Este lunes, 15 de abril, en la Universidad Carlos III de Madrid y en streaming
Imagen: CC
Joan Bagaria, profesor de investigación ICREA en la Universitat de Barcelona (UB) y especialista en matemática lógica y teoría de conjuntos, será el ponente del próximo coloquio de matemáticas, organizado de manera conjunta por el ICMAT y las universidades Autónoma de Madrid, Complutense de Madrid y Carlos III de Madrid. Tendrá lugar este lunes, 15 de abril, en el Salón de grados del Edificio Padre Soler del Campus de Leganés de la Universidad Carlos III de Madrid. También podrá seguirse en directo en este enlace.
En su charla, titulada “The Higher Infinite and its Role in Mathematics”, Bagaria se centrará en aquellos infinitos cardinales tan grandes cuya existencia no puede ser demostrada dentro del sistema de axiomas de ZFC estándar (Zermelo-Fraenkel with Choice) de la teoría de conjuntos. El investigador presentará algunos ejemplos de cardinales grandes y explicará algunas de las aplicaciones a otras áreas de las matemáticas, donde han sido de especial importancia para resolver destacados problemas abiertos.
Coloquio conjunto de matemáticas ICMAT-UAM-UC3M-UCM
“The Higher Infinite and its Role in Mathematics”, Joan Bagaria (Universitat de Barcelona & ICREA)
Fecha: Lunes, 15 de abril de 2024 – 13:00
Lugar: Salón de Grados del Edificio Padre Soler, Campus de Leganés, Universidad Carlos III de Madrid
Resumen: The Higher Infinite refers to the infinite cardinalities studied by set theory, as charted by large cardinal hypotheses known as large cardinal axioms. These axioms assert the existence of infinite cardinals so large that their existence cannot be proved within the standard ZFC system of set theory. Since the weakest of large cardinals, the weakly inaccessible, were first defined and studied by Hausdorff over a century ago, a plethora of different and much stronger large cardinals have since then been identified in a great variety of contexts and taking many different forms. Indeed, after the groundbreaking results of Martin-Steel and Woodin in the 1980s, establishing the tight connection between large cardinals and the determinacy of sets of reals, the theory of large cardinals has been expanding in multiple directions, yielding solutions to many well-known set-theoretic problems, as well as fertile applications to other areas of mathematics, from general to algebraic topology and homotopy theory, to abelian groups, etc. In this talk I will present some examples of large cardinals and will explain their role in mathematics by giving a number of examples in different areas where they have been applied to solve prominent open problems, some of them very recent.