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.
Schedule
The schedule of the summer school is now available.
Courses
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.
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