Visiting Speaker to the UK - June 3 to June 14 2024

LECTURES on the invariant subspace problem in Hilbert spaces:

London, Wednesday, June 5: Seminar at UCL at 3:00 p.m. (LG17 in Bentham House) >>

Oxford, Thursday, June 6: Seminar at Oxford at 4:30 p.m. (C2 in the Andrew Wiles Building) >>

Reading, Tuesday, June 11: Piano recital at 4:00 p.m. in London Road Campus (L29 GO1)

       Wednesday, June 12: Seminar at Reading at 12 noon (Mathematics Building) >>


Copenhagen, Department of Mathematical Sciences, University of Copenhagen

Special Analysis Lecture Wednesday, April 17>>

Piano Recital, Thursday, April>>

Valencia, Departamento de Análisis Matemático, Universidad de Valencia

WORKSHOP ON FUNCTIONAL ANALYSIS, November 16th 2023 >> YouTube >>

Lund, Centre for Mathematical Sciences, Lund University

Colloquium, September 13th 2023 >>

Helsinki, IWOTA 2023 July 31 - August 4, 2023, 34th International Workshop on Operator Theory and its Applications, University of Helsinki >>

Semi-plenary session Tuesday August 1st
Concert Thursday August 3rd at the Conference Dinner 

Online: click here >> arXiv:2305.15442 [pdf,ps,other]

[Submitted on 24 May 2023 (v1), last revised 6 Apr 2024 (this version, v2)]

Proceedings of Symposia in Pure Mathematics >>

Volume:106;2024; 346 pp

MSC:Primary 43; 46; 47

This book provides a comprehensive presentation of recent approaches to and results about properties of various classes of functional spaces, such as Banach spaces, uniformly convex spaces, function spaces, and Banach algebras. Each of the 12 articles in this book gives a broad overview of current subjects and presents open problems. Each article includes an extensive bibliography.

This book is dedicated to Professor Per. H. Enflo, who made significant contributions to functional analysis and operator theory.

A Few Lines on Per Enflo’s Works
Gilles Godefroy, Mohammad Sal Moslehian, and Juan Benigno Seoane-Sepúlveda
Abstract. A brief historical overview of the notable mathematical contributions of Per Enflo is presented.


Graduate students and researchers interested in functional analysis and operator theory.

A history of solving some famous problems in mathematical analysis

This paper provides a historical view of what functional analysis is, a biography of Per H. Enflo and a short view of four fundamental problems in the geometry of Banach spaces.

It gives the story of how Enflo, after several years of work, managed to solve three of these problems. It is a story of trying many ideas, testing them on simpler problems, trying to combine different techniques for handling different aspects of the problems, making many failed attempts and finally succeeding.

In 1966 Enflo found a general strategy for solving many problems in infinite dimensions, by combining appropriate finite-dimensional techniques with induction procedures. When applied to the old, fundamental problems in functional analysis, this has led to new concepts, problems, techniques and results in analysis. These developments have been applied also in several other areas of mathematics and computer science.

Department of Mathematical Sciences, Kent State University, Kent, OH, USA and
Instituto de Matemática Interdisciplinar, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Spain

Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad, Iran
Instituto de Matemática Interdisciplinar (IMI), Facultad de Ciencias Matemáticas, Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, Madrid, Spain

Invariant Subspace Problem in Hilbert Spaces:

Exploring Applications in Quantum Mechanics, Control Theory, Operator Algebras, Functional Analysis and Accelerator Physics - Mostafa Behtouei arXiv:2306.17023

"Per H. Enflo’s recent claim of solving the invariant subspace problem in his recent publication titled ”On the invariant subspace problem in Hilbert spaces.” [4] has generated excitement and anticipation in the mathematical community, as his work could represent a major breakthrough in the field. Enflo’s solution, if validated,would be a groundbreaking achievement in mathematics, resolving a longstanding problem and advancing our understanding of bounded linear operators on Hilbert spaces. Its impact would be significant and far-reaching." From: Mostafa Behtouei, 29 Jun 2023

Interdisciplinary Mathematics Institute (IMI)

25 de mayo de 2023.Boletín del IMI.

A potential definitive answer to the invariant subspace problem in Hilbert spaces. Prof. Per H. Enflo (Kent State University, USA) has just announced via his collaborators from the Interdisciplinary Mathematics Institute (IMI) that he might have just potentially solved the long standing Invariant Subspace Problem in Hilbert Spaces

When did you make the decision to go into math instead of music?

I have never made, and will never make, any such decision

Craiova, Romania, the 20 th October 2023

"Invited to participate as a soloist in the Concert no. 1 in C major for piano and orchestra, op. 15 of Ludwig van Beethvoven was Per Enflo.

A Swede settled in the United States, this respectable gentleman is not only a pianist so good that he has touched all the meridians of the world with his art, but also a renowned mathematician.

Yes, mathematician.

Two fields that seem so far apart, but which, at the highest level, approach asymptotically. Let us think only of Pythagoras and the sacred importance he attached to music.

Per Enflo has not only a remarkable destiny, but also a long-lasting one, which I wish twice as long.

At 80, he still has the energy to let himself be swept up in the gaiety of Beethoven's composition with the enthusiasm of a toddler (until his piece began, he seemed to be struggling to resist the temptation to touch the keyboard).


What is the secret of such a zest for life at such an advanced age?

But perhaps that is not the question, but the answer.

With his lordship's permission, I will also draw a parallel between the way he crossed his hands on the piano keys and the way of multiplying the means and extremes of a proportion.

Photos by my friend Daniel Botea, who, although he is incredibly old, enjoyed the same as me, like a child that is, all the wonders that the concert offered.

Autor: Iris Gottlieb (sursa – www.vox.com)

Google translation from original Romanian, Facebook:


  • "Mathematics and Music - What is the connection?"
    Lecture >> 31 August 2021, Science Festival Strömstad Academy Slides >
  • Beethoven last piano sonata Concert >> Strömstad Academy's Scientific Festival 2021

  • Mozart - Beethoven - Chopin Concert >>  Jubilee Congress of Polish Mathematicians on the 100th Anniversary of Polish Mathematical Society (2019, Krakow)

  • "An infinite-dimensional version of Hilbert's fifth problem with connections to non-linear geometry of Banach spaces"

    Lecture December 2021  Slides >> to Holiday Lecture by Per Enflo  via Zoom - Jani Virtanen (Reading and Helsinki) & Håkan Hedenmalm (KTH and Reading) 

Mathematics >>     Music >>     Interviews & Reviews >>

Per Enflo - mathematician and pianist - was the last laureate of a prize

for solving a scientific problem from the Scottish Book.

Updated June 1, 2024 www.perenflo.com © 2011

Contact  +46(0)721-808 870       per.enflo at gmail.com       www.perenflo.com © 2011