Date/Time : 23 Jul 2021 09:00
Venue : via Zoom
Speaker : Jingrui Cheng, State University of New York at Stony Brook

Join Zoom Meeting https://nus-sg.zoom.us/j/86843946871?pwd=eXk1ZmF6OElwY2s3MjdzM1piV2VQQT09 Meeting ID: 868 4394 6871 Passcode: 398037 I will explain the a priori estimates for the cscK equation on a compact manifold, and how to use these estimates to obtain existence when the associated energy functional is “coercive”. If time permits, I will also explain how we can hope to get existence from a more “algebraic” condition, which might be easier to check in practice.

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Date/Time : 16 Jul 2021 16:00
Venue : via Zoom
Speaker : Anna Wienhard, Heidelberg University

Join Zoom Meeting https://nus-sg.zoom.us/j/81534494468?pwd=dHJqL1NOSjBVR09ZcG9iRk5EN3daZz09 Meeting ID: 815 3449 4468 Passcode: 717949 Semi-simple Lie groups play a role in many areas of mathematics. They are closely related to and naturally arise as isometry groups of symmetric spaces. A key tool in the investigation of discrete subgroups of semisimple Lie groups is the their action on this symmetric space, and on its compactifications. There is a basic dichotomy between rank one Lie groups, when the symmetric space is of strict negative curvature, and Lie groups of higher rank, when the symmetric space is only non-positively curved. For many years, starting with Margulis celebrated superrigidity theorem, rigidity has been the overarching paradigm in higher rank. In recent years we have seen a shift of this paradigm towards a combination of flexibility and rigidity which opened up new research directions. In this talk I will describe some of the key properties of symmetric spaces, describe some of the recent developments, and discuss how the intricate geometry of symmetric spaces can also be leveraged in the context of graph embeddings and in representation learning.

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Date/Time : 18 Jun 2021 16:00
Venue : via Zoom
Speaker : Yash Lodha, Korea Institute for Advanced Study

Join Zoom Meeting https://nus-sg.zoom.us/j/84001105600?pwd=OUc1ZGtOb21KSGtaRHhjN3VWMHJsdz09 Meeting ID: 840 0110 5600 Passcode: 346800 The classification of finite simple groups is one of the most incredible achievements of 20th century mathematics. So what do we know about infinite, finitely generated (or even finitely presented), simple groups? Starting from a beautiful example of Higman from 1951: the first example of a finitely generated infinite simple group, to the striking examples of Thompson, we shall survey this territory full of beautiful phenomena. We shall also discuss some questions that remain mysterious.

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Date/Time : 17 Jun 2021 10:00
Venue : via Zoom
Speaker : Rui Wang, University of California at San Diego

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Modelling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are interpretable but usually require significant computational resources and expertise. While deep learning (DL) provides alternatives for efficiently emulating nonlinear dynamics, it does not necessarily obey the physics laws or generalize well across different systems. Thus, there is a growing need for incorporating prior physics knowledge into DL models so that we can take the best of both types of approaches. We present three physics-guided DL approaches for spatiotemporal forecasting. We first present TF-Net, which marries the numerical techniques with custom-designed neural networks, that can predict accurate physical fields that obey desirable physical characteristics. We also provide two approaches to improve generalization across different systems. One is to design deep equivariant models that respect given symmetries of physical dynamics, and the other one is to infer shared time-invariant characteristics by leveraging meta-learning techniques.

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Date/Time : 04 Jun 2021 16:00
Venue : via Zoom
Speaker : Yves Benoist, CNRS and Université Paris-Saclay

Join Zoom Meeting https://nus-sg.zoom.us/j/85852787585?pwd=MDZWUjV5SlNoaFJDM0trWnRJMWdIdz09 Meeting ID: 858 5278 7585 Passcode: 236000 In this expository talk, I will give three examples where p-adic Lie groups are crucial tools to understand dense subgroups in compact real Lie groups. The first one is the Tits alternative. The second one is the Prasad-Rapinchuk regularity theorem. The third one is the Sarnak spectral gap conjecture for random walk on subgroups with algebraic coefficients.

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Date/Time : 03 Jun 2021 16:00
Venue : via Zoom
Speaker : Liu Yong, Institute of High Performance Computing

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Transformer has been developed as one of most impactful deep neural network architecture for Natural Language Processing (NLP) tasks such as machine translation, question & answer, and reading comprehension. Its effectiveness has been demonstrated by the impressive performance of large language model such as GPT-3 to produce convincing stream of human-like text. This talk will cover the mechanism of transformer and how it has been used for computer vision tasks such as image classification, followed by our recent work on transformer-based medical image segmentation for multiple diseases. Compared with representative existing methods, the proposed method consistently achieved the highest segmentation accuracy, and exhibited good cross-domain generalization capabilities.

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Date/Time : 27 May 2021 16:00
Venue : via Zoom
Speaker : Niangjun Chen, Singapore University of Technology and Design

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Many problems in data science and cloud computing can be cast as online optimization problems. In this talk, we study general online optimization problems with uncertainties, where the payoff or cost information is only known to the decision-maker up to some bounded uncertainty set. We develop an algorithmic framework, CRT, that can be applied to both online cost minimization problems with revenue constraints and online revenue maximization problems with inventory constraints. In both scenarios, we design online algorithms based on the CRT framework and prove their optimality in terms of competitive ratio. Furthermore, while prior works on online nonlinear optimization with inventory constraint require the revenue functions to be concave, we show that CRT-based algorithms have optimal competitive ratios in general online optimization settings with non-convex cost functions or non-concave revenue functions. We demonstrate our proposed algorithms’ practical performance via trace-driven simulations in a cloud computing application against prominent existing algorithms.

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Date/Time : 26 May 2021 15:00
Venue : via Zoom
Speaker : Wen Deng, Chinese Academy of Sciences

Join Zoom Meeting https://nus-sg.zoom.us/j/83402872988?pwd=UWxhOEFKam9oYnk1N1FqT2JCdnFzdz09 Meeting ID: 834 0287 2988 Password: 471879 We consider the stability problem of the Couette flow for the 2D Boussinesq system. Due to the presence of the buoyancy forcing, the energy of the standard Boussinesq equations could grow in time. It is the enhanced dissipation created by the linear non self-adjoint operator in the perturbation equation that makes the stability possible. In this work, we prove the nonlinear stability of the Couette flow for 2D Boussinesq system with full dissipation and with only vertical dissipation in Sobolev spaces. This is a joint work with J. Wu and P. Zhang.

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Date/Time : 21 May 2021 09:00
Venue : via Zoom
Speaker : Yudong Chen, Cornell University

Join Zoom Meeting https://nus-sg.zoom.us/j/82907817525?pwd=bU1tWlNwTXhwbC9sa3R5eDZKOVovQT09 Meeting ID: 829 0781 7525 Passcode: 752172 We consider the problems of learning discrete structures from network data under statistical settings. Popular examples include various planted and block models, Z2 synchronization and mixture models. Semidefinite programming (SDP) relaxation has emerged as a versatile and robust approach to these problems. We show that despite being a relaxation, SDP achieves the optimal Bayes error rate in terms of distance to the target solution. Moreover, SDP relaxation is provably robust under the so-called semirandom model, which frustrates many existing algorithms. Our proof involves a novel primal-dual analysis that establishes what we call the Hidden Integrality property: the SDP relaxation tightly approximates the optimal (yet unimplementable) integer program with oracle information. Joint work with Yingjie Fei (Cornell Ph.D.), who won 2nd place in INFORMS Nicholson Student Paper Competition.

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