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
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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:
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"
https://www.youtube.com/watch?v=w2ZKPSjzhkY
Publications
Selection of publications
- A Metric Fixed Point Theorem and Some of Its Applications (2024)
- Deep Limits and a Cut-Off Phenomenon for Neural Networks (2022)
- From linear to metric functional analysis (2021)
- Subadditive and multiplicative ergodic theorems (2020)
- Spectral Zeta Functions Of Graphs And The Riemann Zeta Function In The Critical Strip (2017)
Recent publications
- Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces (2024)
- The Parametrix Construction of the Heat Kernel on a Graph (2024)
- The resolvent kernel on the discrete circle and twisted cosecant sums (2024)
- A Metric Fixed Point Theorem and Some of Its Applications (2024)
- Complex Variables Functions (2024)
All publications
Articles
- Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces (2024)
- The Parametrix Construction of the Heat Kernel on a Graph (2024)
- The resolvent kernel on the discrete circle and twisted cosecant sums (2024)
- A Metric Fixed Point Theorem and Some of Its Applications (2024)
- Complex Variables Functions (2024)
- Volumes of spheres and special values of zeta functions of Z and Z/nZ (2023)
- Deep Limits and a Cut-Off Phenomenon for Neural Networks (2022)
- Comments on the cosmic convergence of nonexpansive maps (2021)
- Hahn-Banach for metric functionals and horofunctions (2021)
- From linear to metric functional analysis (2021)
- A natural graph of finite fields distinguishing between models (2021)
- Subadditive and multiplicative ergodic theorems (2020)
- Spectral Zeta Functions Of Graphs And The Riemann Zeta Function In The Critical Strip (2017)