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Mathematics

D-Index
31
Citations
3101
World Ranking
3393
National Ranking
22

Overview

Marian Mrozek is an academic affiliated with Jagiellonian University in Poland. The researcher has contributed extensively to the fields of Computer Science and Mathematics, with a particular focus on Computational Theory and Mathematics, Mathematical Physics, Spectroscopy, Statistical and Nonlinear Physics, and Discrete Mathematics and Combinatorics.

The research topics covered by Marian Mrozek include:

  • Topological and Geometric Data Analysis
  • Homotopy and Cohomology in Algebraic Topology
  • Mathematical Dynamics and Fractals
  • Molecular spectroscopy and chirality
  • Quantum chaos and dynamical systems
  • Advanced Combinatorial Mathematics
  • Numerical methods for differential equations

A selection of recent papers authored or co-authored by Marian Mrozek demonstrates involvement in the development of mathematical and computational tools:

  • "CAPD::DynSys: A flexible C++ toolbox for rigorous numerical analysis of dynamical systems" (2020), published in Communications in Nonlinear Science and Numerical Simulation
  • "Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces" (2022), published in Journal of Applied and Computational Topology
  • "Creating Semiflows on Simplicial Complexes from Combinatorial Vector Fields" (2020), published on arXiv (Cornell University)
  • "Computing Connection Matrices via Persistence-Like Reductions" (2024), published in SIAM Journal on Applied Dynamical Systems
  • "Conley Index for Multivalued Maps on Finite Topological Spaces" (2024), published in Foundations of Computational Mathematics

Frequent co-authors in the researcher's collaborations include Thomas Wanner, Michał Lipiński, Tamal K. Dey, Ryan Slechta, and Mateusz Przybylski.

The publication venues where Marian Mrozek has frequently published consist of:

  • arXiv (Cornell University)
  • SIAM Journal on Applied Dynamical Systems
  • Communications in Nonlinear Science and Numerical Simulation
  • Journal of Applied and Computational Topology
  • Leibniz-Zentrum für Informatik (Schloss Dagstuhl)

In addition to research articles, Marian Mrozek has authored a book titled Connection Matrices in Combinatorial Topological Dynamics, which is expected to be published by Springer International Publishing in 2025.

Best Publications

  • Chaos in the Lorenz equations: a computer-assisted proof

    Konstantin Mischaikow;Marian Mrozek

  • Construction of symbolic dynamics from experimental time series

    K. Mischaikow;M. Mrozek;J. Reiss;A. Szymczak

  • Leray functor and cohomological Conley index for discrete dynamical systems

    Marian Mrozek

  • Homology computation by reduction of chain complexes

    T. Kaczyński;M. Mrozek;M. Ślusarek

  • Chaos in the Lorenz equators: a computer assisted proof. part II: details

    Konstantin Mischaikow;Marian Mrozek;Marian Mrozek

  • Isolating Neighborhoods and Chaos

    Konstantin Mischaikow;Marian Mrozek

  • Chapter 9 – Conley Index

    Konstantin Mischaikow;Marian Mrozek

  • Coreduction Homology Algorithm

    Marian Mrozek;Bogdan Batko

  • Conley index for discrete multi-valued dynamical systems

    T. Kaczynski;M. Mrozek

  • Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps

    Shaun Harker;Konstantin Mischaikow;Marian Mrozek;Vidit Nanda

  • Chaos in the Lorenz Equations: A Computer Assisted Proof Part III: Classical Parameter Values

    Konstantin Mischaikow;Marian Mrozek;Andrzej Szymczak

  • Homology algorithm based on acyclic subspace

    Marian Mrozek;Paweł Pilarczyk;Natalia Żelazna

  • CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems

    Tomasz Kapela;Marian Mrozek;Daniel Wilczak;Piotr Zgliczyński

  • Graph Approach to the Computation of the Homology of Continuous Maps

    Konstantin Mischaikow;Marian Mrozek;Pawel Pilarczyk

  • Distributed computation of coverage in sensor networks by homological methods

    P. Dłotko;R. Ghrist;M. Juda;M. Mrozek

  • Topological invariants, mulitvalued maps and computer assisted proofs in dynamics

    M. Mrozek;M. Mrozek

  • Zeta functions, periodic trajectories, and the conley index

    Christopher McCord;Konstantin Mischaikow;Marian Mrozek;Marian Mrozek

  • Coreduction homology algorithm for inclusions and persistent homology

    Marian Mrozek;Thomas Wanner

  • Shape index and other indices of Conley type for local maps on locally compact Hausdorff spaces

    Marian Mrozek

  • The Persistent Homology of a Self-Map

    Herbert Edelsbrunner;Grzegorz Jabłoński;Marian Mrozek

  • Set arithmetic and the enclosing problem in dynamics

    Marian Mrozek;Piotr Zgliczyński

Frequent Co-Authors

Konstantin Mischaikow
Konstantin Mischaikow Rutgers, The State University of New Jersey
Tamal K. Dey
Tamal K. Dey Purdue University West Lafayette
Herbert Edelsbrunner
Herbert Edelsbrunner Institute of Science and Technology Austria
Robert Ghrist
Robert Ghrist University of Pennsylvania

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