Northern lights
Svolvær, Norway
Free Probability Theory
Several types of non-commutative independence
Combinatorial Hopf algebras
Higher algebraic structures: pre-Lie algebras, shuffle algebras, operads
Stochastic processes and random matrices
[8] Schröder trees, antipode formulas and non-commutative probability (with Y. Vargas), arXiv preprint arXiv:2311.07824. Accepted for publication in Annales de l’Institut Henri Poincaré D: Combinatorics, Physics and their Interactions (2025).
[7] Conditionally monotone cumulants via shuffle algebra (with K. Ebrahimi-Fard), to appear in Infinite Dimensional Analysis and Quantum Probability (2024).
[6] Forest formula for pre-Lie exponentials, Magnus’ operator and cumulant-cumulant relations (with F. Patras), arXiv preprint arXiv:2203.11968 (2022).
[5] Multiplicative and semi-multiplicative functions on non-crossing partitions, and relations to cumulants (with K. Ebrahimi-Fard, A. Nica, D. Perales and L. Witzman), Advances in Applied Mathematics 145, 102481 (2023).
[4] Monotone cumulant-moment formula and Schröder trees (with O. Arizmendi), Symmetry, Integrability and Geometry: Methods and Applications 18, 073 (2022).
[3] Cumulant-Cumulant Relations in Free Probability Theory from Magnus’ Expansion (with K. Ebrahimi-Fard, F. Patras and D. Perales), Foundations of Computational Mathematics, 1-23 (2021).
[2] Relations between infinitesimal non-commutative cumulants (with K. Ebrahimi-Fard and D. Perales), Documenta Mathematica 26, 1145-1185 (2021)
[1] Polynomial with cyclic monotone elements with applications to Random Matrices with discrete spectrum (with O. Arizmendi), Random Matrices: Theory and Applications 10(02), 2150020 (2021).
Cumulants in Non-commutative Probability via Hopf Algebras. Ph.D. in Mathematical Sciences. Norwegian University of Science and Technology. December 2022. Trondheim, Norway.
Workshop: 20th Workshop: Noncommutative Probability, Operator Algebras and Related Topics, with Applications. July 6-12, 2025. Będlewo, Poland.
Conference: Roland65 Conference on Free Probability, on the occasion of Roland Speicher's 65th birthday. June 9-13, 2025. Saarland University, Saarbrücken, Germany. Talk: A shuffle approach for Boolean cumulants of free random variables.
Conference: 70 years of Magnus series. July 1-5, 2024. Universitat Jaume I. Castellón, Spain. Talk: Relations between cumulants via Magnus expansion.
Summer School: Combinatorial Hopf algebras and modern Lie theory with applications. June 17-21, 2024. Sophus Lie Conference Centre. Nordfjordeid, Norway.
Workshop: PAGCAP Strobl Workshop. May 15-17, 2024. Strobl, Austria. Talk: Schröder trees, antipode formulas and cumulants.
Conference: Quantum Information Theory and Free Probability. New York University Abu Dhabi. January 8-12, 2024. Abu Dhabi, UAE. Talk: Conditionally monotone cumulants via shuffle algebra.
Free Probability and Operators Seminar. Texas A&M University. November 2023. College Station, Texas, USA. Talk: Schröder trees, antipode formulas and cumulants.
Summer School: Algebraic, Asymptotic and Enumerative Combinatorics. July 31- August 4, 2023. Będlewo, Poland. Poster: Forest formulas and relations between cumulants.
Workshop: PAGCAP Weissensee Workshop. May 14-17, 2023. Weissensee, Austria.
ESI Workshop: Non-commutative Geometry meets Topological Recursion. ESI, University of Vienna. April 24-28, 2023. Vienna, Austria.
GDR Renormalisation Annual Meeting 2022: Hopf Algebras and Applications. Université du Littoral Côte d’Opale. November 14-18, 2022. Calais, France.
1st CODYSMA Workshop. NTNU Trondheim. October 2022. Trondheim, Norway.
Workshop: Geometry and Renormalisation. University of Potsdam. September 26-30, 2022. Potsdam, Germany.
19th Workshop: Noncommutative probability, noncommutative harmonic analysis and related topics, with applications. Stefan Banach Conference Center. August 1-5, 2022. Będlewo, Poland.
Differential Equations and Numerical Analysis (DNA) Seminar. NTNU Trondheim. June 2022. Trondheim, Norway.
Algebraic and Combinatorial Perspectives in Mathematical Sciences Seminar. NTNU Trondheim. May 2022. Trondheim, Norway. Online.
Seminar on Free Probability and Random Matrices. Queen’s University. April 2022. Kingston, Canada. Online.
ESI School and Workshop: Higher Structures Emerging from Renormalisation. ESI, University of Vienna. November 8-19, 2021. Vienna, Austria.
Conference: Noncommutative algebra, probability and analysis in action (Short talk and poster). University of Greifswald. September 20-25, 2021. Greifswald, Germany.
Workshop: Noncommutative geometry meets topological recursion (Gong-talk). University of Münster. August 16-20, 2021. Münster, Germany.
Workshop: Algebraic Combinatorics of the Symmetric Groups and Coxeter Groups. July 2021. Cetraro, Italy.
Graduate Student Seminar. University of Sonora. November 2020. Sonora, Mexico. Online.
Free Probability Seminar. Saarland University. June 2018. Saarbrücken, Germany.
ESI Workshop: Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability. ESI. University of Vienna. February 17-21, 2025. Vienna, Austria.
CIRM Conference: Algebraic Aspects of Random Matrices. 7-11 October, 2024. Marseille, France.
Workshop: Operator Algebras: Free Probability. The Fields Institute. November 13-17, 2023. Toronto, Canada.