95440 Bayreuth, Germany
|Tuesday, 16:15-18:00||in S75|
|7. 10. 2014||Organizational meeting|
|14. 10. 2014||no seminar (Number Theory Group in Luminy)|
|21. 10. 2014||no seminar (Important meeting)|
|24. 10. 2014||Michael Stoll:||Simultaneous torsion x-coordinates in the Legendre family of elliptic curves|
|4. 11. 2014||Benjamin Collas:||Arithmetic of stack inertia in moduli spaces of curves|
|11. 11. 2014||Michael Kiermaier:||Subspace codes and q-analogs of combinatorial designs|
|18. 11. 2014||Joachim König (Würzburg):||The inverse Galois problem and explicit computation of Hurwitz spaces|
By work of Fried, Völklein et al., the regular inverse Galois problem is famously linked to questions about the existence of rational points on certain moduli spaces. In some cases, this existence can be proven by theoretical means; a famous example is Matzat's realization of M24 over Q.
In cases where the theoretical criteria do not work, little is known. I will present techniques for explicit computation of moduli spaces and use them to produce algebraic equations for Hurwitz spaces belonging to the Mathieu group M23, the last remaining sporadic group not yet realized as a Galois group over Q. Suitable rational solutions for these equations would lead to M23-realizations over Q.
Still, finding such points — or proving that they do not exist — remains a difficult problem. I will discuss some approaches that might help.
Similar methods may be used to classify monodromy groups of rational functions over Q. As partial results, I will present new polynomials for several almost simple groups, e.g. the first explicit polynomials with regular Galois groups PSL5(2) and PSL3(4) over Q.
|25. 11. 2014||Stefan Reiter:||On G2-rigid local systems|
|2. 12. 2014||Michael Stoll:||Computing canonical heights on genus 2 Jacobians in polynomial time|
|9. 12. 2014||Julian Tenzler:
||On trace functions on étale sheaves
Talk canceled, moved to January!
|16. 12. 2014||Andreas Kühn:||Torsion subgroups of hyperelliptic Jacobians|
|13. 1. 2015||Julian Tenzler:||On trace functions on étale sheaves|
|23. 1. 2015||Benjamin Collas:||Motives: from Geometry to Homotopy Theory|
|30. 1. 2015||Julian Tenzler:||On trace functions on étale sheaves, II|
|12-14, room TBD|
|9. 4. 2015||Mark Watkins (Sydney):||Number Theory and Algebraic Geometry in Magma|