Date/Time : 15 Jan 2020 15:30
Venue : S17 #04-04 SR3
Speaker : Qi Zhi, Zhejiang University

Date/Time:15 Jan 2020 15:30 Venue: S17 #04-04 SR3 Speaker: Qi Zhi, Zhejiang University A Bessel delta-method and its applications In this talk, I will introduce a new $\delta$-method by a certain Bessel integral and its applications in the theory of exponential sums for $GL(2)$. In particular, it gives a simple proof of the Weyl-type subconvex bound for modular form $L$-functions in the $t$-aspect. This is joint work with Aggarwal, Holowinksy and Lin. Add to calendar: 

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Date/Time : 15 Jan 2020 17:00
Venue : S17 #04-06 SR1
Speaker : Frank Stephan, National University of Singapore

Date/Time:15 Jan 2020 17:00 Venue: S17 #04-06 SR1 Speaker: Frank Stephan, National University of Singapore Measure and Conquer for Max Hamming Distance XSAT This talk gives an overview of the joint work of the speaker’s ecent work on the Hamming XSAT problem. This problem asks for an algorithm to determine which, given an XSAT instance, determines the maximum Hamming distance between two solutions of this instance. The problem has been studied by Dahloef in 2005 in an ISAAC paper who provided an O(1.83848^n) algorithm for this problem. Later Fu, Zhu and Yin presented at JFCST 2012 an O(1.6760^n) algorithm for the related Max Hamming X3SAT problem where all clauses have at most three literals. The current paper provides for the general Max Hamming XSAT problem an O(1.4983^n) algorithm which applies also the technique “Measure and Conquer” in order to prove a better bound than the algorithm would give otherwise. Furthermore, the algorithm does not only provide the maximum Hamming distance of two solutions of the instance, but instead for each k between 0 and n the number of pairs of solutions which have Hamming distance k. For the special case Max Hamming Distant X3SAT, Hoi, Jain and Stephan have the bound O(1.3298^n) at the conference FSTTCS 2019. Add to calendar: 

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Date/Time : 15 Jan 2020 14:00
Venue : S16 #05-98
Speaker : Xinyyi Li , Peiking University

Date/Time:15 Jan 2020 14:00 Venue: S16 #05-98 Speaker: Xinyyi Li, Peiking University Recent Progress on Loop-erased Random Walk In this mini-course, we will give a brief review on the model of Loop-erased Random Walk (LERW) and its relationship with other models from statistical physics, and discuss some of the recent progress on this model, especially in three dimensions. Add to calendar: 

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Date/Time : 15 Jan 2020 14:00
Venue : S17 #04-06 SR1
Speaker : Paul Nelson, ETH Zurich

We will discuss how to study the cubic moment of any family of automorphic L-functions on PGL(2) using regularized diagonal periods of Eisenstein series, following a strategy suggested by Michel–Venkatesh. Applications include generalizations to the setting of number fields of some results of Conrey–Iwaniec and Petrow–Young, improved estimates for representation numbers of ternary quadratic forms over number fields, and improvements to the prime geodesic theorem on arithmetic hyperbolic 3-folds.

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Date/Time : 15 Jan 2020 15:00
Venue : S17 #06-11
Speaker : Georgios Moschidis, UC Berkeley

Date/Time:15 Jan 2020 15:00 Venue: S17 #06-11 Speaker: Georgios Moschidis, UC Berkeley A proof of the instability of AdS spacetime for the Einstein–scalar field system The AdS instability conjecture is a conjecture about the initial-boundary value problem in general relativity. It states that there exist arbitrarily small perturbations to the initial data of AdS spacetime which, under evolution by the vacuum Einstein equations with reflecting boundary conditions on conformal infinity, lead to the formation of black holes after a sufficiently long time. In this talk, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein–scalar field system. The construction of the unstable family of initial data will require working in a low regularity setting, carefully designing a family of initial configurations of localised matter beams and estimating the exchange of energy taking place between interacting beams over a long period of times, as well as estimating the decoherence rate of the beams. Add to calendar: 

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Date/Time : 13 Jan 2020 15:00
Venue : S17 #04-06 SR1
Speaker : Zhu Wei, Duke University

Date/Time:13 Jan 2020 15:00 Venue: S17 #04-06 SR1 Speaker: Zhu Wei, Duke University Applied differential geometry and harmonic analysis in deep learning regularization With the explosive production of digital data and information, data-driven methods, deep neural networks (DNNs) in particular, have revolutionized machine learning and scientific computing by gradually outperforming traditional hand-craft model-based algorithms. While DNNs have proved very successful when large training sets are available, they typically have two shortcomings: First, when the training data are scarce, DNNs tend to suffer from overfitting. Second, the generalization ability of over parameterized DNNs still remains a mystery despite many recent efforts. In this talk, I will discuss two recent works to inject” the “modelling” flavour back into deep learning to improve the generalization performance and interpretability of DNNs. This is accomplished by deep learning regularization through applied differential geometry and harmonic analysis. In the first part of the talk, I will explain how to improve the regularity of the DNN representation by imposing a “smoothness” inductive bias over the DNN model. This is achieved by solving a variation problem with a low-dimensionality constraint on the data-feature concatenation manifold. In the second part, I will discuss how to impose scale-equivariance in network representation by conducting joint convolutions across the space and the scaling group. The stability of the equivalent representation to nuisance input deformation is also proved under mild assumptions on the Fourier-Bessel norm of filter expansion coefficients. Add to calendar: 

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Date/Time : 10 Jan 2020 15:00
Venue : S17 #04-05 SR2
Speaker : Seung-Hyeok Kye, Seoul National University, South Korea

Date/Time:10 Jan 2020 15:00 Venue: S17 #04-05 SR2 Speaker: Seung-Hyeok Kye, Seoul National University, South Korea A lattice arising from quantum information theory The notion of separability/entanglement is one of the central themes in the current quantum information theory, and it is known to be NP hard in general to determine if a given state is separable or entangled. In multipartite systems, the notions of separability depend on partitions of systems to yield the notions of partial separability and partial entanglement. In the simplest multipartite case of the three qubit system, there are three kinds of basic partial separability which give rise to corresponding convex sets. Intersections and convex hulls of them also have been considered by researchers to get more kinds of separability and entanglement. In this talk, we consider the lattice generated by these three convex sets, with respect to two operations: convex hull and intersection. We will discuss mathematical properties of this lattice. This talk is based on three papers: arXiv 1812.01227 (with Kyung Hoon Han), arXiv 1905.07678 (with Kyung Hoon Han) and arXiv 1911.06496 (with Kyung Hoon Han and Szilard Szalay). Add to calendar: 

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Date/Time : 03 Jan 2020 15:00
Venue : S17 #04-05 SR2
Speaker : Paul Van Dooren, Catholic University of Louvain, Belgium

Date/Time:03 Jan 2020 15:00 Venue: S17 #04-05 SR2 Speaker: Paul Van Dooren, Catholic University of Louvain, Belgium Detecting roles in very large graphs Computing meaningful clusters of nodes is crucial to analyze very large networks, but since this is a combinatorial optimization problem, its complexity can be prohibitive. In this talk, we present a pairwise node similarity measure that allows to extract roles, i.e. group of nodes sharing similar flow patterns within a network. We then propose a low rank iterative scheme to approximate the similarity measure for very large networks and we show that our low rank similarity score successfully extracts the different roles in random graphs of Erdös-Renyi type. We then argue that when projecting our similarity measure onto a low rank manifold (say, of rank r), the role models can be recovered using classical clustering techniques in an r-dimensional space, which reduces the complexity significantly. We illustrate these ideas with a number of real world applications including coral spawning in the great barrier reef. Add to calendar: 

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Date/Time : 03 Jan 2020 16:00
Venue : S17 #04-06 SR1
Speaker : HAN Jiequn, Princeton University

Date/Time:03 Jan 2020 16:00 Venue: S17 #04-06 SR1 Speaker: HAN Jiequn, Princeton University Deep BSDE: A Unified Framework for Solving High-Dimensional PDEs, FBSDEs, and Control Problems Developing algorithms for solving high-dimensional partial differential equations (PDEs), forward-backward stochastic differential equations (FBSDEs), and control problems has been an exceedingly difficult task for a long time, due to the notorious difficulty known as the curse of dimensionality. In this talk we introduce the “deep BSDE method” as a unified framework to solve general high-dimensional PDEs and FBSDEs. Starting from the BSDE formulation, we approximate the unknown component by neural networks and design a proper loss function to optimize parameters. Numerical results of a variety of examples, including applications in game theory and eigenvalue problem, demonstrate that the proposed algorithm is quite effective in high- dimensions, in terms of both accuracy and speed. We furthermore provide a theoretical error analysis to illustrate the validity and property of the objective function. Add to calendar: 

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