İrem Portakal*
Max Planck Research Group Leader
''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
Since September 2023, I have been leading the Interdisciplinary Frontiers of Algebraic Geometry research group at the Max Planck Institute for Mathematics in the Sciences in Leipzig. I am also an associate of the Reinhart-Koselleck-Projekt Reflexive Decision and Game Theory led by Wolfgang Spohn.
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 2024: Check out this fun AMS Feature Column titled "Elliptic curves come to date night" that is written on my joint work about dependency equilibria.
April 2024: I am giving a short lecture on algebraic game theory at 5th Graduate Student Meeting in Applied Algebra and Combinatorics.
March 2023: I am giving a survey talk on combinatorics of equilibria in game theory at Combinatorial Coworkspace.
February 2024: New paper on Game theory of undirected graphical models is now out!
December 2023: New paper on Algebraic sparse factor analysis with Mathrepo page is now online!
Interdisciplinary frontiers of algebraic geometry
Current group members
- Matthieu Bouyer, École Polytechnique, long term visitor
- Aryaman Jal, KTH Stockholm, long term visitor
- Elke Neuhaus, PhD Student
- Jutta Rath, Universität Klagenfurt, long term visitor
- Daniel Windisch, postdoc
Former group members and the website of the group
Publications
- 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], to appear in Experimental Mathematics.
- Toric ideals of characteristic imsets via quasi-independence gluing, with Benjamin Hollering, Joseph Johnson and Liam Solus, [arXiv:2209.01834], to appear in Algebraic Statistics.
- 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.
- On real geometry of dependency equilibria, with Daniel Windisch.
Teaching
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
Freie Universität Berlin
WiSe 17/18
- Computeralgebra Vorlesung, (5-16 März 2018).
2016-2018
- What is...? Seminar Series, Berlin Mathematical School.
Galatasaray University
2010-2013
- Analyse à une variable I-II, Introduction à la géométrie torique.
- Abstract Algebra Exercise Session.
Organized Events
- 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.
- 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 Past Activities
Contact
