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DTSTART;TZID=America/New_York:20181114T160000
DTEND;TZID=America/New_York:20181114T170000
DTSTAMP:20240514T184520Z
CREATED:20240213T071016Z
LAST-MODIFIED:20240514T184520Z
UID:10002163-1542211200-1542214800@cmsa.fas.harvard.edu
SUMMARY:The virtual fundamental class in symplectic geometry
DESCRIPTION:Speaker: Dusa McDuff (Columbia University)  \nTitle: The virtual fundamental class in symplectic geometry \nAbstract: Essential to many constructions and applications of symplectic geometry is the ability to count J-holomorphic curves. The moduli spaces of such curves have well understood compactifications\, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem\, so that they a fundamental class that can be used to count curves. In the general case\, when the defining equation is not transverse\, there are various different approaches to constructing a representative for this class\, We will discuss and compare different approaches to such a construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim. \n 
URL:https://cmsa.fas.harvard.edu/event/11-14-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-111418.png
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DTSTART;TZID=America/New_York:20181119T150000
DTEND;TZID=America/New_York:20181119T160000
DTSTAMP:20240514T184752Z
CREATED:20240213T071141Z
LAST-MODIFIED:20240514T184752Z
UID:10002165-1542639600-1542643200@cmsa.fas.harvard.edu
SUMMARY:Computational Principles of Auditory Cortex
DESCRIPTION:Speaker: Xiaoqin Wang (Johns Hopkins University) \nTitle: Computational Principles of Auditory Cortex \nAbstract: Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems\, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process time-varying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices\, auditory cortex must also process and differentiate sounds that are externally generated or self-produced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication.
URL:https://cmsa.fas.harvard.edu/event/11-19-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-111918.png
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DTSTART;TZID=America/New_York:20181128T163000
DTEND;TZID=America/New_York:20181128T173000
DTSTAMP:20240514T184301Z
CREATED:20240213T072819Z
LAST-MODIFIED:20240514T184301Z
UID:10002180-1543422600-1543426200@cmsa.fas.harvard.edu
SUMMARY:Recent progress on mean curvature flow
DESCRIPTION:Speaker: Robert Haslhofer (University of Toronto) \nTitle: Recent progress on mean curvature flow \nAbstract: A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamilton’s Ricci flow from intrinsic geometry. In the first half of the talk\, I will give an overview of the well developed theory in the mean convex case\, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution\, with a precise structure theory for the singular set. In the second half of the talk\, I will report on recent progress in the general case without any curvature assumptions. Namely\, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture\, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular\, assuming Ilmanen’s multiplicity one conjecture\, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits.
URL:https://cmsa.fas.harvard.edu/event/11-28-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-112818-1.png
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