Institut für Mathematik der Universität Osnabrück

Ismael Soudères --- ismael.souderes -at -gmail.com

Former student of the ENS (Cachan), I have done my Ph.D. "Motifs de Tate mixtes et éclatements à la MacPherson-Procesi" at the Institut de Mathématiques de Jussieu (University Paris Diderot-Paris 7 IMJ) under the supervision of Leïla Schneps.

I am a Postdoc at the the University of Osnabrück (Germany).

I study links between geometry of moduli spaces of curves in genus 0 and multiple zeta values (MZV).

My work goes as into purely combinatorial questions links to the Drinfel'd associator as in the geometry of sequences of blow up, studying the mixed Hodge structure of some relative cohomology groups or building explicit algebraic cycles computing motivic cohomology.

Currently, I am working on the Bloch cycle algebra. The goal of my project is to describe, by means of Bloch and Kritz's approach, the coLie algebra of mixed Tate motives over moduli spaces of curves of genus 0 in terms of explicit algebraic cycles. In particular, to do so, I construct algebraic cycles corresponding to multiple polylogarithms with a specialization at the point 1 corresponding to multiple zeta values.

Curriculum Vitae (french version)
Webpage modified the 07/10/2017
Now, I held a fulltime teaching position in C.P.G.E ATS at the Lycée Polyvalent Diderot in Paris (75019).

Last and scheduled talks

• Around functional equations for polylogarithms, « Numbers and Physics » conference , ICMAT, Madrid (2014).
• Lie (co)algebra and Bloch's cycles complex, « (A)round forms, cycles and motives» conference , Mainz (2014).
  
• Bloch cycle complex over a base, Bristol (2014).
  
• (Co)opérade (co)Lie et cycles algébriques, séminaire de Topologie, Lille (2014).
  
• Combinatorics of moduli spaces of curves, Osnabrück (2014).
  
• Quantum groups and TQFT, séminaire de topologie, Osnabrück (2014).
  
• Goncharov’s motivic iterated integrals, seminaire motifs, Essen (2013).
• Toward multiple zeta values cycles : Number Theory seminar, MPIM (2013)
• previous talks

Publications

Scientific Publications

• I. Soudères, Motivic double shuffle (le .pdf) (publié dans I.J.N.T, mars 2010, doi).
• —, Explicit associator relations for multiple zeta values, Mathematical J. Okayama Univ. Vol. 55 (2013).
• —, Multiple zeta value cycles in low weight, “Feynman Amplitudes, Periods and Motives”, AMS Contemporary Mathematics, Vol. 648 (2015), p. 203-247.
• —, The cycle complex over the projective line minus three points : toward multiple zeta values cycles, J. Pure and Applied Algebra, 220, (2016), pp. 2590-2647..
• —, A relative basis for mixed Tate motives over the projective line minus three points, Communications in Number Theory and Physics, International Press, 2016, 10 (1), pp.87-131.
• —, A motivic Grothendieck-Teichmüller group over Z, Algebr. Geom. Topol. Journal 18, No. 2, 635-685 (2018).
• —,Équations fonctionnelles du dilogarithme et espaces de modules, Ann. Inst. Fourier 68, No. 1, 151-169 (2018).

Other Publications

• Author for the H&K editions (Ecole Centrale Mathématiques 1- 2006).

Other Texts

• Detailed notes of master lectures (part 1), M. Klingler "Introduction aux motifs de Voevodsky". Redaction by I. Soudères and B. Collas.

Teaching

Osnabrück Universität (Germany): 2013-2015. • Linear Algebra und analytische geometrie I (WS 2013-2014 and WS 2014-2015) This is a first semester course for first year bachelor students. • Differentialgeometrie (SS 2013-2014) This is a second semester course for second and third year bachelor students. • Mathematik für Anwender (SS 2014-2015) This is a second semester course for first year bachelor students which are not in mathematics bachelor (economy; cognitive sciences; humanities and social sciences, etc.). Duisburg-Essen Universität (Germany): 2010-2012. • Riemann Surfaces (2010-2011, in English). This is a second semester course for graduated students. • Algebraic Topology (2011-2012, in English). This is a second semester course for graduated students.

Paris Diderot - Paris 7 (France): 2006-2010. • Tutorial MK2 (2006-2007 and 2007-2008). It is a personal project oriented course. The students have to write and present a rapport on either some simple problem of applied mathematics or historical aspects about a method they have already learned. Some examples : "the number "; "propagation phenomenas"; " axiomatic and the construction of numbers”, "Arithmetic and geometry". • Analysis II for chemist (2007-2008 and 2008-2009). It is a mathematics course for first year undergraduate students in chemistry. It is a second semester course centered the geometry of curves and surfaces and integral calculus. • Calculus 1 : MT1 (2009-2010). General mathematics for firstyear undergraduate students at the first semester. It corresponds to Analysis and Linear Algebra I.

Other talks

Introduction to multiple zeta values, Durham University, Durham, 2007. Geometry of moduli spaces of curves, Arithmetic Study Group, Durham University, Durham, 2007 (part. 1, part. 2). Motivic double shuffle, Arithmetic Study Group, Durham University, Durham, 2008. Motifs de Tates mixtes et double shuffle, Séminaire Polylogarithmes, IMJ, Paris, 2008. Éclatements et valeurs zêta multiples, Séminaire Des Thésards, IMJ, Paris, 2008. Double mélange motivique, Séminaire Quantique, IRMA, Starsbourg, 2009 (slides, papier). Éclatements à la MacPherson-Procesi et produits de mélanges des MZV, Séminaire d’Algèbre, Institut Camille Jordan, Lyon, 2009. Valeurs zêta multiples et Géométrie, Séminaire Quantique, IRMA, Starsbourg, 2010.

Géometrie des relations de double mélange, Séminaire Chevalley, IMJ, Paris, 2010. Valeurs zêta multiples, espaces de modules de courbe et éclatements, Séminaire GAM, Paris 13, 2010. Around Ayoub specialisation theorem, AGAT Seminar, Duisburg-Essen, Universität, 2010. Motifs de Tate mixtes sur P1 moins 3 points : Lyon, Osnabrück (2013). Cycles complex over P1 minus 3 points : Algebra, geometry and physics seminar MPIM (2013). Cycles and Mixted Tate motives over P1 minus 3 points : conférence « Periods and Motives », ICMAT, Madrid, (2012). - Complexe de cycles sur P1 moins 3 points et polylogarithmes multiples : Grenoble, Strasbourg, Toulouse, Göttigen, Mainz (2012). "diapositives" ou sous formes de notes.

Other Responsabilities

• Organizer of a workgroup on Géométrie des classifiants des groupes de tresses (généralisées) et leurs compactifications, (IMJ, 2009-2010).
• Coorganizer of the Arithmetic Study Group at Durham University in 2007-2008 (cf. site). Web page of the 'ASG
• Coorganizer of a semester "Periods in Geometry, Arithmetic and Physics" at Durham University in 2007-2008
• Ph. D student representant for the CIES (CIES jussieu) DS1.
• Manager and organiser in 2006-2007 of training session to LaTeX for the CIES jussieu.

Mathematics

Publications Teaching Talks Responsabilities The .pdf file of my Ph.D. "Motifs de Tate mixtes et éclatements à la MacPherson-Procesi" Years as Ph.D student 5 months in Durham (U.K) during my Ph.D Some notes on "Introduction aux motifs de Voevodsky" (by Klinger), written with Benjamin Collas. The .pdf covers the 2 first chapters.

6 months in Boston in 2006 L'agrégation Master report : "Périodes des espaces de modules de courbes de genre 0 et valeurs multi-zêta" Year as master student : my DEA. Work group at the ENS Cachan. Maîtrise.

Et pour le reste....

• L'association d'aide au développement de Cachan : Solidarité Normalienne. J'y ai consacré du temps lors de mes premières années à l'ENS puis j'ai passé la main aux nouveaux venus. Je vous invite à aller voir leurs derniers travaux.
• Les images d'un carnet de voyages entre 2000 et 2003. Le carnet de route au format pdf.

Some Links

• Web page at the Duisburg-Essen university.
• Benjamin Collas.
• Jerome Gartner
• Manuel Pégourié-Gonnard
• d'autres liens.

 

 

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Institut Mathématique de Jussieu - Fondation Sciences Mathématiques de Paris - Fédération de recherche Mathématiques Paris Centre