Anders Karlsson
Professor at Department of Mathematics; Academic staff
- Telephone:
- +46 18 471 32 26
- E-mail:
- anders.karlsson@math.uu.se
- Visiting address:
- Ångströmlaboratoriet, Lägerhyddsvägen 1
- Postal address:
- Box 480
751 06 UPPSALA
Download contact information for Anders Karlsson at Department of Mathematics; Academic staff
Professor at Department of Mathematics; Dynamical Systems and Number Theory
- Telephone:
- +46 18 471 32 26
- E-mail:
- anders.karlsson@math.uu.se
- Visiting address:
- Ångströmlaboratoriet, Lägerhyddsvägen 1
- Postal address:
- Box 480
751 06 UPPSALA
Short presentation
My research interests belong to ergodic theory, metric geometry, heat kernels, spectral graph theory, analytic number theory, group theory, and their applications to other branches of mathematics and sciences, such as complex analysis, mathematical physics, and deep learning.
Biography
Born and raised in Haninge outside of Stockholm, Anders Karlsson studied Engineering Physics at KTH, 1991-1994 and was awarded a Honnörsstipendium and the Gunnar Wallquist studiemedalj upon graduation. With the generous support of the Göran Gustafsson Foundation, the Fulbright Commission, the Sweden-America Foundation, the Foundation Blanceflor, he could then start studies in mathematics at Yale University, eventually under the guidance of G.A. Margulis. Karlsson was awarded an Alfred P. Sloan Dissertation Fellowship in 1999 and received a Ph.D in mathematics from Yale in the year 2000.
After postdoctoral years at the ETH, Neuchâtel, Bielefeld, KTH, Yale, he became a research fellow of the Royal Swedish Academy of Sciences (KVA) based at KTH for a few years. In 2010 he started a position as Associate Professor at University of Geneva that he still holds, and he has been Professor at Uppsala University since 2013 (part-time). Karlsson received the Wallenberg Prize of the Swedish Mathematical Society in 2008, the Edlund Prize from KVA in 2015 and the Gårding Prize from The Royal Physiographic Society of Lund in 2017.
List of doctoral students advised or co-advised: math genealogy
Currently his research is supported by the VR and the Swiss NSF. He is a member of Nationalkommitten för matematik and the lead editor of the research journal L'Enseignement Mathématique.
Research
My papers and preprints are available here:
http://www.unige.ch/math/folks/karlsson/papers.html
Media
Geometry of deep learning and explainable ML
Workshop at SLMath (MSRI) program Algorithms, Fairness and Equity, Berkeley, 2023
https://player.vimeo.com/video/859592421
A fixed point theorem for isometries of metric spaces
Conference at ESI, Vienna 2023: "Geometry beyond Riemann: Curvature and Rigidity"

Publications
Selection of publications
A Metric Fixed Point Theorem and Some of Its Applications
Part of Geometric and Functional Analysis, p. 486-511, 2024
- DOI for A Metric Fixed Point Theorem and Some of Its Applications
- Download full text (pdf) of A Metric Fixed Point Theorem and Some of Its Applications
Deep Limits and a Cut-Off Phenomenon for Neural Networks
Part of Journal of machine learning research, 2022
From linear to metric functional analysis
Part of Proceedings of the National Academy of Sciences of the United States of America, 2021
Subadditive and multiplicative ergodic theorems
Part of Journal of the European Mathematical Society (Print), p. 1893-1915, 2020
Spectral Zeta Functions Of Graphs And The Riemann Zeta Function In The Critical Strip
Part of Tohoku mathematical journal, p. 585-610, 2017
Recent publications
The discrete analogue of the Gaussian
Part of Journal of Physics A, 2025
- DOI for The discrete analogue of the Gaussian
- Download full text (pdf) of The discrete analogue of the Gaussian
The Parametrix Construction of the Heat Kernel on a Graph
Part of Complex Analysis and Operator Theory, 2024
Complex Variables Functions: The stars at infinity in several complex variables
Part of Rendiconti Lincei - Matematica e Applicazioni, p. 49-75, 2024
- DOI for Complex Variables Functions: The stars at infinity in several complex variables
- Download full text (pdf) of Complex Variables Functions: The stars at infinity in several complex variables
The resolvent kernel on the discrete circle and twisted cosecant sums
Part of Journal of Mathematical Analysis and Applications, 2024
Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces
Part of Advances in Mathematics, 2024
- DOI for Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces
- Download full text (pdf) of Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces
All publications
Articles in journal
The discrete analogue of the Gaussian
Part of Journal of Physics A, 2025
- DOI for The discrete analogue of the Gaussian
- Download full text (pdf) of The discrete analogue of the Gaussian
The Parametrix Construction of the Heat Kernel on a Graph
Part of Complex Analysis and Operator Theory, 2024
Complex Variables Functions: The stars at infinity in several complex variables
Part of Rendiconti Lincei - Matematica e Applicazioni, p. 49-75, 2024
- DOI for Complex Variables Functions: The stars at infinity in several complex variables
- Download full text (pdf) of Complex Variables Functions: The stars at infinity in several complex variables
The resolvent kernel on the discrete circle and twisted cosecant sums
Part of Journal of Mathematical Analysis and Applications, 2024
Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces
Part of Advances in Mathematics, 2024
- DOI for Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces
- Download full text (pdf) of Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces
A Metric Fixed Point Theorem and Some of Its Applications
Part of Geometric and Functional Analysis, p. 486-511, 2024
- DOI for A Metric Fixed Point Theorem and Some of Its Applications
- Download full text (pdf) of A Metric Fixed Point Theorem and Some of Its Applications
Volumes of spheres and special values of zeta functions of Z and Z/nZ
Part of Acta Arithmetica, p. 161-170, 2023
Deep Limits and a Cut-Off Phenomenon for Neural Networks
Part of Journal of machine learning research, 2022
From linear to metric functional analysis
Part of Proceedings of the National Academy of Sciences of the United States of America, 2021
Comments on the cosmic convergence of nonexpansive maps
Part of Journal of Fixed Point Theory and Applications, 2021
- DOI for Comments on the cosmic convergence of nonexpansive maps
- Download full text (pdf) of Comments on the cosmic convergence of nonexpansive maps
Hahn-Banach for metric functionals and horofunctions
Part of Journal of Functional Analysis, 2021
- DOI for Hahn-Banach for metric functionals and horofunctions
- Download full text (pdf) of Hahn-Banach for metric functionals and horofunctions
A natural graph of finite fields distinguishing between models
Part of Finite Fields and Their Applications, 2021
- DOI for A natural graph of finite fields distinguishing between models
- Download full text (pdf) of A natural graph of finite fields distinguishing between models
Subadditive and multiplicative ergodic theorems
Part of Journal of the European Mathematical Society (Print), p. 1893-1915, 2020
Spectral Zeta Functions Of Graphs And The Riemann Zeta Function In The Critical Strip
Part of Tohoku mathematical journal, p. 585-610, 2017
Chapters in book
Elements of a metric spectral theory
Part of Dynamics, Geometry and Number Theory, p. 276-300, University of Chicago Press, 2022
Part of Discrete and Continuous Models in the Theory of Networks, p. 199-211, Birkhäuser, 2020
Conference papers
Generalized Lyapunov exponents and aspects of the theory of deep learning
Part of New Trends in Lyapunov Exponents, p. 99-118, 2023
- DOI for Generalized Lyapunov exponents and aspects of the theory of deep learning
- Download full text (pdf) of Generalized Lyapunov exponents and aspects of the theory of deep learning
A Proof of the Subadditive Ergodic Theorem
Part of Groups, Graphs and Random Walks, p. 343-354, 2017