Welcome
to Thomas Gobet's webpage !
Course on Braid groups (with G.
Williamson)
Position: I
am an ARC supported postdoc in the Algebra research group of the
University of Sydney, working
under the supervision of
Prof. Anthony Henderson. Here is my University of Sydney research
profile page.
Before this I was an ANR supported postdoc in the Geometry team of the
Institut Elie Cartan de Lorraine in Nancy, working with PierreEmmanuel
Chaput. Before this I was a scientific collaborator in the
Representation theory team of Gunter
Malle at the University of Kaiserslautern. Before this I was a PhD
student of François
Digne in the Group theory team of the University of Amiens.
Email address:
thomas.gobet [at] sydney.edu.au
Postal address:
School of Mathematics and Statistics F07
University of Sydney NSW 2006
Australia
Scientific
interests
 Reflection
groups (finite and infinite), Coxeter groups, root systems,
KazhdanLusztig polynomials and related representation theoretic and
categorical incarnations (in particular Soergel bimodules).
 ArtinTits
groups attached to general Coxeter groups, Garside theory, and related
categorical incarnations (2braid groups or Rouquier complexes,
zigzag algebras, actions on triangulated categories, ...),
representation theory of braid groups.
 Dual approaches
in the study of Coxeter groups and Artin groups: dual braid monoids,
Hurwitz action in generated groups, noncrossing partition lattices,
CoxeterCatalan combinatorics.
 Lie
Theory.
 Hecke,
TemperleyLieb and diagram algebras.
Upcoming
 I will give a
talk in the Representation Theory session of the annual conference of
the Australian Mathematical Society in Adelaide, December 4  7th.
 I will give a
seminar talk in Tours on December 14th.
Publications
 Categorification
of the TemperleyLieb algebra by bimodules, Journal of
Algebra 419 (2014), 277317.
 Noncrossing
partitions and Bruhat order (with Nathan Williams), European
Journal of Combinatorics 53 (2016), 834.
 Noncrossing
partitions, fully commutative elements and bases of the
TemperleyLieb algebra, Journal of Knot Theory and its
Ramifications 25 (2016), no. 6, 27 pp.
 Dual
braid monoids, Mikado braids and positivity in Hecke algebras
(with François Digne), Mathematische Zeitschrift 285 (2017),
no. 12, 215238.
 On
the Hurwitz action in finite Coxeter groups (with Barbara
Baumeister, Kieran Roberts, Patrick Wegener), Journal of Group
Theory 20 (2017), no.1, 103131. Link to the computer
programs we used in this
paper.
 Twisted
filtrations of Soergel bimodules and linear Rouquier complexes
Journal of Algebra 484 (2017), 275309.
 CoxeterCatalan
combinatorics and TemperleyLieb algebras, preprint 2016.
 On
cycle decompositions in Coxeter groups,
Séminaire Lotharingien de Combinatoire 78B
(2017), Article #45, 12 pp.
 Simple
dual braids, noncrossing partitions and Mikado braids of type D_n
(with Barbara Baumeister), Bull. of the London Math. Soc. 49
(2017), no. 6, 10481065.
 On
generalized categories of Soergel bimodules in type A_2 (with
AnneLaure Thiel), C. R. Acad. Sci. 356 (2018), no. 3,
258263.
 Dual
Garside structures and Coxeter sortable elements, preprint
2018.
 A
Soergellike category for complex reflection groups of rank one
(with AnneLaure Thiel), preprint 2018.
My collaborators
Barbara
Baumeister, François
Digne, Kieran
Roberts, AnneLaure
Thiel, Patrick
Wegener, Nathan
Williams.
Course notes
 Lie
algebras, Part II. Notes of a onesemester master course which I
gave in the winter 2014 at the University of Kaiserslautern. It covers
root systems, classification of simple finitedimensional complex Lie
algebras, universal enveloping algebras, classification of
finitedimensional simple modules (using highest weight modules), Weyl
character formulas.
Slides of some
talks

Minicourse

Conference or
seminar talks
PhD thesis
Bases
of TemperleyLieb algebras, supervised by François Digne, defended
on September 29th, 2014. Picture. I got the
2015 PhD Prize of the Regional Council of Picardy for my thesis and this
talk (in French).