Omar León Sánchez

   Turing Research Fellow in Pure Mathematics

 

     Alan Turing Building 


      Department of Mathematics 


      University of Manchester 


      Manchester M13 9PL, UK

      Office #1.111

        Tel. +44 (0) 161275 5885

      Email: omar.sanchez@manchester.ac.uk

    My Manchester Website ManchesterMathOLeonSanchez

 

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Research Interests

 

I mostly work on model theoretic algebra and its applications to other areas of mathematics. In particular, I am interested in the model-theoretic properties of certain classes of fields with operators (such as differential/difference operators and Poisson brackets). I also work on problems related to differential Galois theory and differential algebraic geometry.

 

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List of publications:   omar.sanchez/publications

 

Recent Preprints: 

“Differentially large fields” with M. Tressl. Submitted. https://arxiv.org/pdf/2005.00888.pdf

“Differential Weil descent” with M. Tressl. Submitted. https://arxiv.org/pdf/2003.02886.pdf

“Differential Galois cohomology and Picard-Vessiot extensions” with A. Pillay. Submitted. https://arxiv.org/pdf/1911.06165.pdf

“On coincidence of dimensions in closed ordered differential fields” with P. Eleftheriou and N. Regnault. Submitted. https://arxiv.org/abs/2002.12929

 

  PhD Thesis "Contributions to the model theory of partial differential fields" omar.sanchez/uw-ethesis

 

 

CV  omar.sanchez/CV

 

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  Teaching

 

Š      I am currently co-teaching (with Marianne Johnson) the Foundations of Pure Mathematics course, see MATH10111Website.

Š      Here are the lecture and tutorial notes of an introductory course to ω-stable theories that I taught in the Fall of 2016:

 

           omar.sanchez/Lecturenotes

 

           omar.sanchez/Tutorials

 

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     Seminars

 

I am a co-organizer, together with Gareth Jones and Marcus Tressl, of the Logic Seminar in the Department of Mathematics at the University of Manchester (click on Logic Seminar for upcoming talks). If you are in the UK (based or visiting) and interested in giving a talk, feel free to contact me at omar.sanchez@manchester.ac.uk

 

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     Events

 

        1) Together with P. D’Aquino, P. Eleftheriou and F. Point, I am co-organizing a mini-workshop on “Topological and differential expansions of o-minimal structures”. Oberwolfach, MFO, October 2020.

 

 

(Past meetings)

 

        (1) Together with Stephane Launois and Lewis Topley, I co-organized a meeting on “Interactions between representation theory and model theory”. University of Kent (Canterbury) from 1st July to 5th July 2019. RepresentationandModelTheoryMeeting2019

 

(2) Together with Gareth Jones and Marcus Tressl, I co-organized a meeting on “Applications of the model theory of fields with operators”. University of Manchester, from 17th June to 20th Jun 2019. ModeltheoryMeetingManchester2019

 

(3) Together with Gareth Jones and Marcus Tressl, I co-organized a meeting on “Model-theoretic methods in number theory and algebraic differential equations”. University of Manchester, from August 3 to August 5, 2018.  ModeltheoryMeetingManchester2018