h1

 

In the summer term 2022, I'm offering the following classes:

• Computer Algebra
• Hands-On Workshops
• Seminar Algebra

 

Research:

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

Degenerations of varieties and modules:

• PBW filtration and bases for irreducible modules in type A n
  Transformation groups, 16 (1), 71 - 89, 2011, with E. Feigin and P. Littelmann
• PBW-type filtration on quantum groups of type A n
  Journal of algebra, 449, 321 - 345, 2016, with X. Fang and M. Reineke
• Linear degenerations of flag varieties
  Mathematische Zeitschrift, 287 (1/2), 615-654, 2017, with G. Cerulli Irelli, X. Fang, E. Feigin and M. Reineke
• Essential bases and toric degenerations arising from birational sequences
  Advances in mathematics, 312, 107-149, 2017, , with X. Fang and P. Littelmann
• Favourable modules: Filtrations, polytopes, Newton-Okounkov bodies and flat degenerations
  Transformation groups, 22 (2), 321-352, 2017, with E. Feigin and P. Littelmann
• Degenerate Schubert Varieties in Type A
  Transformation groups, 27 Seiten, 2020, with R. Chirivì and X. Fang

Combinatorics of polytopes:

• Posets, tensor products and Schur positivity
  Algebra & Number theory, 8 (4), 933 - 961, 2014, with V. Chari and D. Sagaki
• Marked chain-order polytopes
  European journal of combinatorics, 58, 267 - 282, 2016, with X. Fang
• A Continuous Family of Marked Poset Polytopes
  SIAM journal on discrete mathematics, 34 (1), 611-639, 2020, with X. Fang and C. Pegel

Modules of generalized loop algebras:

• Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions
  Advances in mathematics, 211 (2), 566 - 593, 2007, with P. Littelmann
• Kirillov–Reshetikhin crystals for nonexceptional types
  Advances in mathematics, 222 (3), 1080 - 1116, 2009, with M. Okado and A. Schilling
• A categorical approach to Weyl modules
  Transformation groups, 15 (3), 517 - 549, 2010, with V. Chari and T. Khandai
• Global Weyl Modules for Equivariant Map Algebras
  International mathematics research notices, 2015 (7), rnt231, 2014, with N. Manning and A. Savage

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:

• Treasurer of "Friends of Oberwolfach"
• Patron of "Syrischer Studierendenverein Aachen"
• Deputy speaker of the CRC/TRR 195 "Symbolic Tools in Mathematics and their Application"

 

Publications

Source	Author(s)
[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 filtration and monomial bases for Demazure modules in types A and C In: Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry, 21 Seiten, 2022 [DOI: 10.1007/s13366-022-00660-0]	Balla, George (Corresponding author) Fourier, Ghislain Paul Thomas Kambaso, Kunda
[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.