mathematics

Matthias Flach (mathematician)

Matthias Flach (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 Matthias Flach (mathematician) rather than just read about it. In short: Matthias Flach is a German mathematician, professor and former executive officer for mathematics (department chair) at California Institute of Technology. Professional overview Research interests includes: Arithmetic algebraic geometry (see Glossary of arithmetic and Diophantine geometry).

Key takeaways

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

Reference excerpt

Matthias Flach is a German mathematician, professor and former executive officer for mathematics (department chair) at California Institute of Technology.

Professional overview Research interests includes:

Arithmetic algebraic geometry (see Glossary of arithmetic and Diophantine geometry). Special values of L-functions. Conjectures of: Bloch Beilinson Deligne Bloch–Kato conjecture (see also List of conjectures). Galois module theory. Motivic cohomology.

Education overview Ph.D. University of Cambridge UK 1991 Dissertation: Selmer groups for the Symmetric Square of an Elliptic Curve – Algebraic geometry Diplom, Goethe University Frankfurt, Germany, 1986

Publications Iwasawa Theory and Motivic L-functions (2009) – Flach, Matthias On Galois structure invariants associated to Tate motives – Matthias Flach and D. Burns, King's College London On the Equivariant Tamagawa Number Conjecture for Tate Motives, Part II. (2006) – Burns, David; Flach, Matthias. Euler characteristics in relative K-groups – Matthias Flach The equivariant Tamagawa number conjecture: A survey (with an appendix by C. Greither) – Matthias Flach A geometric example of non-abelian Iwasawa theory, June 2004, Canadian Number Theory Association VIII Meeting – Flach, Matthias. The Tamagawa number conjecture of adjoint motives of modular forms (2004) – Diamond, Fred; Flach, Matthias; Guo, Li. Adjoint motives of modular forms and the Tamagawa number conjecture (2001) – Fred Diamond; Matthias Flach; Li Guo.

Notes

References ScientificCommons Publication List Archived 2012-02-27 at the Wayback Machine Seminar on Fermat's last theorem By Vijaya Kumar Murty, Fields Institute for Research in Mathematical Sciences The Fermat diary By Charles J. Mozzochi

External links Flach's Homepage at Caltech Archived 2011-07-16 at the Wayback Machine

Worked examples

Example 1 — a first encounter with Matthias Flach (mathematician)

Start with the simplest possible case. Write down what Matthias Flach (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 Matthias Flach (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 Matthias Flach (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 Matthias Flach (mathematician)

In research: Matthias Flach (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 Matthias Flach (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: Matthias Flach (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1963 births, California Institute of Technology faculty, German mathematician stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Matthias Flach (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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How to study Matthias Flach (mathematician) in 20 minutes

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

Frequently asked questions

What is Matthias Flach (mathematician) in simple terms?

Matthias Flach is a German mathematician, professor and former executive officer for mathematics (department chair) at California Institute of Technology. Professional overview Research interests includes: Arithmetic algebraic geometry (see Glossary of arithmetic and Diophantine geometry).

Why does Matthias Flach (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.

How should I study Matthias Flach (mathematician)?

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 Matthias Flach (mathematician).