RESEARCH · TEACHING · COLLABORATION

Karim
Rakhimov.

Complex dynamics and pluripotential theory.

Leading Researcher at the Institute of Mathematics. Associate Professor at the National University of Uzbekistan.

Tashkent, Uzbekistan · PhD, DSc

Karim Rakhimov at the National University of Singapore, 2023
National University of Singapore · 2023
Present

Institute of Mathematics

2023–2024

National University of Singapore

2020–2022

CNRS · University of Lille

PhD · 2020

University of Pisa

ACADEMIC JOURNEY

A life in mathematics.

My research lies in complex dynamical systems, pluripotential theory and complex geometry. I study the dynamics of holomorphic maps, Green currents and the properties of invariant measures.

I obtained my PhD at the University of Pisa in 2020 under the supervision of Professor Marco Abate. I subsequently held research positions at CNRS / the University of Lille and the National University of Singapore. I now work in Tashkent, combining research, teaching and the mentoring of young mathematicians.

RESEARCH AREAS

Questions that guide my work.

At the intersection of complex analysis, dynamics and geometry.

01

Holomorphic dynamics

Hénon-like and polynomial-like maps, dynamical degrees, Green currents and measures of large entropy.

02

Pluripotential theory

Plurisubharmonic functions, capacities, Hölder continuity of extremal functions and the metric properties of Brjuno sets.

03

Complex geometry

Meromorphic connections on Riemann surfaces, flat structures and the long-term dynamics of geodesics.

SELECTED PUBLICATIONS

Recent research.

All publications ↗
2026

Hölder continuity and laminarity of the Green currents for Hénon-like maps

Fabrizio Bianchi · Tien-Cuong Dinh · Karim Rakhimov

Journal of the Institute of Mathematics of Jussieu 25(2), 1363–1392 (2026)

2026

Capacity Dimension of the Brjuno Set in ℂⁿ

Nurali Akramov · Karim Rakhimov

Complex Analysis and Operator Theory 20(5), Article 120 (2026)

2026

Dynamics of Fuchsian meromorphic connections with real periods

Marco Abate · Karim Rakhimov

Annals of Global Analysis and Geometry 69, Article 9 (2026)

TEACHING & COMMUNITY

Sharing knowledge.
Developing ideas.

Through university mathematics, research seminars and olympiad problems, I support young mathematicians in developing independent mathematical thinking.

IsbotBooks, exercises and tests for independent study in mathematics.
01

Sadullaev Seminar

Modern Problems of Complex Analysis. Research talks and mathematical discussions.

02

Complex Dynamics and Geometry

A research seminar in complex dynamical systems and complex geometry.

03

Olympiads and advanced courses

The π Olympiad, Mirzo Ulug‘bek Competition and “Maxsus kurslar” programme for young researchers.

GET IN TOUCH

Let’s talk mathematics.

For research collaborations, seminar invitations or questions about mathematical education, please get in touch.