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4:00pm - ISEB 1200 - Differential Geometry Davide Parise - (UC San Diego) The parabolic U(1)-Higgs equations and codimension-two mean curvature flows Mean curvature flow is the negative gradient flow of the area |
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2:00pm to 3:00pm - 510R Rowland Hall - Combinatorics and Probability Shahar Mendelson - ( Australian National University) Structure preservation via the Wasserstein distance Consider an isotropic measure $\mu$ on $\mathbb R^d$ (i.e., centered and whose covariance is the identity) and let $X_1,...,X_m$ be independent, selected according to $\mu$. If $\Gamma$ is the random operator whose rows are $X_i/\sqrt{m}$, how does the image of the unit sphere under $\Gamma$ typically look like? For example, if the extremal singular values of $\Gamma$ are close to 1, then this random set is "well approximated" by a d-dimensional sphere, and vice-versa. But is it possible to give a more accurate description of that set? I will show that under minimal assumptions on $\mu$, with high probability and uniformly in a unit vector $t$, each vector $\Gamma t$ inherits the structure of the one-dimensional marginal $\langle X,t\rangle$ in a strong sense. If time permits I will also present a few generalisations of this fact - for an arbitrary indexing set. (A joint work with D. Bartl.) |
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9:00am to 10:00am - Zoom - Inverse Problems Pedro Caro - (BCAM) An inverse problem for data-driven prediction in quantum mechanics |
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4:00pm to 5:00pm - RH 306 - Colloquium Shahar Mendelson - (Australian National University) Mean estimation in high dimension Consider an unknown random vector $X$ that takes values in $R^d$. Is it possible to "guess" its mean accurately if the only information one is given consists of $N$ independent copies of $X$? More accurately, given an arbitrary norm on $R^d$, the goal is to find a mean estimation procedure upon receiving a wanted confidence parameter $\delta$ and $N$ independent copies $X_1,\cdots,X_N$ of an unknown random vector $X$ (that has a finite mean $\mu$ and finite covariance) the procedure returns $\hat{\,\,\mu}$ for which the norm of the error $\hat{\,\mu} - \mu$ is as small as possible, with high probability $1-\delta$. |
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1:00pm - MSTB 124 - Graduate Seminar Connor Mooney - (UC Irvine) Nonlinear elliptic equations Nonlinear elliptic PDEs arise in many physical and geometric contexts, for example in models of soap films, crystal surfaces, and cloud motion. I will discuss some of the questions mathematicians aim to answer about such PDEs, using the minimal surface equation and Monge-Ampere equation as guiding examples. |
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10:00am to 5:15pm - NS II 1201 - Number Theory Francesc Castella, Nadia Heninger, Kyle Pratt, Carl Wang-Erickson - (UCSB, UCSD, BYU, University of Pittsburgh) Southern California Number Theory Day
Southern California Number Theory Day at UC Irvine Saturday, October 7th, 2023 SPEAKERS: Francesc Castella (UCSB) Nadia Heninger (UCSD) Kyle Pratt (BYU) Carl Wang-Erickson (University of Pittsburgh) LOCATION: UC Irvine, Natural Sciences II room 1201 The first lecture will begin at 10:00, and the last will end around 5:15. There will be a dinner after the lectures, details TBA. More information is available on the conference web page: https://www.math.uci.edu/~nckaplan/scntd23.html which will be updated when the schedule information and talk titles are available. LIGHTNING TALKS: We are planning a session with LIGHTNING TALKS where number theory graduate students and postdocs are invited to present their research. These talks will be approximately 5-10 minutes. If you would like to give a lightning talk, please contact Nathan Kaplan by September 15th. Please include your name, affiliation, advisor's name (if you are a graduate student), talk title, and brief abstract. There are no fees (except for the dinner), but we need to know how many people to plan for, so please register using the link on the conference web page. Please email Nathan Kaplan if you have any questions. |