaker at the International Congress of Mathematicians in Hyderabad in 2010, with a talk on Tensor Triangular Geometry. In 2012, he became a fellow of the American Mathematical Society. He was awarded the Humboldt Prize in 2015.

References

Worked examples

Example 1 — a first encounter with Paul Balmer

Start with the simplest possible case. Write down what Paul Balmer 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 Paul Balmer 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 Paul Balmer 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 Paul Balmer

In research
Paul Balmer 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 Paul Balmer 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
Paul Balmer is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1970 births, 21st-century American mathematicians, 21st-century Swiss mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Paul Balmer 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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Paul Balmer in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Paul Balmer means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Paul Balmer out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Paul Balmer in simple terms?

Paul Balmer (born 1970) is a Swiss mathematician working in tensor triangular geometry, algebraic geometry, modular representation theory, and homotopy theory. He is a professor of mathematics at the University of California, Los Angeles.

Why does Paul Balmer 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 Paul Balmer?

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 Paul Balmer.

Tags

  • 1970 births
  • 21st-century American mathematicians
  • 21st-century Swiss mathematicians
  • Fellows of the American Mathematical Society
  • Living people
  • University of California, Los Angeles faculty
  • University of Lausanne alumni

Keep exploring