Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

To have your events added or removed from this calendar, please contact OUR at ugresearch@illinois.edu

Department Colloquium: Analysis and Geometry on Singular Spaces

Event Type: Seminar/Symposium
Sponsor: Department of Mathematics
Location: Altgeld 245
Date: May 8, 2025 4:00 pm
Speaker: Paolo Piazza (Rome)
Views: 117
Originating Calendar: Mathematics Colloquium & Named Lectures; Abstract:
Smooth riemannian manifolds enjoy beautiful properties. For example Poincare' duality. Or the fact that the classic geometric operators, such as the Gauss-Bonnet operator on differential forms, or the spin-Dirac operator on spinors, are essentially self-adjoint on $L^2$. Moreover, the analytic properties of these operators are related to the topology of the manifold through, for example, the Atiyah-Singer index theorem. What happens to these beautiful properties when we pass to singular spaces ? For example, when we consider singular projective varieties ? This question has been around for a long time and has generated, especially in the last 50 years, an intense research activity. In this talk I will survey old and new results concentrating, for the most recent contributions, on joint work with Pierre Albin and Markus Banagl.

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