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- The paper "Computing the Noncommutative Inner Rank by Means of Operator-Valued Free Probability Theory" by Johannes Hoffmann, Tobias Mai and Roland Speicher has now been published online in Foundations of Computational Mathematics. Here is a link to the open access article.
- In June 2024 Roland Speicher gave a lecture series of five 90 minutes talks on “Free Probability, Free Cumulants and Random Matrices” at the Beg Rohu Summer School on statistical physics. The lectures, which were intended as an introduction into the subject of free probability for physicists, were recorded and can be watched on youtube: lecture 1, lecture 2, lecture 3, lecture 4, lecture 5.
- A polished version of the lecture notes of the random matrix class has now appeared with EMS Press as Lectures on Random Matrices.
- Tobias Mai and Roland Speicher uploaded their new preprint Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates to the arXiv. More information on this can also be found on this blog post.
Older News
- Roland Speicher wurde als ehemaliger Bundessieger im Wettbewerb Jugend forscht in einem Beitrag im Aktuellen Bericht vom 13.03.24 porträtiert.
- The lecture notes of the course on High Dimensional Analysis: Random Matrices and Machine Learning course are now also available.
- The videos of the High Dimensional Analysis: Random Matrices and Machine Learning course have been uploaded to youtube.
- Die endgültige Version des Analysis 1 Skriptes ist jetzt auch verfügbar.
- The lecture notes of the course Mathematical Aspects of Quantum Mechanics from the winter term 2000/2021 are finally officially available. Thanks to Friedrich Günther for providing a tex-ed version of my notes.
- The article Universality of free random variables: atoms for non-commutative rational functions by Arizmendi, Cebron, Speicher, Yin has finally been published. Here is a Share Link, for free download, valid until April 23.
- The talk Universality of free random variables: atoms for non-commutative rational functions of Roland Speicher at the Follow-up Workshop to TP "Von Neumann Algebras", Bonn, August, 2022 is now online on youtube
- Vom 25. bis 28. September findet in Saarbrücken die Jahrestagung 2023 des SFB-TRR 195 statt.
- There will be a special day on "Free probability, between maths and physics" at IHP, Paris on 25 January 2023. This is part of a two-day conference “Inhomogeneous Random Structures”. For more information on this see also the post on the free probability blog.
- From 12 September 2022 to 9 December 2022, the Focus Semester on Quantum Information will take place at Saarland University. For more information see this webpage.
- Gaëtan Borot, Séverin Charbonnier, Elba Garcia-Failde, Felix Leid, and Sergey Shadrin have uploaded their new preprint on "Analytic theory of higher order free cumulants" to the archive; see also the post on the free probability blog.
- Am 19. Juli um 19:30 Uhr hält Roland Speicher am Wissenschaftsforum MINT-Campus Alte Schmelz einen Vortrag zum Thema Nicht-kommutative Wahrscheinlichkeitstheorie und Zufallsmatritzen - das Wechselspiel zwischen abstrakter Theorie und konkreter Anwendung. Der Vortrag ist für ein allgemeines Publikum, Mathematiker dürfen aber auch gerne zuhören.
- Zum Tag der offenen Tür stellen Professor Speicher und Professor Weber ihre Arbeitsgebiete aus der Quantenmathematik in zwei kleinen Videos vor: nicht-kommutative Wahrscheinlichkeiten (Speicher) und nicht-kommutative Symmetrien (Weber).
- Die noch ausstehenden Videos der Vorlesung HMI 3 sind nun online zugänglich, sowohl unter Moodle wie auch im youtube Kanal. Damit ist der Video-Zyklus für die HMI beendet. Für die HMI 4 Vorlesungen wird es keine Videos geben.
- The Queen's Seminar on Free Probability and Random Matrices is now running online; see also the announcement on the free probability blog.
- Octavio Arizmendi, Guillaume Cebron, Roland Speicher and Sheng Yin have just uploaded their new paper “Universality of free random variables: atoms for non-commutative rational functions“ to the archive. For an appetizer see the blog entry, for the full meal go directly to the preprint.
- Roland Speicher gave a mini-course of three talks on the relation between higher order freeness and topological recursion at the conference Noncommutative geometry meets topological recursion in Münster. All talks were recorded and can be found on the youtube playlist of the conference.
- Since March 1, 2021, Moritz Weber is a Heisenberg professor at Saarland University - see the press release (in German). Congratulations to Moritz!
- The talk "What actually is free probability theory?" by Tobias Mai at the Technion was recorded and can be found here on youtube.
- The talk "Singularity of matrices in non-commuting variables and free probability" by Roland Speicher at the Technion was recorded and can be found here on youtube.
- A PhD position, funded by the DFG, on a project "Free Probability Aspects of Neural Networks" is available - if you are interested see here for details.
- Michael Hartz has been awarded the Barbara and Jaroslav Zemánek Prize (see announcement and a personal laudatio in the blog of Orr Shalit). This is given to young researchers for achievements in functional analysis, with special emphasis on operator theory. Congratulations to Michael!
- Roland Speicher will give a colloquium talk at the Math Department of the Technion, Israel on Monday, January 25 – online, of course. They have the nice option of a pre-colloquium talk, which provides students with some background for the material appearing in the colloquium talk. Tobias Mai agreed to give such a preparation talk. So he will give on Thursday, January 21, an introduction to free probability and its relation with random matrices. Surely a great opportunity for everyone to learn (more) about the subject. See here for more info.
- Moritz Weber was selected for the Heisenberg programme of the German Research Foundation. His own position will be fully funded from early 2021 for five years. That's a great achievement. Congratulations to Moritz!
- Daniel Gromada finished his PhD in September 2020.
- The Lecture Notes on Non-Commutative Distributions (course from summer term 2019) are now online.
- Simon Schmidt finished his PhD in July 2020.
- The talk of Roland Speicher on "Random matrices and their limits" in the Wales MPPM Seminar is now online. May 12, 2020.
- The videos of the three talks of Roland Speicher in the Distinguished Lecture Series at the Fields Institute are now online.
- Miguel Pluma and Sheng Yin finished their PhD in January 2020.
- Stefan Jung finished his PhD in June 2019.
Online Resources
Some appetizer videos:
- Dan-Virgil Voiculescu: visionary operator algebraist and creator of free probability theory
- The curse and the blessing of high dimensions
- What is so amazing about Wigner's semircircle law?
- Why I prefer the Heisenberg picture over the Schrödinger picture
- Die wundersame Welt der Quantenmathematik: nicht-kommutative Wahrscheinlichkeiten
- Das seltsame zeitliche Verhalten von linearen Dglen bei nicht-orthogonalen Eigenvektoren
- Die Relevanz der komplexen Zahlen
ERC Advanced Grant
From 1 February 2014 until 31 January 2019, the European Research Council supported the research of Roland Speicher by an ERC Advanced Grant with the title Non-Commutative Distributions in Free Probability. More info on this can be found here
SFB-TRR 195
Symbolic Tools in Mathematics and their Application
The Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) has established the transregional collaborative research centre (SFB-TRR) 195 “Symbolic Tools in Mathematics and their Application” starting in January 2017. Host university is the University of Kaiserslautern (TU Kaiserslautern), additional applicant universities are RWTH Aachen University and Saarland University.
What actually is Free Probability?
A motivating example
Consider the following three natural questions from the fields of operator algebras, random matrices, and combinatorics, respectively.
- What is the distribution of the real part of the one-sided shift with respect to the canonical vacuum expectation state?
- What is the asymptotic eigenvalue distribution of a Gaussian random matrix in the limit of large matrix size?
- In how many ways can one connect 2n points on a circle pairwisely by n non-intersecting chords?
Surprisingly, all three questions have essentially the same answer: both question 1 and 2 yield the semicircular distribution, and the answer to question 3 is given by the Catalan numbers which are actually the even moments of the semicircular distribution. This coincidence is not just superficial - a conceptual reason is given by Voiculescu's free probability theory and its basic concept of freeness. [...]
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