Mathematik und Statistik
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Schwerpunkt Reelle Geometrie und Algebra > Jun.-Prof. Dr. Arno Fehm

French-German Summer School
Galois Theory and Number Theory
Konstanz, July 18-24 2015

organized by Lior Bary-Soroker (Tel Aviv University), Pierre Dèbes (Université de Lille), Arno Fehm (Universität Konstanz), Zeev Rudnick (Tel Aviv University)

The summer school aims to give an introduction to contemporary Galois theory and its connections with number theory.
Galois theory, on the one side, can be seen as the study of polynomial equations in one variable via their symmetries. Of particular importance is the study of irreducible polynomials and irreducible specializations of polynomials like in the celebrated Hilbert's irreducibility theorem. Number theory, on the other side, studies topics involving natural numbers: for example the distribution of prime numbers, or integer solutions to polynomial equations.
The school will offer three courses that will lead the students to the current state of the art in Galois theory and its interaction with number theory. Building on that, there will be talks on current research in number theory and Galois theory given by renowned experts and younger scientists. Participating students will also get the opportunity to work together on exercises and problems.
The summer school is funded by the Franco-German University with partial support from the European Research Council.

The schedule of the summer school is now available.

Each course will end with a 4th lecture in a research talk format.
The courses build on the following prerequisites and recommended literature.

Research talks
  • Efrat Bank (Tel Aviv University): Prime polynomial values of linear functions in short intervals (abstract, slides)
  • Lior Bary-Soroker (Tel Aviv Univeristy): Statistical number theory in function fields - Sums of two squares (abstract, slides)
  • Pierre Dèbes (Université de Lille): On the Malle conjecture and the self-twisted cover (abstract)
  • Arno Fehm (Universität Konstanz): Varieties of Hilbert type (abstract)
  • Jochen Koenigsmann (University of Oxford): Characterising Q by GQ +epsilon (abstract)
  • François Legrand (Tel Aviv University and The Open University of Israel):On the number or ramified primes in specializations (abstract, slides)
  • Sebastian Petersen (Universität Kassel): Specialization of l-adic Galois representations and Hilbertianity (abstract)
  • Edva Roditty-Gershon (University of Bristol): Arithmetic Statistics in Function Fields (abstract, slides)
  • Zeev Rudnick (Tel Aviv University): Analytic number theory in function fields (abstract, slides)
  • Umberto Zannier (Scuola Normale Superiore di Pisa): A survey on some specialization theorems (abstract)
See also the collection of all abstracts.

Further information
For further questions please write to galois@post.tau.ac.il or contact any of the organizers.