Applications of the model theory of fields with operators
17 June – 20 June 2019, School of Mathematics, University of Manchester, UK
---------- Click on SLIDES to find the slides of some of the talks presented at the workshop --------------
Over the years, and more remarkably in the last two decades, the model theory of fields equipped with distinguished operators (e.g., derivations, automorphisms, exponentials and more generally analytic/pfaffian functions) has demonstrated its far-reaching applications to various areas of Mathematics, such as number theory, diophantine geometry, and algebraic/analytic geometry. The combination of tools from geometric stability and o-minimality (branches of model theory that abstract algebraic and topological properties of fields) has produced remarkable results in "counting points and bounding height problems" and also proofs of “Ax-Lindemann-Weierstrass type results with derivatives " (using differential Galois theory).
The meeting will bring together (to share new ideas and stimulate research collaborations) the diverse groups of researchers working on applications of the model theory of fields to complex exponentiation, real-analytic geometry, number theory, and the study of algebraic differential/difference equations. Early career researchers and students will be exposed to state-of-the-art research and will be invited to discuss/share their ideas.
The main scientific topics of the event will be (but are not restricted to):
1) analytic o-minimal expansions of the reals,
2) complex exponentiation,
3) differential-exponential polynomial rings,
4) Ax-Lindemann theorems with derivatives,
5) model-theoretic properties of algebraic-differential equations,
6) differential/difference Galois theory and its cohomologies.
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NOTE: All talks will take place in Frank Adams Room #1.212 located in the first floor (not ground floor) of the Alan Turing building (School of Maths). Coffee breaks will be in the kitchen/lounge area next to Frank Adams Room.
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Organizers: Gareth Jones, Omar León Sánchez and Marcus Tressl.
The meeting is supported by the School of Mathematics of the University of Manchester, the Dame Kathleen Ollerenshaw Trust, and the Heilbronn Institute for Mathematical Research.