İrem Portakal*
''İ'' is the uppercase of "i" in Turkish. It is pronanciated for example as the German letter "i" or the English letter "e".
About Me
I am a W2 Research Group Leader (fixed-term associate professor) at the Max Planck Institute for Mathematics in the Sciences in Leipzig and since September 2023, I have been leading the Interdisciplinary Frontiers of Algebraic Geometry research group. I am also an associate of the Reinhart-Koselleck-Projekt Reflexive Decision and Game Theory led by Wolfgang Spohn and an associate of DFG priority programme SPP 2458 "Combinatorial Synergies".
Before that, I was a postdoctoral researcher at TU Munich in the research group Mathematical Statistics led by Mathias Drton, in the Nonlinear Algebra Research Group led by Bernd Sturmfels at the MPI MiS Leipzig,
and in the Discrete, Convex, and Toric Geometry research group
led by Benjamin Nill at Otto-von-Guericke-Universität Magdeburg.
I defended my thesis in 2018 at Freie Universität Berlin. I was a PhD student at the Berlin Mathematical School and in the Algebraic Geometry Group led by Klaus Altmann.
Before that, I was a master's student at École Normale Supérieure in Lyon and an undergraduate student at Galatasaray University in Istanbul.
April 2025: New paper on A vector bundle approach to Nash equilibria is now out with supplementary code on MATHREPO.
February 2025: New paper on Matching criterion for identifiability in sparse factor analysis is now out!
January 2025: New paper on Elliptic curves in game theory is now out with supplementary code on MATHREPO.
December 2024: My research intern Matthieu Bouyer was awarded the Louis-Édouard Rivot medal from Ecole Polytechnique in France for exceptional research work.
Interdisciplinary frontiers of algebraic geometry
Current group members
- Linus Kamenz, Besondere Lernleistung (BeLL) Schüler.
- Elke Neuhaus, PhD Student.
- Niharika Chakrabarty Paul, PhD Student (joint with Simon Telen).
- Luca Sodomaco, Postdoc.
Former group members
- Matthieu Bouyer, Master Student Intern, École Polytechnique, 2024.
- Arjaman Jal, Long term visiting PhD, KTH Stockholm, 2024.
- Jutta Rath, Long term visiting PhD, Universität Klagenfurt, 2024.
- Daniel Windisch, Postdoc, 2023-2024.
Former visitors and the website of the group
Publications
- A vector bundle approach to Nash equilibria, with Hirotachi Abo and Luca Sodomaco, [arXiv:2504.03456].
- Matching criterion for identifiability in sparse factor analysis, with Nils Sturma, Miriam Kranzlmueller, Mathias Drton, [arXiv:2502.02986], submitted.
- Elliptic curves in game theory, with Abhiram Kidambi and Elke Neuhaus, [arXiv:2501.14612], submitted.
- Dependency equilibria: Boundary cases and their real algebraic geometry, with Daniel Windisch, [arXiv:2405.19054], to appear in Advances in Applied Mathematics.
- Game theory of undirected graphical models, with Javier Sendra-Arranz, [arXiv:2402.13246], Journal of Algebra Vol. 666 (2025).
- Algebraic sparse factor analysis, with Mathias Drton, Alex Grosdos and Nils Sturma, [arXiv:2312.14762], to appear in SIAM Journal on Applied Algebra and Geometry.
- 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 "A vector bundle approach to Nash equilibria". Supplementary material for the computations performed in the article with Macaulay2.
- MATHREPO for "Elliptic Curves in Game Theory". Supplementary material for the computations performed in the article with Macaulay2, Mathematica and Pari/GP.
- 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.
Teaching
Max Planck Institute for Mathematics in the Sciences
Summer Semester 2025
Freie Universität Berlin
April 2024
Institute for Mathematical and Statistical Innovation Chicago
September 2023
Technische Universität München
SoSe 23
SoSe 22
Otto-von-Guericke-Universität Magdeburg
WiSe 20/21
SoSe 20
- Mathematical Methods 2 Group 1 and 2. Website of the lecture.
WiSe 19/20
-
Leiterin der Hörsaalübung und verantwortlich für die Gruppenübungen:
- Mathematische Methoden I Hörsaalübung.
- Mathematische Methoden I Gruppenübungen 15-16.
SoSe 19
WiSe 18/19
SoSe 18
Korea Institute for Advanced Study
June 2019
Freie Universität Berlin
WiSe 17/18
Université Galatasaray
2010-2013
- Analyse à une variable I-II, Introduction à la géométrie torique.
- Abstract Algebra Exercise Session.
Organized Events
- 1st MPI (Dresden - Leipzig) Day, Max Planck Institute for Mathematics in the Sciences, October 30th, 2024.
- 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.
Selected Invited Past Activities
Contact
