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4:00pm to 5:00pm - Zoom - Applied and Computational Mathematics Deanna Needell - (UCLA) Online nonnegative matrix factorization for Markovian and other real data Online Matrix Factorization (OMF) is a fundamental tool for dictionary learning problems, giving an approximate representation of complex data sets in terms of a reduced number of extracted features. Convergence guarantees for most of the OMF algorithms in the literature assume independence between data matrices, and the case of dependent data streams remains largely unexplored. In this talk, we present results showing that a non-convex generalization of the well-known OMF algorithm for i.i.d. data converges almost surely to the set of critical points of the expected loss function, even when the data matrices are functions of some underlying Markov chain satisfying a mild mixing condition. As the main application, by combining online non-negative matrix factorization and a recent MCMC algorithm for sampling motifs from networks, we propose a novel framework of Network Dictionary Learning that extracts `network dictionary patches' from a given network in an online manner that encodes main features of the network. We demonstrate this technique on real-world data and discuss recent extensions and variations. |
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4:00pm - Zoom - Differential Geometry Aliakbar Daemi - (Washington University in St. Louis) Unitary Representations of 3-manifold Groups and the Atiyah-Floer Conjecture A useful tool to study a 3-manifold is the space of the |
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9:00am to 10:00am - Zoom - Inverse Problems Houssem Haddar - (Ecole Polytechnique) Duality between invisibility and resonance with some applications |
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10:00am to 11:00am - Zoom: https://uci.zoom.us/j/94683355687 - Number Theory Rosa Winter - (MPI Leipzig) Density of rational points on a family of del Pezzo surfaces of degree 1 Del Pezzo surfaces are surfaces that are classified by their degree $d$, which is an integer between 1 and 9; well-known examples (when $d=3$) are the smooth cubic surfaces in $\mathbb{P}^3$. For del Pezzo surfaces with $d\geq2$ over a field $k$, we know that the set of $k$-rational points is Zariski dense provided that the surface has one $k$-rational point to start with (that lies outside a specific subset of the surface for degree 2). However, for del Pezzo surfaces of degree 1 we do not know if the set of $k$-rational points is Zariski dense in general, even though these surfaces always contain a $k$-rational point. This makes del Pezzo surfaces of degree 1 challenging objects.
In this talk I will first explain what del Pezzo surfaces are, and show some of their geometric features, focussing on del Pezzo surfaces of degree 1. I will then talk about a result that is joint work with Julie Desjardins, in which we give necessary and sufficient conditions for the set of $k$-rational points on a specific family of del Pezzo surfaces of degree 1 to be Zariski dense, where $k$ is any field that is finitely generated over $\mathbb{Q}$.
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10:00am to 11:00am - https://uci.zoom.us/j/93076750122?pwd=Y3pLdndoQTBuNUhxQUxFMkQ2QnRFQT09 - Mathematical Physics Oluwadara Ogunkoya - (University of Alabama at Birmingham) Entanglement Entropy Bounds in the Higher Spin XXZ Chain We consider the Heisenberg XXZ spin-$J$ chain ($J\in\mathbb{N}/2$) with anisotropy parameter $\Delta$. Assuming that $\Delta>2J$, and introducing threshold energies $E_{K}:=K\left(1-\frac{2J}{\Delta}\right)$, we show that the bipartite entanglement entropy (EE) of states belonging to any spectral subspace with energy less than $E_{K+1}$ satisfy a logarithmically corrected area law with prefactor $(2\lfloor K/J\rfloor-2)$. This generalizes previous results by Beaud and Warzel as well as Abdul-Rahman, Fischbacher and Stolz, who covered the spin-$1/2$ case. |
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4:00pm to 5:00pm - https://uci.zoom.us/j/97641313435 - Graduate Seminar Zhiqin Lu - (UC Irvine) Non-Euclidean Geometry and Modern Differential Geometry In this talk, I will first give a brief history of the non-Euclidean geometry. After that, I will present the Riemann's point of view of geometry which led the modern differential geometry. The talk will be given by zoom, the link is |
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5:00pm to 5:50pm - - COMP seminar - (UCI) Summer Opportunities A grad panel will give an overview of a subset of summer opportunities grad students can participate with, including summer schools, NSF internships, and outreach and teaching programs. Ingrid Richey will be the featured math community member. Here is the Zoom link for the seminar: Meeting ID: 925 8546 3241 Password: mathcomp |