Integral Representation Formulae and Residue Calculus with Applications - Semi-Plenary

Explore integral representation formulae and multivariate residue theory in this 56-minute semi-plenary talk by Alain Yger from the University of Bordeaux. Delve into the extensive development of integral representation formulae with weights, including Bochner-Martinelli, Cauchy-Weil, and Cauchy-Fantappié, over the past two decades. Discover how multivariate residue theory has become an efficient tool for providing closed formulae of the Kronecker-Jacobi type, explicitly solving the Bézout identity in algebraic settings and weighted algebras of entire functions like the Paley-Wiener algebra. Examine the potential for applying residue calculus techniques to operator theory, despite its reliance on commutativity. Gain insights into the crucial yet often overlooked role of distributions and currents in multivariate complex analysis. Through a selection of concrete examples, understand the motivations behind using residue theory and explore its possible applications in non-commutative contexts. Learn how the speaker's collaboration with D. Alpay has influenced the topics discussed in this presentation, offering a comprehensive overview of recent developments and future directions in this field of mathematics.