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MFH01871_ene.%2010%202020_11-51%20a.%20m

Matthieu Calvez

Postdoc at Heriot-Watt University, Edinburgh, UK, member of the EPSRC EP/S010963/1 project “Geometry of Artin Group Actions”, led by Alexandre Martin.

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In 2020, I was a Teaching and Research assistant at the University of Clermont-Auvergne (France).

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Between 2017 and 2019, I was assistant professor at the University of La Frontera, Temuco, Chile.

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Between 2012 and 2016, I was a postdoc then research assistant under the supervision of Andrés Navas at the University of Santiago, Chile.


Between 2009 and 2012, I was a doctoral student at the University of Rennes 1 and at the University of Seville, under the supervision of Bert Wiest and Juan González-Meneses. 

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​I am interested in braid groups and their generalizations, Artin-Tits groups, Garside groups, Mapping Class Groups.


Contact

​calvez [dot] matthieu [at] gmail [dot] com

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English: Bienvenido

Preprints

1. Euclidean Artin-Tits groups are acylindrically hyperbolic.

2. Morse elements in Garside groups are strongly contracting (with Bert Wiest).

3. Property $R_{\infty}$ for some spherical and affine Artin-Tits groups (with Ignat Soroko).

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Publications

  1. ​Curve graphs for Artin-Tits groups of type B, Ã and ~C are hyperbolic, (with Bruno Cisneros), Transactions of the London Mathematical Society 8 (1) 2021, 151-173.

  2. Hyperbolic structures for Artin-Tits groups of spherical type, (with Bert Wiest), to appear in Contemporary Mathematics.

  3. Conjugacy stability of parabolic subgroups of Artin-Tits groups of spherical type, (with Bruno Cisneros and María Cumplido), Journal of Algebra 556, 2020, 621-633.

  4. Acylindrical hyperbolicity and Artin-Tits groups of spherical type, (with Bert Wiest), Geometriae Dedicata 191 (1), 2017, 199-215.

  5. Curve graphs and Garside groups, (with Bert Wiest),  Geometriae Dedicata 188 (1), 2017, 195-213.

  6. Garside-theoretic analysis of Burau representations, (with Tetsuya Ito), Journal of Knot Theory and its Ramifications 26 (7), 2017.

  7. A fast solution to the conjugacy problem in the four-strand braid group, (with Bert Wiest), Journal of Group Theory 17 (5), 2014,757-800.

  8. Fast Nielsen-Thurston classification of braids, Algebraic and Geometric Topology 14, 2014, 1745-1758.

  9. Dual Garside structure and reducibility of braids, Journal of Algebra 356 (1), 2012, 355-373. 

  10. Fast algorithmic Nielsen-Thurston classification of four-strand braids, (with Bert Wiest), Journal of Knot Theory and its Ramifications 21 (5), 2012.

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My doctoral thesis:    "Algorithmic problems in braid groups"

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Research projects as principal investigator 

  • Artin-Tits groups: hyperbolic features  and applications; a question on parabolic subgroups. Project “Regular” Fondecyt number 1180335. Since 1 April 2018.

  • Geometric group theory. Project for attraction and insertion of investigators Conicyt, number PAI 79160023. 2017-2019.

  • Braid groups: at the interface between surface automorphisms and Garside theory. “Initiation to research” project Fondecyt number 11140090. 2015-2017

  • Geometric and algorithmic aspects of the conjugacy problem in braid groups. Postdoc project Fondecyt number 3130569. 2012-2014.

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Some Talks

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Strongly contracting elements in Garside groups, Workshop "Perspectives on Artin groups", ICMS, Edinburgh, 24 - 27 May 2021. Video.

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Des graphes hyperboliques pour les groupes d'Artin-Tits. Séminaire virtuel francophone "Groupes et Géométrie", 14 mai 2020. Video (in french).

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Minicourse Curve graphs and Artin-Tits groups. Meeting on knots, braids and algebras: algebraic constructions inspired by low-dimensional topology. Mathematics Institute of the National Autonomous University of Mexico (UNAM), Oaxaca. October 2018. Notes (in spanish) by Bruno Cisneros. 

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Conjugacy stability of parabolic subgroups in spherical type Artin-Tits groups. Geometric and Asymptotic Group Theory with Applications (GAGTA-12). KIAS, Seoul, Korea. July 2018.

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Algorithmic problems in Artin-Tits groups. Sub-plenary conference. LXXXVI annual meeting of Chilean Mathematical Society. University of Talca, Chile. November 2017.

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The conjugacy problem in the braid groups. XIX Latine American Algebra Colloquium, Session of Group Theory. University of La Frontera, Pucón, Chile. December 2012.

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Algorithmic consequences of the Linearly Bounded Conjugator Property in braid groups. Conference “Garside theory; state ofthe art and prospects”. Cap Hornu, Baie de Somme, France. June 2012.

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Symmetries, groups and games. Talk (in spanish) on group theory for highschool students. 

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Teaching

Except in 2013 and 2014, I have been teaching constantly since 2009, at all levels of university. 

  • Doctorate. University of La Frontera: abstract algebra, geometric group theory, 2017-2019.

  • Master. University of Rennes 1: tutorials of number theory, 2011-2012.

  • Undergrad. University of Clermont-Auvergne: “Mathematics Semester 1” (basics in linear algebra, real analysis and complex numbers) and ƒ “Math Common Core Course”, 2020. University of La Frontera: linear algebra, differential and integral calculus, 2017-2019. University of Santiago: linear algebra, complex analysis for engineering, 2015-2016. University of Rennes 1: tutorials of linear algebra, 2009-2010.

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    English: Bienvenido
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