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Co-organised with Sylvain Lavau
| Date | Speaker | Title |
|---|---|---|
| September 23 | Emine Yıldırım (Galatasaray University) | A mirror deformation of Markov numbers |
| October 7 | Özge Ülkem (Academia Sinica) | Drinfeld’s analogues of elliptic curves: From Carlitz modules to shtukas |
| October 21 | Begüm Gülşah Çaktı (Galatasaray University) | Fermat’s Last Theorem and Beyond |
| October 27* | Panagiotis Batakidis (Aristotle University of Thessaloniki) | Topological and Delzant-type classification of quaternionic torus actions |
| November 4 | Gökalp Alpan (Sabancı University) | TBA |
| December 2 | Aybike Özer (İstanbul Technical University) | TBA |
* Note that this seminer is Tuesday on October 27th at 13:30 in H307.
Emine Yıldırım (Galatasaray University)
A mirror deformation of Markov numbers
This talk is based on joint work with L. Bittmann, P. Jouteur, E. Kantarcı Oğuz, and M. Molander. We introduce a q-deformation of the Markov equation and study a class of its solutions. We establish a factorization property that leads to the definition of new q-deformed Markov numbers, which we call mirror Markov numbers. These numbers satisfy a mirror mutation rule and admit a geometric interpretation on a punctured sphere with three orbifold points.
Özge Ülkem (Academia Sinica)
Drinfeld’s analogues of elliptic curves: From Carlitz modules to shtukas
Function fields of curves over finite fields behave in many ways like number fields, and this analogy has been a rich source of ideas in both directions. This talk is an introduction to function field arithmetic through Drinfeld’s work. We start with the Carlitz module and Drinfeld module, which is the analogue of elliptic curves. We then move to elliptic sheaves and shtukas, which Drinfeld introduced to prove the Langlands correspondence for GL_2 over function fields. We will emphasize the analogies with number fields throughout. If time permits, we will also discuss some generalizations of elliptic sheaves and shtukas, including recent work of the speaker.
Begüm Gülşah Çaktı (Galatasaray University)
Fermat’s Last Theorem and Beyond
In this talk, we will first discuss Fermat’s Last Theorem and introduce the main objects that made its proof possible. We will then give an overview of the method behind the proof and explain its key ideas. Finally, we will discuss some recent developments concerning generalizations of Fermat’s Last Theorem and explore how this approach can be extended to study these problems.
Panagiotis Batakidis (Aristotle University of Thessaloniki)
Topological and Delzant-type classification of quaternionic torus actions
Let Q=S^3 be the quaternionic torus. We first discuss local Q^n actions on 4n-manifolds and the obstruction to global existence. We then classify such actions via a combinatorial and a cohomological invariant. In the second part of the talk, quaternionic toric geometry is related to tetraplectic geometry, a generalization of symplectic geometry, via lagrangian toric fibrations. For this we use a quaternionic version of the Arnold-Liouville theorem and finally we classify orbit spaces via a quaternionic Delzant theorem. This is joint work with I. Gkeneralis.