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Mathematics

D-Index
32
Citations
4711
World Ranking
3175
National Ranking
1271

Research.com Recognitions

  • 2013 - Fellow of the American Mathematical Society
  • 2000 - Fellow of the American Association for the Advancement of Science (AAAS)

Overview

Michel L. Lapidus is affiliated with the University of California, Riverside in the United States. Their research spans multiple disciplines, primarily focusing on mathematics, physics and astronomy, and computer science. Their subfields include mathematical physics, statistical and nonlinear physics, computational theory and mathematics, condensed matter physics, and computer vision and pattern recognition.

Lapidus's scholarly contributions cover significant topics such as mathematical dynamics and fractals, advanced mathematical theories and applications, topological and geometric data analysis, theoretical and computational physics, advanced mathematical theories, chaos-based image and signal encryption, and stochastic processes and statistical mechanics.

Their recent papers include:

  • Weierstrass fractal drums: II towards a fractal cohomology (2024), published in Mathematische Zeitschrift
  • Minkowski Measurability Criteria for Compact Sets and Relative Fractal Drums in Euclidean Spaces (2020), published in Fractals and dynamics in mathematics, science and the arts
  • p-Adic Fractal Strings of Arbitrary Rational Dimensions and Cantor Strings (2021), published in P-Adic Numbers Ultrametric Analysis and Applications
  • Polyhedral neighborhoods vs. tubular neighborhoods: new insights for fractal zeta functions and complex dimensions (2025), published in The Ramanujan Journal
  • Understanding Fractality: A Polyhedral Approach to the Koch Curve and Its Complex Dimensions (2025), published in Asymptotic Analysis

Frequent coauthors collaborating with Lapidus include:

  • Claire David
  • Machiel van Frankenhuijsen
  • Edward K. Voskanian
  • Goran Radunović
  • Therese-Marie Landry

Lapidus's work appears often in publication venues such as arXiv (Cornell University), Asymptotic Analysis, Advances in Mathematics, Mathematische Zeitschrift, and P-Adic Numbers Ultrametric Analysis and Applications.

In addition to articles, Lapidus has authored books, with at least one published by the American Mathematical Society titled An Invitation to Fractal Geometry (2024).

The academic has been recognized with honors including being named a Fellow of the American Mathematical Society in 2013 and a Fellow of the American Association for the Advancement of Science (AAAS) in 2000.

Best Publications

  • The Feynman Integral and Feynman's Operational Calculus

    Gerald W. Johnson;Michel L. Lapidus

  • Weyl's problem for the spectral distribution of Laplacians on p.c.f. self-similar fractals

    Jun Kigami;Michel L. Lapidus

  • Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings

    Michel L. Lapidus;Machiel van Frankenhuijsen

  • Fractal drum, inverse spectral problems for elliptic operators and a partial resolution of the Weyl-Berry conjecture

    Michel L. Lapidus

  • The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums

    Michel L. Lapidus;Carl Pomerance

  • Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions

    Michel L. Lapidus;Machiel van Frankenhuysen

  • Fractal Geometry, Complex Dimensions and Zeta Functions

    Michel L. Lapidus;Machiel van Frankenhuijsen

  • The Riemann Hypothesis and Inverse Spectral Problems for Fractal Strings

    Michel L. Lapidus;Helmut Maier

  • Riemann zeros and phase transitions via the spectral operator on fractal strings

    Hafedh Herichi;Michel L Lapidus

  • Generalized Minkowski Content, Spectrum of Fractal Drums, Fractal Strings and the Riemann-Zeta-Function

    Christina Q. He;Michel L. Lapidus

  • Fractal Geometry and Number Theory

    Michel L. Lapidus;Machiel van Frankenhuysen

  • Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot

    Michel Lapidus;Machiel van Frankenhuijsen

  • Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman’s operational calculus

    Gerald W. Johnson;Michel L. Lapidus

  • Counterexamples to the modified Weyl-Berry conjecture on fractal drums

    Michel L. Lapidus;Carl Pomerance

  • Dirac operators and spectral triples for some fractal sets built on curves

    Erik Christensen;Cristina Ivan;Michel L. Lapidus

  • Fractal Zeta Functions and Fractal Drums

    Michel L. Lapidus;Goran Radunović;Darko Žubrinić

  • In Search of the Riemann Zeros

    Michel L. Lapidus

  • Spectral and Fractal Geometry: From the Weyl-Berry Conjecture for the Vibrations of Fractal Drums to the Riemann Zeta-Function

    Michel L. Lapidus

  • Snowflake Harmonics and Computer Graphics: Numerical Computation of Spectra on Fractal Drums

    Michel L. Lapidus;J.W. Neuberger;Robert J. Renka;Cheryl A. Griffith

  • Fractal Drum, Inverse Spectral Problems for Elliptic Operators and a Partial Resolution of the Weyl-Berry Conjecture

    Unknown

  • Self-Similarity of Volume Measures for Laplacians on P. C. F. Self-Similar Fractals

    Jun Kigami;Michel L. Lapidus

  • Eigenvalues of Elliptic Boundary Value Problems with an Indefinite Weight Function

    Jacqueline Fleckinger;Michel L. Lapidus

  • Dynamical, Spectral, and Arithmetic Zeta Functions

    Michel L. Lapidus;Machiel van Frankenhuysen

  • Riemann Zeroes and Phase Transitions via the Spectral Operator on Fractal Strings

    Hafedh Herichi;Michel L. Lapidus

Frequent Co-Authors

Carl Pomerance
Carl Pomerance Dartmouth College
Benoit B. Mandelbrot
Benoit B. Mandelbrot Yale University
Ben Hambly
Ben Hambly University of Oxford

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