Date/Time : 18 Nov 2020 16:00
Venue : via Zoom
Speaker : Yu Yue Tony, Universit Paris-Saclay (Paris-Sud)

Join Zoom Meeting https://nus-sg.zoom.us/j/81669932092?pwd=WSt6V01ESFFpY0dVRnhVdEt3cUIrQT09 Meeting ID: 816 6993 2092 Password: 287641 Abstract:  Mirror symmetry is one of the most mysterious dualities in mathematics. My research explores a new approach to mirror symmetry, via non-archimedean geometry. I will give an overview of the recent progress in this direction. I will talk about non-archimedean enumerative geometry, the Frobenius structure conjecture, and derived non-archimedean geometry. I will also describe an application towards cluster algebras, and another application towards the moduli space of Calabi-Yau pairs.

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Date/Time : 17 Nov 2020 09:00
Venue : via Zoom
Speaker : Huang Hao, Emory University

Join Zoom Meeting https://nus-sg.zoom.us/j/86270578593?pwd=cTYreG1hQlExWHJERStZN0hUWjNWQT09 Meeting ID: 862 7057 8593 Password: 313348 Abstract:  The biclique partition number bp(G) is the minimum number of complete bipartite graphs needed to partition the edges of a graph G. Its study was initiated in 1972 by Graham and Pollak, who showed that the complete graph with n vertices has biclique partition number exactly n-1. Since then, this important graph parameter has found many connections with problems arising from discrete geometry, communication complexity and network addressing. In this talk we will explore some of these connections and discuss counterexamples to two decade-old conjectures: one of Alon, Saks, and Seymour in 1991 saying the biclique partition number is strictly greater than the chromatic number; and another one of Erdos from the ’80s on random graphs. At the end of this talk, we will also outline the significance of studying its generalization for hypergraphs.

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Date/Time : 11 Nov 2020 09:00
Venue : via Zoom
Speaker : Yu Hui, Columbia University

Join Zoom Meeting https://nus-sg.zoom.us/j/85408305509?pwd=OHpHQkdtUSt3YzdLN1BTVkxOeTRXQT09 Meeting ID: 854 0830 5509 Password: 843914 Abstract:  The N-membrane problem is the study of shapes of elastic membranes being pushed against each other. The main questions are the regularity of the functions modeling the membranes, and the regularity of the contact regions between consecutive membranes. These are classical questions in free boundary problems. However, very little is known when N is larger than 2. In this case, there are multiple free boundaries that cross each other, and most known techniques fail to apply. In this talk, we discuss, for general N, the optimal regularity of the solutions in arbitrary dimensions, and a classification of blow-up solutions in 2D. Then we focus on the regularity of the free boundaries when N=3. We also discuss how the techniques developed here can be applied to other problems involving multiple free boundaries. This talk is based on two recent joint works with Ovidiu Savin (Columbia University).

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Date/Time : 09 Nov 2020 09:00
Venue : via Zoom
Speaker : Yang Yunan, New York University

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https://nus-sg.zoom.us/j/83496316224?pwd=STdTeDhKQk9pTnlLVFREaWs5UzFkZz09 Meeting ID: 834 9631 6224 Password: 665418

Optimal transport has been one interesting topic of mathematical analysis since Monge (1781). The problem’s close connections with differential geometry and kinetic descriptions were discovered within the past century, and the seminal work of Kantorovich (1942) showed its power to solve real-world problems. Recently, we proposed the quadratic Wasserstein distance from optimal transport theory for inverse problems, tackling the classical least-squares method’s longstanding difficulties such as nonconvexity and noise sensitivity. The work was soon adopted in the oil industry. As we advance, we discover that the advantage of changing the data misfit is more general in a broader class of data-fitting problems by examing the preconditioning and “implicit” regularization effects of different mathematical metrics as the objective function in optimization, as the likelihood function in Bayesian inference, and as the measure of residual in numerical solution to PDEs.

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Date/Time : 21 Jan 2020 15:00
Venue : S17 #04-04 SR3
Speaker : Xu Zhouli, Massachusetts Institute of Technology

Date/Time:21 Jan 2020 15:00 Venue: S17 #04-04 SR3 Speaker: Xu Zhouli, Massachusetts Institute of Technology In and around stable homotopy groups of spheres The computation of stable homotopy groups of spheres is one of the most fundamental problems in topology. Despite its simple definition, it is notoriously hard to compute. It has connections to many areas of mathematics. In this talk, I will discuss a recent breakthrough on this problem, which depends on motivic homotopy theory in a critical way. I will also talk about applications to smooth structures on spheres, and towards the open problem of Kervaire invariant one in dimension 126. This talk is based on several joint work with Bogdan Gheorghe, Daniel Isaksen, and Guozhen Wang. Add to calendar: 

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Date/Time : 20 Jan 2020 15:00
Venue : S17 #04-06 SR1
Speaker : Sohail Bahmani, Georgia Institute of Technology

Date/Time:20 Jan 2020 15:00 Venue: S17 #04-06 SR1 Speaker: Sohail Bahmani, Georgia Institute of Technology Convex Programming for Statistical Estimation: A New Perspective A critical aspect of statistical procedures in many engineering and scientific applications is their computational efficiency. Convex programming provides a versatile framework to design computationally tractable algorithms for many statistical tasks such as regression, classification, and variable selection. The estimation procedures based on convex programming are traditionally designed independent of the statistical model. We will discuss new approaches that use the statistical model to design estimators with convex formulations. These approaches can be applied in a broader set of problems and be computationally favourable. In particular, we consider a broad class of parametric regression problems where the signal is observed through random nonlinear functions with a difference of convex (DC) form. This general statistical model includes familiar special cases such as phase retrieval/quadratic regression and blind deconvolution/bilinear regression. Given the DC decomposition of the observation functions as well as an approximate solution, we formulate a convex program as an estimator that operates in the natural space of the signal. In the mentioned special cases, the proposed approach is computationally superior to the methods based on semidefinite/sum-of-squares relaxation—tailored for polynomial observation functions—and can compete with the non-convex methods. Under some regularity assumptions, the proposed convex estimators achieve a desirable sample complexity. 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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