Matthias Flach is a

German German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also Ge ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

and former executive officer for mathematics (department chair) at

California Institute of Technology The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes ...

Professional overview

Research interests includes: *Arithmetic

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

(see

Glossary of arithmetic and Diophantine geometry A glossary (from , ''glossa''; language, speech, wording), also known as a vocabulary or clavis, is an alphabetical list of terms in a particular domain of knowledge with the definitions for those terms. Traditionally, a glossary appears at ...

). * Special values of L-functions. *

Conjectures In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), hav ...

of: **

Bloch Bloch is a surname of German origin. Notable people with this surname include: A *Adele Bloch-Bauer (1881–1925), Austrian entrepreneur *Albert Bloch (1882–1961), American painter *Alexandre Bloch (1857–1919), French painter *Alfred Bloch ( ...

** Beilinson **

Deligne Pierre René, Viscount Deligne (; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord P ...

** Bloch–Kato conjecture (see also

List of conjectures This is a list of notable mathematical conjectures. Open problems The following conjectures remain open. The (incomplete) column "cites" lists the number of results for a Google Scholar search for the term, in double quotes . Conjectures now pr ...

). *

Galois module In mathematics, a Galois module is a ''G''-module, with ''G'' being the Galois group of some extension of fields. The term Galois representation is frequently used when the ''G''-module is a vector space over a field or a free module over a ring i ...

theory. *

Motivic cohomology Motivic cohomology is an invariant of algebraic varieties and of more general schemes. It is a type of cohomology related to motives and includes the Chow ring of algebraic cycles as a special case. Some of the deepest problems in algebraic geome ...

Education overview

*Ph.D.

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

UK 1991 Dissertation:

Selmer group In arithmetic geometry, the Selmer group, named in honor of the work of by , is a group constructed from an isogeny of abelian varieties. Selmer group of an isogeny The Selmer group of an abelian variety ''A'' with respect to an isogeny ''f'' ...

s for the Symmetric Square of an

Elliptic Curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If the ...

– Algebraic geometry *Diplom,

Goethe University Frankfurt Goethe University Frankfurt () is a public research university located in Frankfurt am Main, Germany. It was founded in 1914 as a citizens' university, which means it was founded and funded by the wealthy and active liberal citizenry of Frankfurt ...

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

, 1986

Publications

Iwasawa Theory In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite Tower of fields, towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic ...

and Motivic L-functions (2009) – Flach, Matthias *On Galois structure invariants associated to Tate motives – Matthias Flach and D. Burns,

King's College London King's College London (informally King's or KCL) is a public university, public research university in London, England. King's was established by royal charter in 1829 under the patronage of George IV of the United Kingdom, King George IV ...

*On the Equivariant Tamagawa Number Conjecture for Tate Motives, Part II. (2006) – Burns, David; Flach, Matthias. *

Euler characteristic In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's ...

s in relative K-groups – Matthias Flach *The

equivariant In mathematics, equivariance is a form of symmetry for functions from one space with symmetry to another (such as symmetric spaces). A function is said to be an equivariant map when its domain and codomain are acted on by the same symmetry group, ...

Tamagawa number In mathematics, the Tamagawa number \tau(G) of a semisimple algebraic group defined over a global field is the measure of G(\mathbb)/G(k), where \mathbb is the adele ring of . Tamagawa numbers were introduced by , and named after him by . Tsuneo ...

conjecture: A survey (with an appendix by C. Greither) – Matthias Flachhttp://www.math.caltech.edu/papers/baltimore-final.pdf *A geometric example of non- abelian

Iwasawa theory In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite Tower of fields, towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic ...

, June 2004, Canadian

Number Theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

Association VIII Meeting – Flach, Matthias. *The Tamagawa number conjecture of adjoint motives of

modular forms In mathematics, a modular form is a holomorphic function on the Upper half-plane#Complex plane, complex upper half-plane, \mathcal, that roughly satisfies a functional equation with respect to the Group action (mathematics), group action of the ...

(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 ListSeminar on Fermat's last theorem By Vijaya Kumar Murty, Fields Institute for Research in Mathematical SciencesThe Fermat diary By Charles J. Mozzochi

External links

Living people 1963 births {{germany-mathematician-stub