# Profile

# Prof Mohamed Saidi

## Professor of Pure Mathematics

Telephone: **01392 725277**

Extension: **(Streatham) 5277**

- Born in Algiers (Algeria).
- Algerian citizenship (only).
- Attended school, junior school, and High school in Algeria.
- Graduated from Constantine university in Mathematics (option analysis) (Jun 1990).
- DEA in Pure Mathematics from Universitie Bordeaux I. Mention tres bien (Sep 1991).
- PhD in Pure Mathematics from Universitie Bordeaux I under the supervision of Prof. Michel Matignon. Mention felicitations des membres du jury (Jun 1994).
- Post-Doc at Munster University (Germany), with Prof. S. Bosch, (Sep 1994 - Sep 1995).
- Post-Doc at the Max-Planck Institut for Mathematics in Bonn (Germany) (Oct 1994 - Dec 1994).
- Post-Doc at Heidelberg university (Germany), with Prof. B.H.Matzat (Jun 1996- Aug 1997).
- Post-Doc at Bonn-University (Germany), with Prof. F.Pop, (Sep 1997 - Jul 1999).
- Visiting Professor at Stellenbosch University (South Africa) (Aug 1998 - Sep 1998).
- Post-Doc at MSRI (Berkley), special Galois semester, (Aug 1999 - Dec 1999).
- Lecturer in Pure Mathematics at Durham University (UK) (Jan 2000 - Jul 1004).
- Visiting Professor at the Max-Planck-Institut for Mathematics in Bonn (Germany), (Mar 2003 - Jun 2004).
- Reader at Exeter University (Jul 2004 onwards).
- Visiting Professor at the Research Institut for Mathematical Sciences (Kyoto university), (Sep 2005 - Oct 2006).
- Associate Professor at Exeter University (2007).
- Profossor of pure mathematics at Exeter university (2015).
- I regularly visit the Research Institute for Mathematical Sciences at Kyoto university (RIMS) as an invited professor (for a period of three months), recent visits include the summers 2019-2018-2017-2016-2014-2013-2012-2011.

- I occasionally visit the Max-Planck-Institute for Mathematical Sciences in Bonn as an invited researcher, recent visits include: 10/2019-03/2020, and 02/2015-05/2015.

Languages: Arabic, French, English, German, some basic Japanese.

**Research Interests**

I am interested in several research areas related to arithmetic geometry, algebraic geometry and number theory. I am especially interested in questions and problems related to algebraic and arithmetic fundamental groups over various fields of interest: fields of positive characteristics, finite fields, finitey generated fields, and p-adic local fields. These include:

- The anabelian geometry of curves over finite, p-adic, and number fields .
- The anabelian geometry of finitely generated fields.
- Sections of arithmetic fundamental groups.
- Arithmetic fundamental groups and Diophantine geometry.
- Local-global principles for torsors under fundamental groups.
- Structure of fundamental groups in positive characteristics.
- Etale fundamental groups of rigid analytic varieties.
- Arithmetic of abelian varieties over finitely generated fields.
- Arithmetic of rigid analytic p-adic varieties.
- Liftings and degeneration of covers of curves, semi-stable reduction of covers of arithmetic curves.
- Ramification theory.

**Recent Research Achievements**

- Together with my collaborator Akio Tamagawa we established a far reaching refined version of the Grothendieck anabelian conjecture for hyperbolic curves over finite fields.
- Recently we established a much refined version of the Grothendieck birational anabelian conjecture for finitely generated fields.
- We also proved that the structure of the geometric fundamental group is not constant in a non-isotrivial family of curves in positive characteristics.
- Together with (my former PhD student) Mike Tyler we proved that the birational Grothendieck section conjecture holds true over finitely generated fields if it holds true over number fields.
- Initiated the theory of cuspidalisation of sections of arithmetic fundamental groups in the search of rational points.
- Proved new results regarding the structure of geometric etale fundamental groups of affinoid p-adic curves.
- Established a local-global principle for torsors under prosolvable fundamental groups.
- Found new examples of non-geometric sections of arithmetic fundamental groups.

**Teaching Interests**

I have an experience in teaching the following courses :

- Number theory.
- Real analysis.
- Complex analysis.
- p-adic numbers.
- Algebra.
- Group, Rings, and Fields.
- Algebraic curves.
- Representation of finite groups.

**Other Relevant Information**

- I have been awarder an Advanced EPSRC Fellowship Oct 2002 - Sep 2007.
- I am co-organizing with John Coates, Peter Schneider, Minhyong Kim and Florian Pop a special semester at the Isaac Newton Institute for Mathematical Sciences in Cambridge on "Non-abelian Fundamental Groups in Arithmetic Geometry" from Jul - Dec 2009, for more details, see: http://www.newton.cam.ac.uk/programmes/NAG/index.html
- Refereed papers for several research journals: the American Journal of Mathematics, Mathematishe Annalen, Publication of RIMS kyoto university, Compositio, Journal of Algebra.
- I have been external examiner in PHD examinations.

**Qualifications** PhD in Pure Mathematics