Omar León Sánchez

   Lecturer of Pure Mathematics

 

     Alan Turing Building 


      Department of Mathematics 


      University of Manchester 


      Manchester M13 9PL, UK

      Office #1.118

        Tel. +44 (0) 161275 XXXX

      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: 

“More on Galois cohomology, definability and differential algebraic groups” with D. Meretzky and A. Pillay. Submitted. https://arxiv.org/pdf/2105.13053.pdf

“Model theory of differential fields with finite group actions” with D. Hoffmann. Submitted. https://arxiv.org/pdf/2012.14376.pdf

“A Poisson basis theorem for symmetric algebras of infinite-dimensional Lie algebras” with S. Sierra. Submitted. https://arxiv.org/pdf/2008.02845.pdf

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

 

  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 taught Foundations of Pure Mathematics  B in Semester 1 2020/21.

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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     Students’ Work

 

Š      Kathleen Lamont. MSc Dissertation 2021, University of Manchester:  Remarks on the differential versions of the primitive element theorem and Hilbert basis theorem.

 

Š      Alberto Miguel Gómez, Summer Project 2021 (funded by an LMS UG Research Bursary):     Properties of algebraically-d-closed fields

 

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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) (Cancelled due to COVID19) 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