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DTSTART;TZID=America/New_York:20231204T163000
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UID:10002830-1701707400-1701711000@cmsa.fas.harvard.edu
SUMMARY:Analysis of ALH* gravitational instantons
DESCRIPTION:Speaker: Xuwen Zhu (Northeastern) \nTitle: Analysis of ALH* gravitational instantons \nAbstract: Gravitational instantons are non-compact Calabi-Yau metrics with L^2 bounded curvature and are categorized into six types. We will discuss one such type called ALH* metrics which has a non-compact end modelled by the Calabi ansatz with inhomogeneous collapsing near infinity. Such metrics appeared recently in the works on SYZ conjecture\, as well as the scaling bubble limits for codimension-3 collapsing of K3 surfaces\, where the study of its Laplacian played a central role. In this talk I will talk about the Fredholm mapping property and L^2 cohomology of such metrics. This is ongoing work joint with Rafe Mazzeo.
URL:https://cmsa.fas.harvard.edu/event/colloquium-12423/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-12.04.2023.docx-1.png
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DTSTART;TZID=America/New_York:20231211T163000
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UID:10002828-1702312200-1702315800@cmsa.fas.harvard.edu
SUMMARY:Homology\, higher derived limits\, and set theory
DESCRIPTION:Colloquium \nSpeaker: Justin Moore (Cornell University) \nTitle: Homology\, higher derived limits\, and set theory \nAbstract: Singular homology has a number of well-known defects when used to study spaces such as the Hawaiian earring and solenoids. It may not reflect the “shape” of the space and can give counterintuitive information about its dimension. One remedy of this is to develop a homology theory based on approximating spaces by polyhedra\, computing their homologies\, and then taking a limit. This is the approach taken by Steenrod-Sitnikov homology and Lisica and Mardesic’s strong homology. Even within the class of locally compact second countable spaces though\, the properties of these homology theories — and the higher derived limits which underly them — are dependent on axioms of set theory beyond ZFC. Recently it was shown that it is consistent with (and therefore independent of) ZFC that strong homology and Steenrod Sitnikov homology coincide in the class of locally compact second countable spaces — and therefore each of these homology theories enjoys the desirable properties of the other. These results also point to how we might develop variants of these homology theories which enjoy their desirable properties\, but which are less sensitive to set theory. This is joint work with Nathaniel Bannister\, Jeff Bergfalk\, and Stevo Todorcevic.
URL:https://cmsa.fas.harvard.edu/event/colloquium-121123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-12.11.2023.png
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