**Wednesday, 21 February 2018, 1:30PM**-- DC 1304 true*Algorithms and Complexity Group PhD Seminar*-- Computer Science*Speaker:*Dimitrios Skrepetos, David R. Cheriton School of Computer Science*Title:**"Faster Approximate Diameter and Distance Oracles in Planar Graphs"*

*Abstract:*We present an algorithm that computes a (1+\varepsilon)-approximation of the diameter of a weighted, undirected planar graph of n vertices with non-negative edge lengths in O(n \log n (\log n + (1/\varepsilon)^5)) expected time, improving upon the O(n ((1/\varepsilon)^4 \log^4 n + 2^{O(1/\varepsilon)}))-time algorithm of Weimann and Yuster [ICALP 2013].Our algorithm makes two improvements over that result: first and foremost, it replaces the exponential dependency on 1/\varepsilon with a polynomial one, by adapting and specializing Cabello's recent abstract-Voronoi-diagram-based technique [SODA 2017] for approximation purposes; second, it shaves off two logarithmic factors by choosing a better sequence of error parameters during recursion.

Moreover, using similar techniques, we improve the (1+\varepsilon)-approximate distance oracle of Gu and Xu [ISAAC 2015] by first replacing the exponential dependency on 1/\varepsilon on the preprocessing time and space with a polynomial one and second removing a logarithmic factor from the preprocessing time.

**Wednesday, 21 February 2018, 3:00PM**-- DC 2102*Scientific Computation Group PhD Seminar*-- Computer Science*Speaker:*Edward Cheung, David R. Cheriton School of Computer Science*Title:**"Nonsmooth Frank-Wolfe with Uniform Affine Approximations"*

*Abstract:*Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to their ability to efficiently solve large problems that admit a sparse structure (e.g., sparse vectors and low-rank matrices). However the performance of the existing FW method hinges on the quality of the linear approximation. This typically restricts FW to smooth functions for which the approximation quality, indicated by a global curvature measure, is reasonably good.In this paper, we propose a modified FW algorithm amenable to nonsmooth functions by optimizing for approximation quality over all affine functions given a neighbourhood of interest. We analyze theoretical properties of the proposed algorithm and demonstrate that it overcomes many issues associated with existing methods in the context of nonsmooth low-rank matrix estimation.

**Friday, 23 February 2018, 2:30PM**-- MC 5403*Geometry & Topology Seminar Seminar*-- Pure Mathematics*Speaker:*Sebastien Picard, Columbia University*Title:**"The Anomaly flow over Riemann surfaces"*

*Abstract:*The Anomaly flow is a geometric flow which implements the Green-Schwarz anomaly cancellation mechanism originating from superstring theory, while preserving the conformally balanced condition of Hermitian metrics. Its stationary points satisfy the Hull-Strominger system of partial differential equations. The Anomaly flow allows metrics with torsion, and we hope to use it to study non-Kahler complex geometry. We will discuss the behavior of this flow on fibrations over Riemann surfaces, where the flow can be reduced to a single scalar PDE on the Riemann surface. This is joint work with T. Fei and Z. Huang.

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