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

Download contact information for Anders Karlsson at Department of Mathematics; Dynamical Systems and Number Theory

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

"Connections between spectral zeta functions of graphs and spaces" - a lecture held at the Summer School: Analysis, Arithmetics and Geometry: Zeta-Functions, Trace Formulas, and Around. Institut Mittag-Leffler, 2023. NOTE: the recorded lectures can be found at the bottom of the page via this link.

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"

https://www.youtube.com/watch?v=w2ZKPSjzhkY

Publications

Selection of publications

A Metric Fixed Point Theorem and Some of Its Applications

Karlsson, Anders

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

Avelin, Benny; Karlsson, Anders

Part of Journal of machine learning research, 2022
- Download full text (pdf) of Deep Limits and a Cut-Off Phenomenon for Neural Networks
From linear to metric functional analysis

Karlsson, Anders

Part of Proceedings of the National Academy of Sciences of the United States of America, 2021
- DOI for From linear to metric functional analysis
Subadditive and multiplicative ergodic theorems

Gouezel, Sebastien; Karlsson, Anders

Part of Journal of the European Mathematical Society (Print), p. 1893-1915, 2020
- DOI for Subadditive and multiplicative ergodic theorems
Spectral Zeta Functions Of Graphs And The Riemann Zeta Function In The Critical Strip

Friedli, Fabien; Karlsson, Anders

Part of Tohoku mathematical journal, p. 585-610, 2017
- DOI for Spectral Zeta Functions Of Graphs And The Riemann Zeta Function In The Critical Strip

Recent publications

All publications

Articles in journal

Chapters in book

Elements of a metric spectral theory

Karlsson, Anders

Part of Dynamics, Geometry and Number Theory, p. 276-300, University of Chicago Press, 2022
- DOI for Elements of a metric spectral theory
Spectral zeta functions

Karlsson, Anders

Part of Discrete and Continuous Models in the Theory of Networks, p. 199-211, Birkhäuser, 2020
- DOI for Spectral zeta functions
- Download full text (pdf) of Spectral zeta functions

Conference papers

Generalized Lyapunov exponents and aspects of the theory of deep learning

Karlsson, Anders

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

Karlsson, Anders

Part of Groups, Graphs and Random Walks, p. 343-354, 2017
- DOI for A Proof of the Subadditive Ergodic Theorem