Profiles Luis Caffarelli

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Mathematics professor Luis Caffarelli discusses the role of math in his life and his experience researching the famously complex Navier-Stokes equations. • Music: • Map and Above the Leaves by Unseen • Video by Jeff Mertz","styleRuns":[{"startIndex":0,"length":220,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":220,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CLoBELsvGAIiEwi9y4jS4eWLAxW16UIFHV9QIcU=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC0lENWltckFpcjI4GAYyJSIRIgtJRDVpbXJBaXIyODAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CLoBELsvGAIiEwi9y4jS4eWLAxW16UIFHV9QIcU=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CLkBELovIhMIvcuI0uHliwMVtelCBR1fUCHF"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"tdUBLu4fHbw","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/tdUBLu4fHbw/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLDiQXmECTuk6r-2HbiIPMx32cAcow","width":168,"height":94},{"url":"https://i.ytimg.com/vi/tdUBLu4fHbw/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLCT6M9ZfwI5S4AtJByz45rSGHTA5Q","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Luis A. 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