Current group members

• Matthieu Bouyer, École Polytechnique, long term visitor
• Elke Neuhaus, PhD Student

Former group members

• Daniel Windisch, 26.12.23 - 30.06.24.
• Arjaman Jal, 01.03.24 - 31.05.24.
• Jutta Rath, 15.01.24 - 20.04.24.

Former visitors and the website of the group

• Dependency equilibria: Boundary cases and their real algebraic geometry, with Daniel Windisch, [arXiv:2405.19054], submitted.
• Game theory of undirected graphical models, with Javier Sendra-Arranz, [arXiv:2402.13246].
• Algebraic sparse factor analysis, with Mathias Drton, Alex Grosdos and Nils Sturma, [arXiv:2312.14762], submitted.
• Combinatorics of correlated equilibria, with Marie-Charlotte Brandenburg and Benjamin Hollering, [arXiv:2209.13938], Experimental Mathematics (2024).
• Toric ideals of characteristic imsets via quasi-independence gluing, with Benjamin Hollering, Joseph Johnson and Liam Solus, [arXiv:2209.01834], Algebraic Statistics, 14-2 (2023), 109-131.
• Nash conditional independence curve, with Javier Sendra-Arranz, [arXiv:2206.07000], Journal of Symbolic Computation, Vol. 122 (2024).
• Geometry of dependency equilibria, with Bernd Sturmfels, [arXiv:2201.05506], Rendiconti dell'Istituto di Matematica dell'Università di Trieste, Vol. 54 (5) (2022).
• Complexity of the usual torus action on Kazhdan-Lusztig varieties, with Maria Donten-Bury and Laura Escobar-Vega, [arXiv:2111.13540], Algebraic Combinatorics, Vol. 6 (3) (2023).
• Families of polytopes with rational linear precision in higher dimensions with Isobel Davies, Eliana Duarte, and Miruna-Stefana Sorea, [arXiv:2109.08151], Foundations of Computational Mathematics, Vol. 23 (2023).
• Rigid Gorenstein toric Fano varieties arising from directed graphs, with Selvi Kara and Akiyoshi Tsuchiya, [arXiv:2103.06404], Collectanea Mathematica 74 (2023).
• Rigid toric matrix Schubert varieties, [arXiv:2001.11949], Journal of Algebraic Combinatorics, Vol. 57 (2023).
• On rigidity of toric varieties arising from bipartite graphs, [arXiv:1905.02445], Journal of Algebra, Vol. 569 (2021).
• A note on deformations and mutations of fake weighted projective planes, [arXiv:1809.04470], Algebraic and Geometric Combinatorics on Lattice Polytopes (2019).

Code

• MATHREPO for "Algebraic sparse factor analysis". Supplementary material for the computations performed in the article with Macaulay2.
• MATHREPO for "Combinatorics of correlated equilibria". Supplementary material for the computations performed in the article with SageMath, Mathematica and Macaulay2.
• Polynomial systems arising from Nash equilibria. A story about how game theory meets multilinear systems and product of simplices with using HomotopyContinuation.jl in Julia.
• Rigid toric bipartite graphs. Polymake and Singular scripts for investigating the rigidity of toric varieties arising from a bipartite graph.

Others

• Nonlinear Algebra in Game Theory, in the Oberwolfach Report of the conference “Algebraic Structures in Statistical Methodology” [DOI 10.14760/OWR-2022-55], 2022.

Ongoing projects

• A vector bundle approach to Nash equilibria, with Hirotachi Abo and Luca Sodomaco.
• Geometric aspects of noncrossing matchings, with Arjaman Jal and Akiyoshi Tsuchiya.

• MEGA: Effective Methods in Algebraic Geometry, Max Planck Institute for Mathematics in the Sciences, July 29 - August 02, 2024.
• Minisymposium: Algebraic Methods in Graphical Models, at SIAM Conference on Applied Algebraic Geometry, July 10-14, 2023.
• 13th polymake conference and developer meeting, Technical University Berlin, January 20-22, 2022.
• What is...? Seminar Series, Berlin Mathematical School, 2016-2018.
• Short course by Ian Morrison on Geometric Invariant Theory, Galatasaray University, Istanbul, April 25-May 21, 2014.
• CIMPA/TÜBİTAK/GSU Summer School Algebraic Geometry and Number Theory, In collaboration with IPM (Iran) and CAMS (Liban), Galatasaray University, Istanbul, June 2-13, 2014.
• Master Class on Finsler Geometry and Applications, Galatasaray University, Istanbul, April 10-17, 2014.
• Japanese Turkish Joint Geometry Meeting II, Galatasaray University, Istanbul, March 19-23,2014.
• Japanese Turkish Joint Geometry Meeting, Galatasaray University, Istanbul, November 21-24, 2013.

• International Congress on Mathematical Software 2024, Durham University, United Kingdom, 22-25 July, 2024.
• 5th Graduate Student Meeting in Applied Algebra and Combinatorics, Freie Universität Berlin, 10-12 April, 2024.
• Combinatorial Coworkspace 2024, Haus Bergkranz, Kleinwalsertal, Austria, March 18-23, 2024.
• Applied CATS, KTH Stockholm, February 13th, 2024.
• European Workshop on Algebraic Statistics and Graphical Models, Riessersee Hotel, Garmisch-Partenkirchen, February 1-2, 2024.
• Mathematics and Decision conference at UM6P Ben Guerir, Morocco, December 11 – 15, 2023.
• Algebraic Economics, IMSI Chicago, November 6 — 10, 2023.
• Invitation to Algebraic Statistics and Applications, IMSI Chicago, September 18 — 22, 2023.
• Conference on Applied Algebra, Osnabrück University, September 6 – 8, 2023.
• SIAM Conference on Applied Algebraic Geometry (AG23), Eindhoven University of Technology, July 10 - 14, 2023.
• Issues in Dynamic Decision Theory, Konstanz University, July 6 – 8, 2023.
• BIRS-CMO Workshop: Computations and Data in Algebraic Statistics, May 14-19, 2023, Casa Matemática Oaxaca (CMO).
• Oberseminare Algebra, 24th of January, 2023, Osnabrück University.
• Algebraic Structures in Statistical Methodology, Mathematisches Forschungsinstitut Oberwolfach, 5-9 December, 2022.
• Toric Degenerations, Banff International Research Station, 5-9 December, 2022.
• Tensors in statistics, optimization and machine learning, IMPAN, Warsaw, Poland, 21-25 November, 2022.
• Oberseminar Diskrete Mathematik Geometrie und Optimierung, Goethe-Universität Frankfurt am Main, October 25th, 2022.
• ETH-UCPH-TUM Workshop on Graphical Models, Science and Study Center Raitenhaslach, October 10-14, 2022.
• DMV Annual Meeting 2022, Freie Universität Berlin, September 12-16, 2022.
• Group actions in Algebraic Geometry, Cetraro, July 11-15, 2022.
• AlCoVE: an Algebraic Combinatorics Virtual Expedition, June 6-7, 2022.
• Algebraic Statistic, University of Hawaii at Manoa, May 16-20, 2022.
• Women in Algebra and Symbolic Computations II, November 29th - December 1st, 2021.
• Konstanz Women in Mathematician Special Lecture in celebration of the Women in Mathematics Day, June 17, 2021.
• Oberseminar zur Algebra und Zahlentheorie, Augsburg University, February 9, 2021.
• 13th polymake conference and developer meeting, TU Berlin, January 21, 2022.
• 12th polymake conference and developer meeting, TU Berlin, January 29, 2021.
• UCGEN (online seminar around topics near algebraic geometry), Istanbul Center for Mathematical Sciences, October 21, 2020.
• Oberseminar Darstellungstheorie, RWTH Aachen University, July 16, 2020.
• Research visit at Faculty of Mathematics, University of Warsaw, March 3-13, 2020.
• Research seminar "Non-Linear Algebra", Max Planck Institute Leipzig, February 19, 2020.
• Research seminar "Algebra/Algebraic Geometry", Freie Universität Berlin, February 6-7, 2020.
• Research seminar "Discrete Geometry", Freie Universität Berlin, December 5, 2019.
• Research visit at St. Louis Washington University, St. Louis, August 26-30, 2019.
• Workshop Mutations: Mirror Symmetry, Deformations, and Combinatorics, at Banff International Research Station, August 11-16, 2019.
• Lectures on Algebraic and Symplectic Aspects in Degenerations of Complex Surfaces, Seoul, June 24-28, 2019.
• MEGA: Effective Methods in Algebraic Geometry 2019, Madrid, June 17-21, 2019.
• Graduate Student Meeting on Applied Algebra and Combinatorics, MPI for Mathematics in the Sciences, February 18-20, 2019.
• Summer School on Lattice Polytopes, Osaka, July 23 - August 10, 2018.
• Thematic Program on Combinatorial Algebraic Geometry, Fields Institute, Toronto, October 2016.
• CIMPA-ICTP Research School, Toric methods in geometry, arithmetics, and dynamics, Pontificia Universidad Catlica de Chile, Santiago de Chile, January 11 - 22, 2016.
• Cox Rings and Mori Dream Spaces, University of Warsaw, Lukecin, September 6-10, 2015.
• Summer School of the IRTG Moduli and Automorphic Forms, Recent advances in algebraic and arithmetic geometry, University of Siena, August 24-28, 2015.
• New Techniques on Birational Geometry, Simons Center for Geometry and Physics, Stony Brook, April 7-11, 2015.
• Toric degenerations and mirror symmetry, Sophus Lie Conference Center, Nordfjordeid, June 16-20, 2014.
• Master Class : Around Thurston-Grothendieck-Teichmüller theories, Institut de Recherche Mathématique Avancée, Strasbourg, May 9-17, 2014.
• NoGAGS (Northern German Algebraic Geometry Seminar),, Humboldt Universität Berlin, November 7-8, 2013.
• Syzygies in Berlin, Freie Universität Berlin, May 27-31, 2013.
• Istanbul Toric and Tropical Geometry Meetings, University of Galatasaray, Istanbul, Spring 2012.
• Istanbul Workshop on Teichmuller Theory, University of Galatasaray, Istanbul, October 11-14, 2012.
• Goutelas-eleves, Chateau de Goutelas, Marcoux, A conference with Vaughan Jones on Knot Theory, March 2-4, 2012.
• Functoriality and Pairing, A course with Robert Langlands, Ilhan Ikeda, Ali Altug, Cihan Saçlıoglu, University of Galatasaray, Istanbul, March 30-April 27, 2011.
• Algebra II Workshop in Honour of Prof. Dr. Cemal Koç, Bogazici University, Istanbul, July 3-5, 2010.
• TMD Summer School, Nesin Mathematics Village Şirince - Selçuk - Izmir, 2008, 2011.
• GTEM Summer School-Geometry and Arithmetic of Moduli Spaces of Coverings, University of Galatasaray, Istanbul, June 9- 20, 2008.