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Mathematics

D-Index
39
Citations
7382
World Ranking
2165
National Ranking
61

Overview

Andrei A. Agrachev is affiliated with the International School for Advanced Studies in Italy. Their research primarily spans the fields of Mathematics and Physics and Astronomy, with notable contributions to Applied Mathematics, Statistical and Nonlinear Physics, Computational Theory and Mathematics, Control and Systems Engineering, and Geometry and Topology.

Their main topics of work include:

  • Geometric Analysis and Curvature Flows
  • Advanced Differential Equations and Dynamical Systems
  • Model Reduction and Neural Networks
  • Nonlinear Partial Differential Equations
  • Quantum chaos and dynamical systems
  • Advanced Neuroimaging Techniques and Applications
  • Topological and Geometric Data Analysis

Andrei Agrachev has published in various prominent venues. Frequent publication venues include:

  • arXiv (Cornell University)
  • Journal of Dynamical and Control Systems
  • Nonlinearity
  • Florence Research (University of Florence)
  • Nonlinear Analysis

A selection of recent papers illustrates the range and focus of their work:

  • "Control on the Manifolds of Mappings with a View to the Deep Learning", 2021, Florence Research (University of Florence)
  • "Control on the Manifolds of Mappings with a View to the Deep Learning", 2021, Journal of Dynamical and Control Systems
  • "Jacobi fields in optimal control: Morse and Maslov indices", 2021, Nonlinear Analysis
  • "Jacobi Fields in Optimal Control: One-dimensional Variations", 2020, Journal of Dynamical and Control Systems
  • "Index theorems for graph-parametrized optimal control problems", 2023, Nonlinearity

Their frequent co-authors include:

  • Ivan Beschastnyi
  • Bettina Kazandjian
  • Andrey Sarychev
  • Stefano Baranzini
  • Luca Rizzi

Best Publications

  • Control Theory from the Geometric Viewpoint

    Andrei A. Agrachev;Yuri L. Sachkov

  • Lie-Algebraic Stability Criteria for Switched Systems

    Andrei A. Agrachev;Daniel Liberzon

  • Introduction to Riemannian and Sub-Riemannian geometry

    Andrei A. Agrachev;Davide Barilari;Ugo Boscain

  • Abnormal sub-riemannian geodesics : Morse index and rigidity

    A.A. Agrachev;A.V. Sarychev

  • The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups

    Andrei A. Agrachev;Ugo Boscain;Jean-Paul Gauthier;Francesco Rossi

  • Strong Optimality for a Bang-Bang Trajectory

    Andrei A. Agrachev;Gianna Stefani;PierLuigi Zezza

  • A Comprehensive Introduction to Sub-Riemannian Geometry

    Andrei Agrachev;Davide Barilari;Ugo Boscain

  • A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds

    Andrei A. Agrachev;Ugo Boscain;Mario Sigalotti

  • Nonlinear and Optimal Control Theory

    Andrei A. Agrachev;A. Stephen Morse;Eduardo D. Sontag;Héctor J. Sussmann

  • Sub-riemannian sphere in Martinet flat case

    A. Agrachev;Bernard Bonnard;Monique Chyba;I. Kupka

  • Exponential mappings for contact sub-Riemannian structures

    A. A. Agrachev

  • Chronological algebras and nonstationary vector fields

    A. A. Agrachev;R. V. Gamkrelidze

  • Sub-Riemannian structures on 3D lie groups

    A. Agrachev;D. Barilari

  • Local Invariants of Smooth Control Systems

    A. A. Agrachev;R. V. Gamkrelidze;A. V. Sarychev

  • Feedback-invariant optimal control theory and differential geometry - I. Regular extremals

    A. A. Agrachev;R. V. Gamkrelidze

  • Geometry of Jacobi Curves. I

    A. A. Agrachev;I. Zelenko

  • Some open problems

    Andrei A. Agrachev

  • ON THE SUBANALYTICITY OF CARNOT-CARATHEODORY DISTANCES

    Andrei A. Agrachev;Jean-Paul Gauthier

  • Symplectic Geometry for Optimal Control

    A. A. Agrachev;R. V. Gamkrelidze

  • On the Hausdorff volume in sub-Riemannian geometry

    Andrei A. Agrachev;Davide Barilari;Ugo Boscain

  • Optimal transportation under nonholonomic constraints

    Andrei A. Agrachev;Paul Lee

  • Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds

    Andrei Agrachev;Andrei Agrachev;Paul W. Y. Lee

  • Any sub-Riemannian metric has points of smoothness

    Andrei Agrachev;Andrei Agrachev

Frequent Co-Authors

Ugo Boscain
Ugo Boscain Sorbonne University
Daniel Liberzon
Daniel Liberzon University of Illinois at Urbana-Champaign
A. Stephen Morse
A. Stephen Morse Yale University
Eduardo D. Sontag
Eduardo D. Sontag Northeastern University
Yakov G. Sinai
Yakov G. Sinai Princeton University
Héctor J. Sussmann
Héctor J. Sussmann Rutgers, The State University of New Jersey

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