Colóquio de Matemática - Looking for poles of solutions of Painlevé equations

Sala 6.2.33, FCUL, Lisboa

Por Davide Masoero (Faculdade de Ciências da Universidade de Lisboa).

Sumário: Since the early work of Gauss and Riemann on the hypergeometric function, the study of singularities of linear ordinary differential equations in the complex plane is a central topic in mathematical physics. Their efforts culminated in Hilbert's twenty-first problem, which was solved - negatively - in recent years.

The striking feature of a linear ODE is that the locus of the singularities of its solutions is a subset of the locus of the singularities of the coefficients of the equation. On the contrary, the singularity pattern of solutions of a nonlinear ODE can be wildly intricate even when the coefficients of the equation are regular. To overcome this essential difficulty, in the late 19th century Weierstrass, Kowaleskaya and Painlevé introduced the notion of Painlevé equations, which are those six nonlinear ODEs whose solutions extend to meromorphic (i.e. single-valued) functions in the complex plane, with poles as their only singularities. Nowadays, Painlevé equations (and especially the distribution of poles of their solutions) are one of the most active areas of research in contemporary mathematical physics, with applications in many fields such as algebraic geometry, nonlinear PDEs, string theory and random matrices.

In this colloquium I will present the basic concepts and applications of the theory of Painlevé equations and I will then show how the distribution of poles can be studied by means of techniques tracing back to the work of Gauss, Riemann, Hilbert and other giants of 19th and 20th-century mathematics.

14h30
Departamento de Matemática

Seminário de Tese no âmbito do Doutoramento em Biologia e Ecologia das Alterações Globais.

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Logótipo do evento, sobre um fundo branco

Understanding plant water relations at several scales under climate change is the theme of the XV Portuguese-Spanish Water relations Symposium: “Water relations under climate change: from genes to ecosystem”.

Seminário Helena Avelar de Astronomia e Astrologia Antiga, por Martin Gansten (Lund University e Umeå University).

Logótipos ERC e EIC

A sessão visa apresentar os programas ERC e EIC e as potenciais sinergias que podem ser estabelecidas entre ambos.

Fotografia de candidatos, acompanhada do título "M23 2022|2023"

A ULisboa promove o Dia Aberto M23, um evento que pretende aproximar o público adulto do meio universitário.

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Fotografia de placa de identificação de zona de plantação de vinha

Candidaturas até 28 de fevereiro de 2022.

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