Fourier Copyright: © Peter Winandy

Person

Prof. Dr. rer. nat.

Ghislain Fourier

Universitätsprofessor
Chair of Algebra and Representation Theory

Address

Building: 1952

Room: 403

Pontdriesch 10-16

52062 Aachen

Contact

WorkPhone
Phone: +49 241 80 94528
Fax Fax: +49 241 80 92777
Website

Office hour

by appointment
 

More informations

 

In the winter term 2023/24, I'm offering the following classes:

Lie algebras
Aspects of Mathematics
Hands-On Workshops

 

More informations

 

Research:

A selection of publications in three subject areas of my research.

Degenerations of varieties and modules:

Combinatorics of polytopes:

Modules of generalized loop algebras:

Curriculum Vitae:

  • since 07/2018: Lehrstuhl Algebra and Representation Theory (former Lehrstuhl B für Mathematik), RWTH Aachen University
  • 10/2016 - 07/2018: Professor for Pure Mathematics Leibniz University Hannover
  • 09/2013 - 09/2016: Lectureship for Pure Mathematics, University of Glasgow
  • 01/2013: Habilitation, University of Cologne
  • 10/2007: Promotion, University of Cologne
  • 10/2000 - 10/2004: Diplom Mathematics, Bergische University Wuppertal

Further:

 

Publications

Source Author(s)
[Journal Article]
PBW filtration and monomial bases for Demazure modules in types A and C
In: Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry, 64, 887-907, 2022
[DOI: 10.1007/s13366-022-00660-0]		Balla, George (Corresponding author)
Fourier, Ghislain Paul Thomas
Kambaso, Kunda
[Journal Article]
Gröbner Bases for Fusion Products
In: Algebras and representation theory, 2022
[DOI: 10.1007/s10468-022-10179-6]		Flake, Johannes Matthias
Fourier, Ghislain Paul Thomas (Corresponding author)
Levandovskyy, Viktor
[Journal Article]
PBW Degenerations of Lie Superalgebras and their Typical Representations
In: Journal of Lie theory, 31 (2), 313-334, 2021		Fourier, Ghislain Paul Thomas (Corresponding author)
Kus, Deniz
[Journal Article]
Cones from quantum groups to tropical flag varieties
In: Journal of algebraic combinatorics, 54 (3), 815-835, 2021
[DOI: 10.1007/s10801-021-01022-0]		Fang, Xin (Corresponding author)
Fourier, Ghislain Paul Thomas
Reineke, Markus
[Journal Article]
Degenerate Schubert Varieties in Type A
In: Transformation groups, 26 (4), 1189-1215, 2020
[DOI: 10.1007/s00031-020-09558-4]		Chirivì, Rocco (Corresponding author)
Fang, Xin
Fourier, Ghislain Paul Thomas
[Journal Article]
Linear degenerations of flag varieties : partial flags, defining equations, and group actions
In: Mathematische Zeitschrift, 296 (1/2), 453-477, 2019
[DOI: 10.1007/s00209-019-02451-1]		Cerulli Irelli, Giovanni
Fang, Xin (Corresponding author)
Feigin, Evgeny
Fourier, Ghislain Paul Thomas
Reineke, Markus
[Journal Article]
The Minkowski Property and Reflexivity of Marked Poset Polytopes
In: The electronic journal of combinatorics, 27 (1), P1.27, 2020
[DOI: 10.37236/8144]		Fang, Xin (Corresponding author)
Fourier, Ghislain Paul Thomas (Corresponding author)
Pegel, Christoph (Corresponding author)
[Journal Article]
A Continuous Family of Marked Poset Polytopes
In: SIAM journal on discrete mathematics, 34 (1), 611-639, 2020
[DOI: 10.1137/18M1228529]		Fang, Xin (Corresponding author)
Fourier, Ghislain Paul Thomas (Corresponding author)
Litza, Jan-Philipp (Corresponding author)
Pegel, Christoph
[Journal Article]
String cone and superpotential combinatorics for flag and Schubert varieties in type A
In: Journal of combinatorial theory : JCTA / Series A, 167, 213-256, 2019
[DOI: 10.1016/j.jcta.2019.04.006]		Bossinger, Lara (Corresponding author)
Fourier, Ghislain Paul Thomas
[Journal Article]
Weighted PBW degenerations and tropical flag varieties
In: Communications in contemporary mathematics, 21 (1), 1850016, 2019
[DOI: 10.1142/S0219199718500165]		Fang, X.
Feigin, E.
Fourier, Ghislain Paul Thomas
Makhlin, I.
[Journal Article]
Symmetries on plabic graphs and associated polytopes
In: Comptes rendus mathématiques de l'Académie des Sciences, 356 (6), 581-585, 2018
[DOI: 10.1016/j.crma.2018.05.003]		Fang, Xin (Corresponding author)
Fourier, Ghislain Paul Thomas (Corresponding author)
[Journal Article]
Toric Degenerations of Gr(2, n) and Gr(3, 6) via Plabic Graphs
In: Annals of combinatorics, 22 (3), 491 - 512, 2018
[DOI: 10.1007/s00026-018-0395-z]		Bossinger, L.
Fang, X.
Fourier, Ghislain Paul Thomas
Hering, M.
Lanini, M. (Corresponding author)
[Contribution to a book]
On toric degenerations of flag varieties
In: Representation Theory, 187-232, 2017
[DOI: 10.4171/171-1/8]		Fang, Xin
Fourier, Ghislain Paul Thomas
Littelmann, Peter
[Journal Article]
Favourable modules: Filtrations, polytopes, Newton-Okounkov bodies and flat degenerations
In: Transformation groups, 22 (2), 321-352, 2017
[DOI: 10.1007/s00031-016-9389-2]		Feigin, Evgeny (Corresponding author)
Fourier, Ghislain Paul Thomas
Littelmann, Peter
[Journal Article]
Essential bases and toric degenerations arising from birational sequences
In: Advances in mathematics, 312, 107-149, 2017
[DOI: 10.1016/j.aim.2017.03.014]		Fang, Xin (Corresponding author)
Fourier, Ghislain Paul Thomas
Littelmann, Peter
[Journal Article]
Degree cones and monomial bases of lie algebras and quantum groups
In: The Glasgow mathematical journal, 59 (03), 595-621, 2017
[DOI: 10.1017/S0017089516000422]		Backhaus, Teodor (Corresponding author)
Fang, Xin (Corresponding author)
Fourier, Ghislain Paul Thomas (Corresponding author)
[Journal Article]
Linear degenerations of flag varieties
In: Mathematische Zeitschrift, 287 (1/2), 615-654, 2017
[DOI: 10.1007/s00209-016-1839-y]		Cerulli Irelli, Giovanni
Fang, X.
Feigin, E.
Fourier, Ghislain Paul Thomas
Reineke, M. (Corresponding author)
[Journal Article]
PBW-type filtration on quantum groups of type A n
In: Journal of algebra, 449, 321 - 345, 2016
[DOI: 10.1016/j.jalgebra.2015.09.054]		Fang, Xin
Fourier, Ghislain Paul Thomas (Corresponding author)
Reineke, Markus
[Journal Article]
Marked poset polytopes: Minkowski sums, indecomposables, and unimodular equivalence
In: Journal of pure and applied algebra, 220 (2), 606-620, 2016
[DOI: 10.1016/j.jpaa.2015.07.007]		Fourier, Ghislain Paul Thomas (Corresponding author)
[Journal Article]
PBW-degenerated Demazure modules and Schubert varieties for triangular elements
In: Journal of combinatorial theory / A, 139, 132-152, 2016
[DOI: 10.1016/j.jcta.2015.12.001]		Fourier, Ghislain Paul Thomas (Corresponding author)
[Journal Article]
Torus fixed points in Schubert varieties and normalized median Genocchi numbers
In: Séminaire Lotharingien de Combinatoire, B75f, 2016		Fang, Xin
Fourier, Ghislain Paul Thomas
[Journal Article]
Marked chain-order polytopes
In: European journal of combinatorics, 58, 267 - 282, 2016
[DOI: 10.1016/j.ejc.2016.06.007]		Fang, Xin (Corresponding author)
Fourier, Ghislain Paul Thomas (Corresponding author)
[Preprint]
Marked poset polytopes : Minkowski sums, indecomposables, and unimodular equivalence, 2015		Fourier, Ghislain Paul Thomas
[Journal Article]
New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules
In: Moscow mathematical journal, 15 (1), 49-72, 2015
[DOI: 10.17323/1609-4514-2015-15-1-49-72]		Fourier, Ghislain Paul Thomas
[Journal Article]
Minuscule Schubert Varieties: Poset Polytopes, PBW-Degenerated Demazure Modules, and Kogan Faces
In: Algebras and representation theory, 18 (6), 1481 - 1503, 2015
[DOI: 10.1007/s10468-015-9548-5]		Biswal, Rekha
Fourier, Ghislain Paul Thomas (Corresponding author)
[Journal Article]
On Multigraded Generalizations of Kirillov-Reshetikhin Modules
In: Algebras and representation theory, 17 (2), 519 - 538, 2014
[DOI: 10.1007/s10468-013-9408-0]		Bianchi, Angelo
Chari, Vyjayanthi
Fourier, Ghislain Paul Thomas (Corresponding author)
Moura, Adriano
[Journal Article]
Extended partial order and applications to tensor products
In: The Australasian journal of combinatorics, 58, 178-196, 2014		Fourier, Ghislain Paul Thomas
[Journal Article]
Weyl modules and Levi subalgebras
In: Journal of Lie theory, 24 (2), 503-527, 2014		Fourier, Ghislain Paul Thomas
[Journal Article]
Posets, tensor products and Schur positivity
In: Algebra & number theory, 8 (4), 933 - 961, 2014
[DOI: 10.2140/ant.2014.8.933]		Chari, Vyjayanthi (Corresponding author)
Fourier, Ghislain Paul Thomas (Corresponding author)
Sagaki, Daisuke (Corresponding author)
[Journal Article]
Global Weyl Modules for Equivariant Map Algebras
In: International mathematics research notices, 2015 (7), rnt231, 2014
[DOI: 10.1093/imrn/rnt231]		Fourier, Ghislain Paul Thomas (Corresponding author)
Manning, N.
Savage, A.
[Journal Article]
Schur Positivity and Kirillov-Reshetikhin Modules
In: Symmetry, integrability and geometry: methods and applications, 10, 058, 2014
[DOI: 10.3842/SIGMA.2014.058]		Fourier, Ghislain Paul Thomas
[Journal Article]
The degree of the Hilbert-Poincar\'e polynomial of PBW-graded modules
In: Comptes rendus mathematique, 352 (12), 959-963, 2014		Backhaus, Teodor
Bossinger, Lara
Desczyk, Christian
Fourier, Ghislain Paul Thomas
[Journal Article]
Global Weyl modules for the twisted loop algebra
In: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 83 (1), 53 - 82, 2013
[DOI: 10.1007/s12188-013-0074-2]		Fourier, Ghislain Paul Thomas (Corresponding author)
Manning, Nathan
Senesi, Prasad
[Contribution to a book]
PBW-filtration over ℤ and Compatible Bases for V ℤ(λ) in Type A n and C n
In: Symmetries, Integrable Systems and Representations / edited by Kenji Iohara, Sophie Morier-Genoud, Bertrand Rémy, 35-63, 2013
[DOI: 10.1007/978-1-4471-4863-0_3]		Feigin, Evgeny
Fourier, Ghislain Paul Thomas
Littelmann, Peter (Corresponding author)
[Journal Article]
Demazure modules and Weyl modules: The twisted current case
In: Transactions of the American Mathematical Society, 365 (11), 6037-6064, 2013
[DOI: 10.1090/S0002-9947-2013-05846-1]		Fourier, Ghislain Paul Thomas (Corresponding author)
Kus, Deniz (Corresponding author)
[Journal Article]
Local Weyl modules for equivariant map algebras with free abelian group actions
In: Journal of algebra, 350 (1), 386 - 404, 2012
[DOI: 10.1016/j.jalgebra.2011.10.018]		Fourier, Ghislain Paul Thomas
Khandai, Tanusree
Kus, Deniz
Savage, Alistair (Corresponding author)
[Journal Article]
PBW filtration and bases for irreducible modules in type A n
In: Transformation groups, 16 (1), 71 - 89, 2011
[DOI: 10.1007/s00031-010-9115-4]		Feigin, Evgeny
Fourier, Ghislain Paul Thomas
Littelmann, Peter
[Contribution to a book]
Perfectness of Kirillov-Reshetikhin crystals for nonexceptional types
In: Quantum affine algebras, extended affine Lie algebras, and their applications : Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, March 2-7, 2008, Banff International Research Station, Banff, Canada / Yun Gao ... [et al.], editors, 2010		Fourier, Ghislain Paul Thomas
Okado, Massato
Schilling, Anne
[Journal Article]
A categorical approach to Weyl modules
In: Transformation groups, 15 (3), 517 - 549, 2010
[DOI: 10.1007/s00031-010-9090-9]		Chari, Vyjayanthi
Fourier, Ghislain Paul Thomas
Khandai, Tanusree
[Journal Article]
Kirillov-Reshetikhin crystals for nonexceptional types
In: Advances in mathematics, 222 (3), 1080 - 1116, 2009
[DOI: 10.1016/j.aim.2009.05.020]		Fourier, Ghislain Paul Thomas
Okado, Masato
Schilling, Anne
[Contribution to a conference proceedings]
Perfectness of Kirillov-Reshetikhin crystals for nonexceptional types
In: [21st International Conference on Formal Power Series and Algebraic Combinatorics], 2009		Fourier, Ghislain Paul Thomas
Okado, Masato
Schilling, Anne
[Journal Article]
Weyl modules for the twisted loop algebras
In: Journal of algebra, 319 (12), 5016 - 5038, 2008
[DOI: 10.1016/j.jalgebra.2008.02.030]		Chari, Vyjayanthi
Fourier, Ghislain Paul Thomas
Senesi, Prasad
[Journal Article]
Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions
In: Advances in mathematics, 211 (2), 566 - 593, 2007
[DOI: 10.1016/j.aim.2006.09.002]		Fourier, Ghislain Paul Thomas
Littelmann, P.
[Journal Article]
Demazure structure inside Kirillov-Reshetikhin crystals
In: Journal of algebra, 309 (1), 386-404, 2007
[DOI: 10.1016/j.jalgebra.2006.09.019]		Fourier, Ghislain Paul Thomas
Schilling, Anne
Shimozono, Mark
[Journal Article]
Tensor Product Structure of Affine Demazure Modules and Limit Constructions
In: Nagoya mathematical journal, 182, 171 - 198, 2006
[DOI: 10.1017/S0027763000026866]		Fourier, Ghislain Paul Thomas
Littelmann, P.
 

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