Boletín Nº 168
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Boletín del IMI
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Dear IMI members:
It is a pleasure to announce that the IMI has welcomed four new members since last week. Federico Herrero Hervás and Oscar Carballal Sobrido have research contracts and are working on their theses. Meanwhile, Jesús Llorente Jorge has returned to the IMI after a short stay at Universidad Politécnica de Madrid. Lastly, Gustavo da Silva Araújo is currently a visiting professor at UCM, coming from the Federal University of Paraíba in Brazil. I wish you all a fruitful collaboration with the IMI and give you my warmest welcome.
Gustavo Adolfo Muñoz Fernández
2) Activities from 27 March to 4 April
Curso de Doctorado
Título: Espacios topológicos cerodimensionales
Ponente: Francisco Gallego Lupiáñez
where 0 < a < 1, b is any odd integer and ab > 1 + 3π=2.
Figure 1: A sketch of Weierstrass' monster for a = 1=2 and b = 13 on the interval [-2-20; 2-20].
Fechas: Cada jueves del 20 de febrero al 8 de mayo, 2025
Lugar: Seminario 225, Facultad de CC. Matemáticas, UCM
Hora: 15:00
Coorganizado por: Instituto de Matemática Interdisciplinar (IMI)
Seminario de Análisis Matemático y Matemática Aplicada
Title: Reversed Kakeya conditions and cantorvals
Speaker: Franciszek Prus-Wisniowski (Universidad de Szczecin, Polonia)
Date: March 27, 2025
Place: Seminario Alberto Dou (Aula 209)
Hour: 13:00
Organized by: Departamento de Análisis Matemático y Matemática Aplicada e Instituto de Matemática Interdisciplinar (IMI)
Seminario de Doctorandos
Título: Grafos de Caley con un conjunto de geodésicas regular
Doctorando: Paloma López Larios (UCM)
Día: 27 de marzo, 2025
Lugar: Seminario Alberto Dou (209)
Hora: 17:00
Organizado por: Facultad de Ciencias Matemáticas UCM y Red de Doctorandos UCM, con la colaboración del Instituto de Matemática Interdisciplinar (IMI)
Seminario de Análisis Matemático y Matemática Aplicada
Title: A Signorini type problem in a domain with inclusions
Speaker: Carmen Perugia (University of Sannio, Benevento, Italy)
Date: April 1, 2025
Place: Seminario Alberto Dou (Aula 209)
Hour: 12:15
Organized by: Departamento de Análisis Matemático y Matemática Aplicada e Instituto de Matemática Interdisciplinar (IMI)
Seminario de Análisis Matemático y Matemática Aplicada
Title: Elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary
Speaker: Giuseppe Cardone (University of Naples “Federico II”, Naples, Italy)
Date: April 1, 2025
Place: Seminario Alberto Dou (Aula 209)
Hour: 13:00
Organized by: Departamento de Análisis Matemático y Matemática Aplicada e Instituto de Matemática Interdisciplinar (IMI)
Seminario de Álgebra, Geometría y Topología
Título: Refining Yoneda's Lemma under finiteness constraints and applications
Orador: Antonio Viruel (Universidad de Málaga)
Fecha: 1 de abril, 2025
Lugar: Seminario 238
Hora: 13:00
Organizado por: Departamento de Álgebra, Geometría y Topología e Instituto de Matemática Interdisciplinar (IMI)
Seminario de Análisis Matemático y Matemática Aplicada
Title: Spectral inequalities for Schrödinger operators
Speaker: Eugenia Malinnikova (Stanford University)
Date: April 3, 2025
Place: Seminario Alberto Dou (Aula 209)
Hour: 13:00
Organized by: Departamento de Análisis Matemático y Matemática Aplicada and Instituto de Matemática Interdisciplinar (IMI)
P. Bégout, J. I. Díaz. Strong stabilization of damped nonlinear Schrödinger equation with saturation on unbounded domains. Journal of Mathematical Analysis and Applications, 538(1). 2024. DOI: 10.1016/J.JMAA.2024.128329
4) Other planned activities
Concurso de Integración Rápida
Fechas: 7 y 9 de abril, 2025
Organizado por: Proyecto Cometas e Instituto de Matemática Interdisciplinar (IMI)
Seminario de Análisis Matemático y Matemática Aplicada
Title: Stable cones in the Alt-Phillips free boundary problem
Speaker: Tomás Sanz-Perela (Universitat de Barcelona)
Date: May 8, 2025
Place: Seminario Alberto Dou (Aula 209)
Hour: 13:00
Organized by: Departamento de Análisis Matemático y Matemática Aplicada and Instituto de Matemática Interdisciplinar (IMI)
5) 1+400. Divulgación con 1 imagen y 400 palabras
Juan Seoane Sepúlveda. How a "monster" started a trend
Boletín del IMI, Nº 168 (27 marzo 2025), Sección "1+400. Divulgación con 1 imagen y 400 palabras."
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En esta sección se publican artículos cortos de divulgación, con una imagen y un máximo de 400 palabras (sin tener en cuenta en estas restricciones los datos de los autores). Las personas que quieran publicar un artículo pueden enviarlo a secreadm.imi@mat.ucm.es
La colección de todos los artículos publicados en esta sección se puede ver en www.ucm.es/imi/1mas400
Since 2005 Juan Seoane has achieved over 200 research publications on Real and Complex Analysis, Functional Analysis, Hypercyclicity, Chaotic Semigroups, Series and Summability, Bohr radius problem, Geometry of Banach spaces, Lineability and Spaceability, Set Theory, Foundations of Mathematics and History of Mathematics.He also authored nine books. His academic education started by earning a Ph.D. at Universidad de Cádiz (Spain, 2005) and, afterwards, a Ph.D. at Universität Karlsruhe (Germany, 2005) and a Ph.D. at Kent State University (USA, 2006). He is currently a Full Professor at UCM and member of the IMI at the same university.
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How a "monster" started a trend
Juan Seoane SepúlvedaUniversidad Complutense de Madrid
It came as a general shock when, in 1872, and during a presentation before the Berlin Academy, K. Weierstrass provided the classical example of a function that was continuous everywhere but differentiable nowhere (see Figure 1). The particular example was defined as
This apparent shock was a consequence of the general thought that most mathematicians shared: A continuous function must have derivatives at a significant set of points (even A.M. Ampère attempted to give a theoretical justification for this). Although the first published example is certainly due to Weierstrass, already in 1822 the Czech mathematician B. Bolzano exhibited a continuous nowhere differentiable function. Later, it was learnt that mathematicians such as M. Ch. Cellérier (1830), B. Riemann (1861), or H. Hankel (1870) had already constructed functions of this type. After 1872 many other mathematicians such as H.A. Schwarz (1873), M.G. Darboux (1874), G. Peano (1890), D. Hilbert (1891), T. Takagi (1903), W. Sierpiński (1912), G.H. Hardy (1916), or S. Banach (1931) also constructed similar functions.
In the literature, this example is widely known as Weierstrass' monster. This famous example led mathematician Vladimir I. Gurariy (1935-2005) to ask the following question: How many examples like Weierstrass' are there for us to find? This, apparent, innocent question has been thoroughly studied since the 1960's. In 1966 Gurariy proved that the set of Weierstrass' monsters on [0,1] contains (except for {0}) an infinite dimensional vector space. Afterwards, Fonf, Gurariy and Kadeč (1999) showed that the set of Weierstrass' monster on [0,1] is spaceable (that is, there is a closed, infinite dimensional subspace X ⊂ C[0,1], the Banach space of continuous functions on [0,1], every non-zero element of which is nowhere diferentiable on [0; 1]). This cascade of results led Aron, Gurariy and the author ([2]) to introduce in 2004 the terminology of lineability and (as already mentioned above) spaceability. In other words, how often (in linear terms) can we expect a "bad" property to happen?
This search for linear subspaces of elements enjoying certain "pathological" property became, in the last decade, a sort of a trend in many different areas of Mathematics and, as a consequence of this, a vast literature on this topic has recently been built, having the American Mathematical Society introducing the new classification 15A03 and 46B87 for this topic. Thus, a property that (apparently) seems very uncommon or even "rare" might end up being "everywhere" (in a linear sense!). This is an example of how a mathematical object that, at first, no one believed that it could even exist ends up being algebraically generic, that is, linearly "everywhere". Other properties that are lineable are, for instance, being differentiable and nowhere monotone (also called being a "differentiable monster") or being a real valued function attaining every real value on each real interval (also called being "everywhere surjective"). The interested reader could take a look at [1-4] in order to find a very large selection of results within this topic.
[1] R. M. Aron, L. Bernal González, D. M. Pellegrino, and J. B. Seoane Sepúlveda, Lineability: the search for linearity in mathematics, Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, FL, 2016.
[2] R. M. Aron, V. I. Gurariy, and J. B. Seoane-Sepúlveda, Lineability and spaceability of sets of functions on R, Proc. Amer. Math. Soc. 133 (2005), no. 3, 795-803.
[3] L. Bernal-González, D. Pellegrino, and J. B. Seoane-Sepúlveda, Linear subsets of nonlinear sets in topological vector spaces, Bull. Amer. Math. Soc. (N.S.) 51 (2014), no. 1, 71-130.
[4] P. H. En o, V. I. Gurariy, and J. B. Seoane-Sepúlveda, Some results and open questions on spaceability in function spaces, Trans. Amer. Math. Soc. 366 (2014), no. 2, 611-625.
[4] P. H. En o, V. I. Gurariy, and J. B. Seoane-Sepúlveda, Some results and open questions on spaceability in function spaces, Trans. Amer. Math. Soc. 366 (2014), no. 2, 611-625.
6) La viñeta matemática
Viñeta enviada por los hermanos Ángel y José Luis González Fernández, creadores de "Troncho y Poncho".
7) Math Puzzle
Puzzle sent by Rik Tangerman.
The solution will be provided in the next issue of Boletin del IMI.
The letter box
Level: Advanced
A rectangle with a diameter and two inscribed squares. What is its area in terms of the square areas A and B?
Solution to last issue's Math Puzzle, sent by Kjartan Poskitt and published on issue No. 167 of the Boletín del IMI:
8) Math Art
Math Art sent by Javad Taba
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