Igor Balla

Contact Info

E-mail address:	iballa1990gmail.com
Office address:	Room 321, Neues Augusteum
	Augustusplatz 10, 04109 Leipzig
	Faculty of Mathematics and Computer Science, Leipzig University

I am a Postdoc at Leipzig University working in the group of Dan Kráľ. Previously, I was a Strauch Postdoctoral Fellow at the Simons Laufer Mathematical Sciences Institute (SLMath). I completed my PhD in mathematics at ETH Zürich under the guidance of Benny Sudakov. In the past, I have received a master's degree from New York University, a bachelor's degree from Carnegie Mellon University, and held postdoc positions at Tel Aviv University, the Hebrew University of Jerusalem, and Masaryk University.

I am broadly interested in combinatorics and linear algebra, as well as their interplay with other fields. A significant portion of my research has focused on extremal problems lying at the intersection of these areas. Apart from being beautiful and interesting in their own right, these problems have connections to probability, geometry, topology, applied mathematics, theoretical computer science, and quantum physics.
Check out my research featured in Quanta magazine - A New Path to Equal-Angle Lines

Curriculum Vitae: CV

Papers

Submitted

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• Curves on the torus with few intersections. Balla, I., Filakovský, M., Kielak, B., Kráľ, D., & Schlomberg, N. (2024).
  arXiv:2412.18002. Submitted.
• Equiangular lines via improved eigenvalue multiplicity. Balla, I., & Bucić, M. (2024).
  arXiv:2409.16219. Submitted.

Accepted

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• Factorization norms and an inverse theorem for MaxCut. Balla, I., Hambardzumyan, L., & Tomon, I. (2025).
  Mathematische Annalen, to appear.
  Accepted to the 66th Annual Symposium on Foundations of Computer Science (FOCS 2025).

Published

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• Equiangular lines via matrix projection. Balla, I. (2025).
  Advances in Mathematics, 482 Part B, 110620.
• Orthonormal representations, vector chromatic number, and extension complexity. Balla, I. (2024).
  Bulletin of the London Mathematical Society, 56 (9), 2911-2921.
• Small Codes. Balla, I. (2024).
  Bulletin of the London Mathematical Society, 56 (5), 1680-1686
• On MaxCut and the Lovász theta function. Balla, I., Janzer, O., & Sudakov, B. (2024).
  Proceedings of the American Mathematical Society, 152 (5), 1871-1879.
• Orthonormal representations of H-free graphs. Balla, I., Letzter, S., & Sudakov, B. (2020).
  Discrete & Computational Geometry, 64 (3), 654-670.
• The Minrank of Random Graphs over Arbitrary Fields. Alon, N., Balla, I., Gishboliner, L., Mond, A., & Mousset, F. (2020).
  Israel Journal of Mathematics, 235 (1), 63-77.
• Equiangular subspaces in Euclidean spaces. Balla, I., & Sudakov, B. (2019).
  Discrete & Computational Geometry, 61 (1), 81-90.
• Ramsey goodness of bounded degree trees. Balla, I., Pokrovskiy, A., & Sudakov, B. (2018).
  Combinatorics, Probability and Computing, 27 (3), 289-309.
• Equiangular Lines and Spherical Codes in Euclidean Space. Balla, I., Dräxler, F., Keevash, P., & Sudakov, B. (2018).
  Inventiones Mathematicae, 211 (1), 179-212.
• A remark on Hamilton cycles with few colors. Balla, I., Pokrovskiy, A., & Sudakov, B. (2017).
  Moscow J. Combinatorics and Number Theory, 7 (3), 259-263.
• Union-closed families of sets. Balla, I., Bollobás, B., & Eccles, T. (2013).
  Journal of Combinatorial Theory Series A, 120 (3), 531-544.

Preprints

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• Note on the second eigenvalue of regular graphs. Balla, I., Räty, E., Sudakov, B., & Tomon, I. (2023).
  arXiv:2311.07629.
• Minimum density of union-closed families. Balla, I. (2011).
  arXiv:1106.0369.

Teaching

• Fall 2024 - lecturer for Graph Theory, Masaryk University.
• Spring 2024 - lecturer for Advanced Combinatorics, Masaryk University.
• Spring 2019 - teaching assistant for Graph Theory, ETH Zurich.
• Fall 2018 - teaching assistant for Algebra I, ETH Zurich.
• Spring 2017 - teaching assistant for Graph Theory, ETH Zurich.
• Spring 2016 - teaching assistant for Seminar on Elementary Number Theory, ETH Zurich.
• Spring 2012 - teaching assistant for Matrix Theory, Carnegie Mellon University.
• Spring 2010 - teaching assistant for Graph Theory, Carnegie Mellon University.

Talks

• November 2025 - The state of the art on equiangular lines, Seminar on Nonlinear Algebra, Leipzig University.
• November 2025 - The factorization norm and an inverse theorem for MaxCut, Graz Combinatorics Seminar, TU Graz.
• August 2025 - Equiangular lines via improved eigenvalue multiplicity, Random Structures and Algorithms, Vienna.
• July 2025 - Laplacians and equioverlapping vectors, SampTA, Vienna.
• April 2025 - MaxCut, orthonormal representations, and extension complexity of polytopes, Extremal Combinatorics Seminar, SLMath, Berkeley.
• March 2025 - MaxCut, orthonormal representations, and extension complexity of polytopes, Research seminar in Discrete Mathematics, BIMSA, Beijing.
• December 2024 - MaxCut, orthonormal representations, and extension complexity of polytopes, Combinatorics Seminar, Alfréd Rényi Institute of Mathematics.
• November 2024 - The state of the art on equiangular lines, Number Theory Seminar, Charles University.
• November 2024 - MaxCut, orthonormal representations, and extension complexity of polytopes, DIMEA Combinatorial Potluck 2024, Masaryk University.
• November 2024 - MaxCut, orthonormal representations, and extension complexity of polytopes, Discrete Mathematics Seminar, Princeton University.
• September 2024 - Equiangular lines via matrix projection, (Invited speaker) Analysis Seminar (conference), Innsbruck.
• August 2024 - Equiangular lines via matrix projection[YOUTUBE], Codes and Expansions (CodEx) Seminar.
• July 2024 - Small codes and set-coloring Ramsey numbers, Summit280, Budapest.
• June 2024 - Small codes, Recent Progress on Optimal Point Distributions and Related Fields, ICERM.
• April 2024 - Equiangular lines and regular graphs (Invited speaker), Czech-Slovak Conference on Graph Theory, Czech Republic.
• April 2024 - Small codes and set-coloring Ramsey numbers, Seminar on Foundations of Computing, Masaryk University.
• December 2023 - Equiangular lines via matrix projection, Discrete Mathematics Seminar, Princeton University.
• December 2023 - Equiangular lines via matrix projection, Richard P. Stanley Seminar in Combinatorics, MIT/Harvard.
• June 2023 - Equiangular lines via matrix projection, Combinatorics Seminar, Technion.
• May 2023 - Equiangular lines via matrix projection, Combinatorics Seminar, Bar Ilan University.
• April 2023 - Equiangular lines via matrix projection, Combinatorics Seminar, The Hebrew University of Jerusalem.
• December 2022 - A recent breakthrough on the union-closed conjecture, KU-Jerusalem Lunch Seminar
• August 2022 - Equiangular lines and regular graphs, Random Structures and Algorithms, Gniezno.
• March 2022 - Equiangular lines and regular graphs[YOUTUBE], Codes and Expansions (CodEx) Seminar.
• February 2022 - Equiangular lines and regular graphs, Combinatorics, Physics and Probability Seminar, CMSA, Harvard University.
• December 2021 - Equiangular lines and regular graphs, Combinatorics Seminar, The Hebrew University of Jerusalem.
• November 2021 - Equiangular lines and regular graphs, Combinatorics Seminar, Tel Aviv University.
• June 2021 - Equiangular lines and graph spectra, Combinatorics Research Seminar, The Free University of Berlin
• December 2019 - Orthonormal representations of H-free graphs, TAU Combinatorics Seminar, Tel Aviv University.
• September 2019 - The Minrank of Random Graphs over Arbitrary Fields, Discrete Mathematics Seminar, Princeton University.
• July 2019 - The Minrank of Random Graphs over Arbitrary Fields, Random Structures and Algorithms, Zurich.
• February 2019 - The Minrank of Random Graphs over Arbitrary Fields, Mittagsseminar, ETH Zurich.
• October 2017 - Equiangular Subspaces, Mittagsseminar, ETH Zurich.
• August 2017 - Equiangular Lines and Subspaces in Euclidean Spaces, Eurocomb, Vienna.
• August 2017 - Ramsey Goodness of Bounded Degree Trees, Random Structures and Algorithms, Gniezno.
• January 2017 - Equiangular Lines and Spherical Codes, Workshop on Combinatorics, Oberwolfach.
• June 2016 - Ramsey Goodness of Bounded Degree Trees, SIAM Conference on Discrete Mathematics, Georgia State University.
• April 2016 - Equiangular Lines, Mittagsseminar, ETH Zurich.
• November 2014 - Noisy population recovery, CS Student Seminar, Courant Institute, NYU.
• September 2012 - Extremal results for union-closed families, Discrete Mathematics Seminar, Rutgers University.
• March 2012 - Extremal results for union-closed families, Algorithms, Combinatorics, and Optimization Seminar, Carnegie Mellon University.