Borel Combinatorics and Approximations (BORCA)

This project concerns research on the boundary between analysis, logic and combinatorics, more specifically, investigates problems in descriptive set theory and their interactions with measure theory, dynamical systems, computer science and graph limits, through the study of measurability properties of combinatorial problems on infinite graphs.

Publications

1. (with O. Pikhurko) Large deviation principles for graphon sampling, submitted (2023), [arXiv].
2. (with C. Higgins) Complexity of Finite Borel Asymptotic Dimension, preprint (2024), [arXiv].

Talks

1. Descriptive Set Theory & Dynamics conference, Warsaw, Poland, 20.8.-25.8.2023 (45 minute talk Derandomization in descriptive graph combinatorics),
2. UCLA logic colloquium, LA, USA, 11.10.2023 (50 minute talk Complexity of Borel colorings),
3. UCLA combinatorics seminar, LA, USA, 16.11.2023 (50 minute talk Edge colorings and distributed computing),
4. WIAS Material Modelling seminar, Berlin, Germany, online, 21.11.2023 (50 minute talk Large deviation principles for graphon sampling),
5. CMU logic seminar, Pittsburgh, USA, 28.11.2023 (50 minute talk Borel equivalence relations induced by actions of tsi Polish groups),
6. UCI Logic Set Theory seminar, Irvine, USA, 1.4.2024 (80 minute talk Lossless expansion and measure hyperfiniteness),
7. UCI Combinatorics and Probability seminar, Irvine, USA, 3.4.2024 (50 minute talk Measurable tilings),
8. BLAST 2024, UNT Denton, USA, 6.4.-9.4.2024 (30 minute talk Edge colorings in measurable combinatorics and distributed computing),
9. Caltech logic seminars, Caltech, USA, online, 12.6.2024 (50 minute talk Translational tilings of the plane by a polygonal set),
10. Borel Combinatorics Seminar, Eötvös University, Budapest, Hungary, 8.7.2024 (50 minute talk Translational tilings of the plane by a polygonal set),
11. ADGA 2024 @ DISC, Madrid, Spain, 28.10.2024 (45 minute talk Measurable combinatorics),

Visits

1. 27 Nov-1 Dec 2023, JG visits CMU, Pittsburgh, USA,
2. 4 Dec-8 Dec 2023, JG visits UC Berkeley, Berkeley, USA,
3. 19 Feb-24 Feb 2024, JG visits UC Berkeley, Berkeley, USA,
4. 1 Apr-3 Apr 2024, JG visits UC Irvine, Irvine, USA,
5. 18 May-25 May 2024, JG visits Jagiellonian University, Kraków, Poland,
6. 27 May-28 May 2024, JG visits Masaryk University, Brno, Czechia,
7. 15 Jun-6 Jul 2024, JG visits Renyi Institute, Budapest, Hungary,

Visitors

1. 7 - 9 May 2024, Amanda Wilkens visits UCLA,
2. 10 - 14 Aug 2024, Amanda Wilkens visits UCLA,
3. 10 - 16 Dec 2024, Oleg Pikhurko visits MU,

Organizing

1. 28 Jan - 3 Feb, 2024 A. Bartos, D. Chodounsky, JG, C. Lambie-Hanson organize Winter School in Abstract Analysis 2024, Hejnice, Czechia
2. 20 May - 24 May 2024: JG co-organize AlgoMaNet – Algorithms and Mathematics Network, Jagiellonian University, Kraków, Poland
3. Spring 2024: JG and Mariana Vicaria organize UCLA logic colloquium, UCLA, Los Angeles, USA
4. Spring 2024: JG, A. Kechris, O. Pikhurko, S. Todorcevic, and Z. Vidnyanszky organize Measurable Combinatorics, Erdos Center, Budapest, Hungary
5. 9 September - 13 Septmeber 2024: JG co-organize AlgoMaNet – Algorithms and Mathematics Network, University of Warsaw, Warsaw, Poland
6. 15 Novemeber - 16 Novemeber 2024: M. Filakovsky and JG organize One day Combinatorics meeting, Masaryk Unviersity, Brno, Czechia
7. 25 Jan - 1 Feb, 2025 A. Bartos, D. Chodounsky, JG, C. Lambie-Hanson organize Winter School in Abstract Analysis 2025, Hejnice, Czechia

Other

1. Interview (in Czech) at Faculty of Informatics about this project, MU, Czechia
2. Talk at Grants week 2024 about this project, MU, Czechia