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Nonnegative Ricci curvature, nilpotency, and asymptotic geometry

Recent progress on geometric analysis and Riemannian geometry October 21, 2024 - October 25, 2024

October 22, 2024 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Jiayin Pan (University of California, Santa Cruz)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Nonnegative Ricci curvature, nilpotency, and asymptotic geometry

Abstract

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The interplay between geometry and topology is always one of the central topics in Riemannian geometry. For open (noncompact and complete) manifolds with nonnegative Ricci curvature, it is known that the fundamental groups could be torsion-free nilpotent. This is distinct from open manifolds with nonnegative sectional curvature, whose fundamental groups are virtually abelian. This talk will cover how the virtual nilpotency/abelianness of the fundamental group is related to various geometric quantities and equivariant asymptotic geometry.

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Nonnegative Ricci curvature, nilpotency, and asymptotic geometry

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