Séminaire Analyse
organisé par l'équipe Analyse
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Siarhei Finski
Toeplitz Operators: Equidistribution, Small Eigenvalues, and Mabuchi Geometry
18 septembre 2025 - 11:00Salle de conférences IRMA
The spectral theory of Toeplitz operators originates in Szegő’s classical work on the eigenvalue distribution of Toeplitz matrices and was later extended by Boutet de Monvel and Guillemin to general complex manifolds. This talk has two objectives. First, we present a generalization of these results in the framework of arbitrary Bernstein-Markov measures on complex manifolds. Second, we investigate the asymptotic behavior of the smallest eigenvalue of Toeplitz operators, a problem that — unexpectedly — turns out to be closely related to Mabuchi geometry originally introduced in connection with constant scalar curvature Kähler metrics. Our aim is to show how techniques from Kähler geometry and pluripotential theory emerge organically in the asymptotic analysis of Toeplitz operators. -
Kiyoon Eum
Partition functions of determinantal point processes on polarized Kähler manifolds
25 septembre 2025 - 11:00Salle de séminaires IRMA
Online seminar Abstract: Determinantal point processes (DPPs) on polarized Kähler manifolds are random point processes that can be seen as higher-dimensional generalizations of 2D Coulomb gases. In this talk, I will discuss Zabrodin–Wiegmann type expansions of partition functions and show how they are connected to several concepts in Kähler geometry. In some sense, the asymptotic expansion of the DPP partition function generates geometric objects that generalize some classical ones in Kähler geometry. I will also touch on the effective action of higher-dimensional quantum Hall systems and on random Kähler metrics. -
Soumyajit Saha
TBA
2 octobre 2025 - 11:00Salle de conférences IRMA
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Yousuke Ohyama
TBA
23 octobre 2025 - 11:00Salle de conférences IRMA
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Nathan Réguer
TBA
6 novembre 2025 - 11:00Salle de conférences IRMA