Friday, February 18, 2022
Time | Items |
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All day |
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9am |
02/18/2022 - 9:00am We discussĀ topics of common interest in the areas of geometry, probability, and combinatorics. Location: |
12pm |
02/18/2022 - 12:00pm It is well known that chaos arises from 3-body problems (both in the planetary sense as in Reuben's talk and in the romantic sense). In this talk, we will discuss the (not) more general statement that "3 implies chaos". Topics to be surveyed are the classical example of the logistic function, connections to the Mandelbrot set and the classical results of Li--Yorke and Sharkovsky, giving a streamlined proof of the latter due to Burns-Hasselblatt. Location: |
2pm |
02/18/2022 - 2:00pm Abstract: In the recent decade, the Almgren-Pitts min-max theory has advanced the existence theory of minimal surfaces in a closed Riemannian manifold $(M^{n+1}, g)$. When $2 \leq n+1 \leq 7$, many properties of these minimal hypersurfaces (geodesics), such as areas, Morse indices, multiplicities, and spatial distributions, have been well studied. However, in higher dimensions, singularities may occur in the constructed minimal hypersurfaces. This phenomenon invalidates many techniques helpful in the low dimensions to investigate these geometric objects. In this talk, I will discuss how to overcome the difficulty in a generic 8-dimensional closed manifold, utilizing various deformation arguments. En route to obtaining generic results, we prove the generic regularity of minimal hypersurfaces in dimension 8. This talk is partially based on joint works with Zhihan Wang. Location: |