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12:00pm - zoom - Probability and Analysis Webinar Roman Vershynin - (UC Irvine) Szemeredi regularity, matrix decompositions, and covariance loss We will discuss a new kind of weak Szemeredi regularity lemma. It allows one to decompose a positive semidefinite matrix into a small number of "flat" matrices, up to a small error in the Frobenius norm. The proof utilizes randomized rounding based on Grothendieck’s identity. The regularity lemma can be interpreted as a probabilistic statement about "covariance loss" – the amount of covariance that is lost by taking conditional expectation of a random vector. This talk is based on a joint work with March Boedihardjo and Thomas Strohmer. |
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4:00pm to 5:00pm - RH 306 - Applied and Computational Mathematics Chiu-Yen Kao - (Claremont Mckenna College) Computational Approaches to Construct Free Boundary Minimal Surface via Extremal Steklov Eigenvalue Problems Recently Fraser and Schoen showed that the solution of a certain extremal Steklov eigenvalue problem on a compact surface with boundary can be used to generate a free boundary minimal surface, i.e., a surface contained in the ball that has (i) zero mean curvature and (ii) meets the boundary of the ball orthogonally. In this talk, we discuss new numerical approaches that use this connection to realize free boundary minimal surfaces. Our numerical method involves (i) using conformal uniformization of multiply connected domains to avoid explicit parameterization for the class of metrics, (ii) accurately solving a boundary-weighted Steklov eigenvalue problem in multi-connected domains, and (iii) developing gradient-based optimization methods for this non-smooth eigenvalue optimization problem. For genus zero with many different numbers of boundary components, we numerically solve the extremal Steklov problem for the first eigenvalue. The corresponding eigenfunctions generate a free boundary minimal surface, which we display in striking images. (Joint work with Braxton Osting at University of Utah, Èdouard Oudet at Universite ́ Grenoble Alpes, France)
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4:00pm - ISEB 1200 - Differential Geometry Catherine Cannizzo - (UC Riverside) Homological Mirror Symmetry for Theta Divisors Symplectic geometry is a relatively new branch of geometry.
Joint with Geometry and Topology Seminar. |
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4:00pm - ISEB 1200 - Geometry and Topology Catherine Cannizzo - (UC Riverside) Homological Mirror Symmetry for Theta Divisors Symplectic geometry is a relatively new branch of geometry.
Joint with Differential Geometry Seminar. |
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1:00pm to 2:00pm - 440R Rowland Hall - Combinatorics and Probability Bjarne Schuelke - (Caltech) Beyond the broken tetrahedron Here we consider the hypergraph Tur\'an problem in uniformly dense hypergraphs as was suggested by Erd\H{o}s and S\'os. Given a $3$-graph $F$, the uniform Tur\'an density $\pi_u(F)$ of $F$ is defined as the supremum over all $d\in[0,1]$ for which there is an $F$-free uniformly $d$-dense $3$-graph, where uniformly $d$-dense means that every linearly sized subhypergraph has density at least $d$. Recently, Glebov, Kr\'al', and Volec and, independently, Reiher, R\"odl, and Schacht proved that $\pi_u(K_4^{(3)-})=\frac{1}{4}$, solving a conjecture by Erd\H{o}s and S\'os. There are very few hypergraphs for which the uniform Tur\'an density is known. In this work, we determine the uniform Tur\'an density of the $3$-graph on five vertices that is obtained from $K_4^{(3)-}$ by adding an additional vertex whose link forms a matching on the vertices of $K_4^{(3)-}$. Further, we point to two natural intermediate problems on the way to determining $\pi_u(K_4^{(3)})$ and solve the first of these.
This talk is based on joint work with August Chen. |
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9:00am to 9:50am - Zoom - Inverse Problems Ekaterina Sherina - (University of Vienna) Inversion Methods for Strain and Stiffness Reconstruction in Quantitative Optical Coherence Elastography |
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11:00am - RH 306 - Harmonic Analysis José Ramón Madrid Padilla - (University of Geneva) On maximal operators, progress and open problems In this talk we will discuss some results about the regularity of maximal operators on Sobolev and BV spaces. We will also discuss many related open problems. |
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1:00pm to 2:00pm - RH 510R - Algebra Harold Polo - (University of Florida) Polynomial semidomains A subset $S$ of an integral domain $R$ is called a semidomain provided that the pairs $(S,+)$ and $(S,\cdot)$ are semigroups with identities. The study of factorizations in integral domains was initiated by Anderson, Anderson, and Zafrullah in 1990, and this are has been systematically investigated since then. We study the divisibility and arithmetic of factorizations in the more general context of semidomains. We are especially concerned with the ascent of the most standard divisibility and factorization properties from a semidomain to its semidomain of (Laurent) polynomials. This is joint work with Felix Gotti. |