Boletín Nº 91
Nº 91 (25 de mayo de 2023)
Boletín del IMI, Nº 91 (25 de mayo de 2023) https://doi.org/10.57037/b-imi.00091
This issue is full of interesting contents but I would like to highlight the news about the potential definitive answer to the invariant subspace problem in Hilbert spaces, which is made public here and which I encourage you to read, because of its relevance. I am very grateful to Prof. Enflo for making this news known through the Boletín del IMI and to Gustavo A. Muñoz Fernández and Juan B. Seoane Sepúlveda (IMI members), for writing it.
Many thanks to all three of you!
Ángel Manuel Ramos del Olmo
25 May 2023 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) at Universidad Complutense de Madrid (UCM) that he might have just potentially solved the long standing Invariant Subspace Problem in Hilbert Spaces (for more information on this problem see https://en.wikipedia.org/wiki/Invariant_subspace_problem).
Prof. Enflo (https://perenflo.com/),1500 originally from Sweden, became famous (among other scientific milestones) for solving several fundamental problems in functional analysis in the 1970’s and 1980’s, some of which were open for more than half a century (such as the basis problem, the approximation problem, or the invariant subspace problem for Banach spaces). His solutions to these problems led to new concepts, theories, problems, techniques and results in Mathematical Analysis. His developments have also been applied in several other areas of Mathematics, and in Computer Science, especially computer algebra and approximation algorithms. Per is also a renowned concert pianist and, currently, an active collaborator and coauthor of several IMI members.
Certainly, and although he is a world expert on Functional Analysis, Per himself is still cautious regarding his solution, since its correctness still needs to be checked by expert referees. However, he has been nice enough with the mathematical community as to share a first draft of his manuscript (that will appear soon in arXiv, as soon as the arXiv moderators process the files). IMI will keep you posted on this piece of news (Note: After the writing of this news item, the manuscript was made public online at https://arxiv.org/abs/2305.15442)
From the Interdisciplinary Mathematics Institute (IMI) at UCM we congratulate Per for his life achievements.
Gustavo A. Muñoz Fernández and Juan B. Seoane Sepúlveda
Interdisciplinary Mathematics Institute (IMI) at UCM
24 de mayo de 2023. TRECE TV - COPE. Entrevista en directo a Ángel Manuel Ramos en el programa de televisión "TRECE Al Mediodía", hablando sobre las Matemáticas a tener en cuenta en las elecciones.
Ver vídeo a partir de la hora:minuto:segundo 1:16:35
23 de mayo de 2023. La Nueva España. Oslo recibe a Luis Caffarelli para su esperado "Abel" de matemáticas, el "Nobel" de la especialidad. Arropado por sus colaboradores españoles, como el asturiano Juan Luis Vázquez, el catedrático argentino hará historia al recibir el galardón. El Prof. Juan Luis Vázquez, miembro del Instituto de Matemática Interdisciplinar (IMI), nos pone al día desde Oslo sobre este premio.
I. Flores, M. T. Ortuño, G. Tirado. A goal programming model for early evacuation of vulnerable people and relief distribution during a wildfire. Safety Science. 2023, 164. https://doi.org/10.1016/j.ssci.2023.106117
P. García-Segador, P. Miranda. On the Polytope of 3-Tolerant Fuzzy Measures. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. 2023, 31,1. https://doi.org/10.1142/S0218488523500058
|Puzzle sent by Kjartan Poskitt.
The solution will be provided in the next issue of Boletin del IMI.
The puzzle was: Two isosceles triangles are placed as shown. What is the proportion of the line segments a and b?
Like with so many geometry problems involving triangles, one should search for similar ones. In this case they can be found by drawing the line segment connecting the apexes of the isosceles triangles. This vertical line is the symmetry axis of the diamond, dividing it into two 30-60-90 triangles.
Now two other triangles can be discerned, shown in red in the figure. After some angle chasing the corresponding acute angles turn out to be equal, therefore these triangles are similar. Because of the 30-60-90 triangle, their long sides are in proportion 1:2 and therefore a and b are in proportion 1:2 as well.
|Instituto de Matemática Interdisciplinar
Universidad Complutense de Madrid
Plaza de Ciencias 3, 28040, Madrid
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