Analysis and Mathematical Physics
Linear Stability of Shrinking Ricci Solitons and First Eigenvalue Estimates
Ricci solitons, introduced by R. Hamilton in the mid-80s, are self-similar solutions to the Ricci flow and natural generalizations of Einstein manifolds. Shrinking Ricci solitons, in particular, model Type I singularities of the Ricci flow and arise as critical points of Perelman's $\nu$-entropy. In this talk, after a quick introduction on (gradient) Ricci solitons, we shall discuss the linear stability of shrinking Ricci solitons with respect to Perelman's \nu-entropy and the first eigenvalue estimates of the Laplace–Beltrami/Lichnerowicz-type Laplacian operators.
Date & Time
February 10, 2026 | 2:30pm – 3:30pm
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02/10/2026 14:30
02/10/2026 15:30
Analysis and Mathematical Physics
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Topic: Linear Stability of Shrinking Ricci Solitons and First Eigenvalue Estimates
Speakers: Huai-Dong Cao, Institute for Advanced Study
More: https://www.ias.edu/math/events/analysis-and-mathematical-physics-74
Ricci solitons, introduced by R. Hamilton in the mid-80s, are
self-similar solutions to the Ricci flow and natural generalizations
of Einstein manifolds. Shrinking Ricci solitons, in particular,
model Type I singularities of the Ricci flow and arise as critical
points of Perelman's $\nu$-entropy. In this talk, after a quick
introduction on (gradient) Ricci solitons, we shall discuss the linear
stability of shrinking Ricci solitons with respect to Perelman's
\nu-entropy and the first eigenvalue estimates of the
Laplace–Beltrami/Lichnerowicz-type Laplacian operators.
Simonyi Hall 101 and Remote Access
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Location
Simonyi Hall 101 and Remote AccessSpeakers
Huai-Dong Cao, Institute for Advanced Study