Dr. Tobias MaiResearch group Prof. Dr. SpeicherFree Probability Theory Saarland University Faculty of Mathematics D66123 Saarbruecken Germany room 225 (building E 2 4) phone: +496813023006 mail: mai [at] math.unisb.de postal address Universitaet des Saarlandes Fachrichtung Mathematik Postfach 151150 D66041 Saarbruecken Germany 

Education
2017  PhD in Mathematics at Saarland University, Saarbrücken 
Advisor: Prof. Dr. Roland Speicher  
PhD Thesis: On the analytic theory of noncommutative distributions in free probability  
2011  Master of Science (Mathematics) at Saarland University, Saarbrücken 
Advisor: Prof. Dr. Ernst Albrecht  
Master Thesis: On the Theory of Faber Polynomials (in German)  
(Course of studies finished on October 25, 2010)  
2009  Bachelor of Science (Mathematics) at Saarland University, Saarbrücken 
Advisor: Prof. Dr. Ernst Albrecht  
Bachelor Thesis: Compactness Criteria for Composition Operators on Bergman Type Spaces (in German)  
(Date of the last examination: October 15, 2008)  
2005  General Higher Education Entrance Qualification ("Allgemeine Hochschulreife"), 
ArnoldJanssenGymnasium St. Wendel 
Distinctions and awards
 Best teaching award (Summer term 2017) awarded by the student
association mathematics for the lecture Complex Analysis II
 Dr. Eduard MartinPreis 2017
Teaching
Conferences and Seminars
2021
 Minicourse and Workshop on the Noncommutative Function Theory (November 16  18, 2021)
as part of the Focus Program on Analytic Function Spaces and their Applications
Fields Institute, Toronto, Canada
July 1  December 31, 2021
 IWOTA 2020: International Workshop on Operator Theory and its Applications
Special Session on Noncommutative Probability and Random Matrices
Lancaster University, Lancaster, England
August 16  20, 2021
 UniMelbBielefeld RMT Seminar
The University of Melbourne (remote talk)
June 9, 2021
(talk: Noncommutative rational functions evaluated in random matrices)
 Technion Math Colloquium, PreColloquium Talk
Technion, Haifa, Israel (remote talk)
January 21, 2021
(talk: What actually is free probability theory?, recording of the talk)
2020
 postponed: IWOTA 2020: International Workshop on Operator Theory and its Applications
Special Session on Noncommutative Probability and Random Matrices
Lancaster University, Lancaster, England
August 17  21, 2020
 canceled: Free Probability  on the occasion of Roland Speicher's 60th birthday
Saarbrücken, Germany
June 8  12, 2020
 postponed: Quantitative methods in random matrix theory
Toulouse, France
June 3  5, 2020
 UC Berkeley Probabilistic Operator Algebra Seminar
Berkeley, US (remote talk)
April 20, 2020
(talk: Free and cyclic differential calculus and characterizations of gradients)
 Real Algebraic Geometry with a View Toward Hyperbolic Programming
and Free Probability (Workshop ID 2010)
Mathematical Research Institute of Oberwolfach, Germany
March 1  7, 2020
(talk: Free probability: operator theoretic aspects and regularity properties of noncommutative distributions)
2019
 Random Matrices (Workshop ID 1950)
Mathematical Research Institute of Oberwolfach, Germany
December 8  14, 2019
(talk: Limit laws of random matrices beyond the Dyson equation)
 Kyoto Operator Algebra Seminar
Kyoto University, Department of Mathematics
talk 1 (November 8, 2019): Free differential calculus I: on the L²theory for free differential operators
and regularity of noncommutative distributions
talk 2 (November 12, 2019): The free field meets free probability theory
talk 3 (November 13, 2019): Free differential calculus II: characterizations of free and cyclic gradients
 IWOTA 2019: International Workshop on Operator Theory and its Applications
Special Session on Free Analysis and Free Probability
Instituto Superior Tecnico, Lisbon, Portugal
July 22  26, 2019
(talk: Regularity properties of spectral distributions: from free probability to random matrix theory)
 Oberseminar Stochastics
University of Bonn, Institute for Applied Mathematics
July 11, 2019
(talk: Spectral distributions of noncommutative functions: from free probability to random matrix theory)
 Workshop on Applications to Random Matrices and Free Probability of Free
Noncommutative Functions (June 17  21, 2019)
as part of the Focus Program on Applications of Noncommutative Functions
Fields Institute, Toronto, Canada
June 10  July 5, 2019
(talk: Noncommutative functions and regularity properties of spectral distributions)
 New Developments in Free Probability and Applications
Centre de Recherches Mathématiques, Montreal, Canada
March 1  31, 2019
(talk: The free field meets free probability theory)
2018
 Free Probability Theory (Workshop ID 1849)
Mathematical Research Institute of Oberwolfach, Germany
December 2  8, 2018
(talk: Regularity properties of noncommutative distributions)
 Sums and Products of Random Matrices
Centre for Interdisciplinary Research (ZiF), Bielefeld, Germany
August 27  31, 2018
(talk: Regularity properties of limiting eigenvalue distributions by means of free probability theory)
Publications
published
 Mai, T., Speicher, R.
A Note on the Free and Cyclic Differential Calculus
appeared in: Journal of Operator Theory, Volume 85, Issue 1, Winter 2021, pp. 183215
arXiv:1910.07570 [math.OA] (2019)  Banna, M., Mai, T.
Hölder Continuity of Cumulative Distribution Functions for
Noncommutative Polynomials under Finite Free Fisher Information
appeared in: Journal of Functional Analysis, Volume 279, Issue 8, 1 November 2020
arXiv:1809.11153 [math.PR] (2018)  Cébron, G., Fathi, M., Mai, T.
A note on existence of free Stein kernels
appeared in: Proceedings of the American Mathematical Society
arXiv:1811.02926 [math.OA] (2018)  Mai, T., Speicher, R.
Free Probability, Random Matrices, and Representations of NonCommutative Rational Functions
appeared in: Computation and Combinatorics in Dynamics, Stochastics and Control.
Abelsymposium 2016. Abel Symposia, vol 13. Springer, Cham
 Helton, J. W., Mai, T., Speicher, R.
Applications of Realizations (aka Linearizations) to Free Probability
appeared in: Journal of Functional Analysis, Volume 274, Issue 1, 2018, pp 179
arXiv:1511.05330 [math.OA] (2015)  Mai, T., Speicher, R., Weber, M.
Absence of algebraic relations and of zero divisors under the assumption
of full nonmicrostates free entropy dimension
appeared in: Advances in Mathematics, Volume 304, 2017, pp 10801107
arXiv:1502.06357 [math.OA] (2015)  Belinschi, S., Mai, T., Speicher, R.
Analytic subordination theory of operatorvalued free additive convolution
and the solution of a general random matrix problem
appeared in: Journal für die reine und angewandte Mathematik (Crelles Journal)
ISSN (Online) 14355345, ISSN (Print) 00754102, DOI: 10.1515/crelle20140138, April 2015
arXiv:1303.3196 [math.OA] (2013)  Mai, T., Speicher, R.
Operatorvalued and multivariate free BerryEsseen theorems
appeared in: Limit Theorems in Probability, Statistics and Number Theory,
Springer Proceedings in Mathematics & Statistics Volume 42, 2013, pp 113140
arXiv:1202.2740 [math.OA] (2012)  Speicher, R., Vargas, C., Mai, T.
Free Deterministic Equivalents, Rectangular Random Matrix Models,
and OperatorValued Free Probability Theory
appeared in: Random Matrices: Theory and Applications, Volume 01, Issue 02, April 2012
arXiv:1110.1237 [cs.IT] (2011)
preprints
 Banna, M., Mai, T.
BerryEsseen bounds for the multivariate Bfree CLT and operatorvalued matrices
arXiv:2105.02044 [math.PR] (2021)  Collins, B., Mai, T., Miyagawa, A., Parraud, F., Yin, S.
Convergence for noncommutative rational functions evaluated in random matrices
arXiv:2103.05962 [math.OA] (2021)  Mai, T., Speicher, R., Yin, S.
The free field: realization via unbounded operators and Atiyah property
arXiv:1905.08187 [math.OA] (2019)  Mai, T., Speicher, R., Yin, S.
The free field: zero divisors, Atiyah property and realizations via unbounded operators
arXiv:1805.04150 [math.OA] (2018)  Mai, T.
Regularity of distributions of Wigner integrals
arXiv:1512.07593 [math.OA] (2015)  Mai, T., Speicher, R., Weber, M.
Absence of algebraic relations and of zero divisors under the assumption
of finite nonmicrostates free Fisher information
arXiv:1407.5715 [math.OA] (2014)
updated: 9 June 2021 Tobias Mai  Impressum 