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4:00pm - ISEB 1200 - Geometry and Topology Lei Ni - (UC San Diego) The geometry of k-Ricci curvature and a Monge-Ampere equation A joint Geometry and Analysis seminar.
Abstract: The k-Ricci curvature interpolates between the Ricci curvature and holomorphic sectional curvature. For the positive case, a recent result asserts that the compact Kaehler manifolds with positive k-Ricci are projective and rationally connected. This generalizes the previous results of Campana, Kollar-Miyaoka-Mori for the Fano case and the Heirer-Wong and Yang for holomorphic sectional curvature case. For the negative case, all compact Kaehler manifolds with negative k-Ricci admit a Kaehler-Einstein metric with negative scalar curvature. I shall explain how to get this result by solving a complex Monge-Ampere equation. |
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4:00pm to 5:00pm - ISEB1200 - Analysis Lei Ni - (UCSD) The geometry of k-Ricci curvature and a Monge-Ampere equation. The k-Ricci curvature interpolates between the Ricci curvature and holomorphic sectional curvature. For the positive case, a recent result asserts that the compact Kaehler manifolds with positive k-Ricci are projective and rationally connected. This generalizes the previous results of Campana, Kollar-Miyaoka-Mori for the Fano case and the Heirer-Wong and Yang for holomorphic sectional curvature case. For the negative case, all compact Kaehler manifolds with negative k-Ricci admit a Kaehler-Einstein metric with negative scalar curvature. I shall explain how to get this result by solving a complex Monge-Ampere equation. |
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2:00pm to 3:00pm - 510R Rowland Hall - Combinatorics and Probability Roman Vershynin - (UCI) Mathematics of synthetic data. III. Superregular random walks and private measures. In this last talk of the series, we construct a superregular random walk. This will be done by modifying a standard construction of the Brownian motion. Then we will use it to create private synthetic data on the interval. Using sspace-filling curves will allow to extend the construction to higher dimensions. Joint work with March Boedihardjo and Thomas Strohmer, https://arxiv.org/abs/2204.09167 |
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9:00am to 10:00am - Zoom - Inverse Problems Yang Yang - (Michigan State University) Acoustic Source and Speed of Sound Imaging with Application to Photoacoustic Tomography: A Numerical Study |
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2:00pm - 510R Rowland Hall - Combinatorics and Probability Vishesh Jain - (Stanford University) Optimal minimization of the covariance loss Let $X$ be a random vector valued in $\mathbb{R}^m$ such that $\|X\|_{2} \leq 1$ almost surely. In this talk, I will discuss two proofs -- one based on the pinning lemma from statistical physics and another based on randomized rounding -- showing that for every $k \geq 3$, there exists a sigma algebra $\mathcal{F}$ generated by a partition of $\mathbb{R}^{m}$ into $k$ sets such that |
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1:00pm to 2:00pm - 306 - Mathematical Physics Jiranan Kerdboon - (Mississippi State) Anderson Localization for Schrödinger Operators with Monotone Potentials over Circle Diffeomorphisms, 2 We generalize localization results on 1D quasiperiodic Schrödinger operators with monotone potentials over Diophantine irrational rotations to the results over circle diffeomorphisms with irrational rotation numbers. Our results show that the class of irrational rotation numbers can be extended to weakly Liouville irrat |