Torben Krüger
Contact
Email:
torben.krueger(at)fau.de
Address:
Department Mathematik der FAU Erlangen-Nürnberg
Cauerstraße 11, 91058 Erlangen, Germany
Office 2.332
I am chair for stochastics at FAU Erlangen-Nürnberg. The main focus of my research lies on the areas of random matrix theory (RMT), probability theory and mathematical physics. I apply and develop robust mathematical methods in order to rigorously study statistical properties of large complex systems that typically originate from applications in physics, statistics or engineering. My research group is dedicated to the study of disordered quantum systems and dynamic evolution on random networks through the use of RMT.
Dynamics on Correlated Networks
Our group started a new project that studies dynamic evolution of activities on high dimensional correlated networks. For more information please visit the project webpage:
Universality in Disordered Quantum Systems
My research group studies universal phenomena in disordered quantum systems. For more information please visit the project webpage:
Research
Currently, I am working on the following topics:
Local laws and spectral universality for a wide class of random matrices.
Spectral properties of non-Hermitian random matrix models.
Applications of random matrices in physics, neural networks, communication theory and statistics.
Operator-valued free probability
Fluctuations in specific zero sum games.
Connection between random matrices and random Schrödinger operators in the weak coupling regime.
Dyson-Brownian motion
Supersymmetric methods in random matrix theory and other disordered systems
Quantum diffusion
Quantum transport and conductance in disordered media
Randomly coupled differential equations / dynamic evolution on correlated networks
Teaching
Summer Term 2024
Wahrscheinlichkeitstheorie (Probability Theory)
Seminar: Markov-Ketten (Markov-Chains)
Winter Term 2023/24
Stochastic Models for Integrated Life Science
Stochastische Modellbildung (Stochastic Modelling)
Stochastic Analysis
Seminar in Probability for Bachelor
Summer Term 2023
Wahrscheinlichkeitstheorie (Probability Theory)
Winter Term 2022/23
Stochastic Models for Integrated Life Science
Stochastische Modellbildung (Stochastic Modelling)
Summer Term 2022
Wahrscheinlichkeitstheorie (Probability Theory)
Seminar: Spin Glasses with Applications to Deep Learning
Winter Term 2021/22
Wahrscheinlichkeitstheorie (Probability Theory)
Mathematical Analysis and Probability for Computer Scientists
Winter Term 2020/21
Mathematical Analysis and Probability for Computer Scientists
Summer Term 2019
Graduate Seminar: Supersymmetry in Probability
Heidelberg Graduate Days 2019: Random Matrices: Universality in Disordered Quantum Systems
Winter Term 2018/19
Graduate Seminar: Random Matrices, Spin Glasses and Deep Learning
Summer Term 2018
Graduate Seminar: Universality Phenomena in Dyson Brownian Motion
Short Lectures
Publications and preprints
with J. Alt
preprint, arXiv:2404.17573, 2024
with Jacob Fronk and Yuriy Nemish
preprint, arXiv:2308.16778, 2023
with Seung-Yeop Lee and Meng Yang
preprint, arXiv:2306.12263, 2023
with Yuriy Nemish
preprint, arXiv:2303.17020, 2023
with D. Renfrew
preprint, arXiv:2108.08811, 2021
with J. Alt
Bernoulli, 28(2): 886-909, 2022
with J. Alt
J. Funct. Anal., 281(7):109120, 2021
with L. Erdős and Yu. Nemish
Ann. Henri Poincaré, Vol. 22, 4205-4269, 2021
with L. Erdős and D. Renfrew
to appear in Ann. Appl. Probab., 2019
with J. Alt and L. Erdős
Prob. Math. Phys., Vol. 2, No. 2, 2019
with G. Cipolloni, L. Erdős and D. Schröder
Pure Appl. Anal., 1(4):615–707, 2019
with L. Erdős and D. Schröder
Commun. Math. Phys., 378:1203–1278, 2020
with L. Erdős and Yu. Nemish
J. Funct. Anal., 278(12):108507, 2020
with J. Alt and L. Erdős
Doc. Math. 25:1421-1539, 2020
with J. Alt, L. Erdős and D. Schröder
Ann. Probab., 48(2):963–1001, 2020
with L. Erdős and D. Renfrew
SIAM Journal on Mathematical Analysis, 50(3):3271–3290, 2018
with J. Alt, L. Erdős and Y. Nemish
Ann. Inst. Henri Poincaré Probab. Stat., 55(2):661–696, 2019
with L. Erdős and D. Schröder
Forum of Mathematics, Sigma, 7:e8, 2019
with J. Alt and L. Erdős
Ann. Appl. Probab., Vol. 28, No. 1, 148-203, 2016
with J. Alt and L. Erdős
Electron. J. Probab. 22, no. 25, 41 pp., 2017
O. Ajanki and L. Erdős
Probab. Theory Related Fields, 173(1):293–373, 2019
with O. Ajanki and L. Erdős
J. Stat. Phys., 163(2):280–302, 2016
with O. Ajanki and L. Erdős
Comm. Pure Appl. Math., 70(9):1672–1705, 2017
with O. Ajanki and L. Erdős
Probab. Theory Related Fields, 169(3):667-727, 2017
with O. Ajanki and L. Erdős
to appear in Mem. Amer. Math. Soc., 2015
with J. Knebel, M. F. Weber and E. Frey
Nat Comms 6:6977, 2015
with O. Ajanki and L. Erdős
Electron. Commun. Probab. 19, no. 33, 1–9, 2014
with J. Knebel, M. F. Weber and E. Frey
Phys Rev Lett, vol. 110 (16) pp. 168106-5, 2013
My papers on arXiv.
Brief Curriculum Vitae:
Employment
2021-present Professor at FAU Erlangen-Nürnberg
2020-2023 Associate Professor at University of Copenhagen
2017 - 2020 Postdoctoral researcher at University of Bonn
2015 - 2017 Postdoctoral researcher at IST Austria
2014 - 2015 Research assistant at IST Austria
2012 - 2014 Research assistant at Ludwig-Maximilians-University Munich (LMU)
Education
2015 Ph.D. in mathematics at LMU Munich
2013 Diploma in physics at LMU Munich
2012 Diploma in mathematics at LMU Munich
Teaching before 2022
2021 Mathematical Analysis and Probability for Computer Scientists at Copenhagen University
2020 Mathematical Analysis and Probability for Computer Scientists at Copenhagen University
2019 Graduate seminar on Supersymmetry at HCM Bonn
2019 Lecture series at Heidelberg Graduate Days
2018 - 2019 Graduate seminar on Random Matrices, Spin Glasses and Deep Learning at HCM Bonn
2018 Graduate seminar on Dyson Brownian motion at HCM Bonn
2017 Teaching assistant at PCMI 2017
2014 - 2016 Teaching assistant for lectures at IST Austria, including 'Random Matrices' and 'Random Schrödinger Operators'
2009 - 2011 Crash courses in 'Stochastics' and 'Probability Theory' at LMU Munich
2008 - 2013 Teaching assistant for various lectures at LMU Munich, including 'Stochastic Processes', 'Probability Theory', 'Mathematical Quantum Mechanics' and 'Functional Analysis'
Selected Invited Talks
2024 Non-commutative Function Theory and Free Probability (Oberwolfach, Germany)
2023 One world IMPA seminar (Online)
2023 Workshop of Young Researchers in Mathematical Physics (Feldkirchen-Westerham, Germany)
2023 Rhein-Main Probability Kolloquium (Mainz, Germany)
2021 Holomorphic Day (Copenhagen, Denmark)
2020 RMTA-2020 (New York, USA)
2019 QMath14 (Aarhus, Denmark)
2018 Vilnius IMS-2018 (Vilnius, Lithuania)
2018 Sums & Products of Random Matrices (Bielefeld, Germany)
2017 PCMI (Park-City, USA)
2017 QMath Kick-off (Copenhagen, Denmark)
2016 Methods of Modern Mathematical Physics (Toronto, Canada)
2015 ICMP (Santiago, Chile)
2015 Think & Drink talk at IST Austria (Klosterneuburg, Austria)
2014 SFB TR12 Workshop (Bad Honnef, Germany)
Honors & Awards
2021 NNF project grant (2.7 Mio. DKK)
2020 Villum Young Investigator Award (9.3 Mio. DKK)
2017 Carathéodory dissertation prize at LMU Munich
2006 Student scholarship German National Academic Foundation
Thesis
2015 Local spectral universality for random matrices with independent entries (PhD Thesis)
2012 Formulierung der Theorie des zweitquantisierten elektromagnetischen Feldes im Schrödingerbild (The external current problem for the second quantized electromagnetic field in the Schrödinger picture) (Physics Diploma Thesis)
2011 Konstruktion der unitären Dynamik eines Photonenfeldes in L2-Räumen über Distributionen (Construction of unitary dynamics for the photon field in L2-spaces on distributions) (Mathematics Diploma Thesis)
--- Last updated on January 01, 2023 ---