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DTSTART;TZID=America/New_York:20260916T090000
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SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Robert Gompf: On classifying smoothings of R^4–from the beginning to the present
DESCRIPTION:CMSA/Tsinghua Math-Science Literature Lecture \nDate: September 16\, 2026 \nTime: 9:00 – 10:30 am ET \nLocation: CMSA G10\, 20 Garden Street & via Zoom Webinar \n  \nPlease register to attend \nIn-person registration\n \nZoom Webinar registration \n  \n \nSpeaker: Robert E. Gompf\, University of Texas\, Austin \nTitle: On classifying smoothings of R^4–from the beginning to the present \nAbstract: The field of 4-manifold topology was born around 1981 with two independent revolutionary breakthroughs\, by Fields medalists Michael Freedman and Simon Donaldson. Freedman showed that topological 4-manifolds obeyed the well-developed theory of higher-dimensional manifolds\, while Donaldson used nonlinear analysis (gauge theory) to show that smooth 4-manifolds are quite different from their high-dimensional counterparts. The clash between the two theories makes 4-manifold topology uniquely intricate within manifold theory. One of the most startling consequences is that unlike in other dimensions\, Euclidean 4-space R^4 admits exotic smoothings. Equivalently\, there are smooth 4-manifolds that are homeomorphic\, but not diffeomorphic\, to R^4. We will trace the classification theory of these manifolds from their discovery to the most recent development (joint with Aristotelis Panagiotopoulos) that they cannot be classified by any countable family of numerical invariants. \n  \n\nBeginning in Spring 2020\, the CMSA began hosting a lecture series on literature in the mathematical sciences\, with a focus on significant developments in mathematics that have influenced the discipline\, and the lifetime accomplishments of significant scholars. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathscilit2026_rg/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mathlit_91626.png
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