Dr. Tobias MaiResearch group Prof. Dr. SpeicherFree Probability Theory Saarland University Faculty of Mathematics D-66123 Saarbruecken Germany room 225 (building E 2 4) phone: +49-681-302-3006 mail: mai [at] math.uni-sb.de postal address Universitaet des Saarlandes Fachrichtung Mathematik Postfach 151150 D-66041 Saarbruecken Germany |
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Education
| 2017 | PhD in Mathematics at Saarland University, Saarbrücken |
| Advisor: Prof. Dr. Roland Speicher | |
| PhD Thesis: On the analytic theory of non-commutative 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"), |
| Arnold-Janssen-Gymnasium 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 Martin-Preis 2017
Teaching
Conferences and Seminars
2021
- Mini-course and Workshop on the Non-commutative 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
- UniMelb-Bielefeld RMT Seminar
The University of Melbourne (remote talk)
June 9, 2021
(talk: Noncommutative rational functions evaluated in random matrices)
- Technion Math Colloquium, Pre-Colloquium 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 L²-theory 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. 183-215
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 Non-Commutative 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 1-79
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 non-microstates free entropy dimension
appeared in: Advances in Mathematics, Volume 304, 2017, pp 1080-1107
arXiv:1502.06357 [math.OA] (2015) - Belinschi, S., Mai, T., Speicher, R.
Analytic subordination theory of operator-valued 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) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle-2014-0138, April 2015
arXiv:1303.3196 [math.OA] (2013) - Mai, T., Speicher, R.
Operator-valued and multivariate free Berry-Esseen theorems
appeared in: Limit Theorems in Probability, Statistics and Number Theory,
Springer Proceedings in Mathematics & Statistics Volume 42, 2013, pp 113-140
arXiv:1202.2740 [math.OA] (2012) - Speicher, R., Vargas, C., Mai, T.
Free Deterministic Equivalents, Rectangular Random Matrix Models,
and Operator-Valued 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.
Berry-Esseen bounds for the multivariate B-free CLT and operator-valued 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 non-microstates free Fisher information
arXiv:1407.5715 [math.OA] (2014)
| updated: 9 June 2021 Tobias Mai | Impressum |
