Date/Time : 14 Jan 2022 09:00
Venue : via Zoom
Speaker : Alexander Kiselev, Duke University

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https://nus-sg.zoom.us/j/81290641127?pwd=eUowVGZYN3REWndWVHRKK2piQ1pUUT09

Meeting ID: 812 9064 1127
Passcode: 612753

Abstract: The Euler equation describing motion of ideal fluid goes back to 1755. The analysis of the equation is challenging since it is nonlinear and nonlocal. Its solutions are often unstable and spontaneously generate small scales. The fundamental question of global regularity vs finite time singularity formation remains open for the Euler equation in three spatial dimensions. In this lecture, I will review the history of this question and its potential connection with the arguably greatest unsolved problem of classical physics, turbulence. Results on small scale and singularity formation in two dimensions and for a number of related models will also be presented.

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Date/Time : 13 Jan 2022 09:00
Venue : via Zoom
Speaker : Holden Lee, Duke University

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https://nus-sg.zoom.us/j/81518116179?pwd=bGkvanY2aTlra1pLeEpKQzBSaVdBdz09

Meeting ID: : 815 1811 6179
Passcode: 461200

Abstract: Probabilistic methods in machine learning have made impressive progress in generating realistic images and videos, as well as building interpretable models with uncertainty quantification. In this talk, I will provide algorithms for two fundamental problems in probabilistic machine learning: sampling from multimodal distributions and estimating normalizing constants. I will show how to combine Langevin dynamics–an algorithm based on gradient descent with Gaussian noise–with tools from statistical physics and numerical analysis to design faster algorithms for these problems. Finally, I will touch on an application to understanding the representational power of normalizing flows, a deep generative model that provides explicit likelihood computation and produces high-resolution natural images.

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Date/Time : 12 Jan 2022 16:00
Venue : via Zoom
Speaker : Jia Jia, National University of Singapore

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https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09

Meeting ID: 875 1147 6637
Passcode: 468399

This is a joint work with Doctor Takahiro Shibata and Professor De-Qi Zhang. The potential density problem of varieties over number fields asks whether the set of rational points of becomes Zariski dense after a finite extension of the base field. In this talk, I will explain how to get potential density from some dynamic conditions on the varieties. I will also talk about the existence of densely many rational points with the maximal arithmetic degree over a sufficiently large number field.

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Date/Time : 12 Jan 2022 09:00
Venue : via Zoom
Speaker : Cheng Mao, Georgia Tech

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https://nus-sg.zoom.us/j/85910065038?pwd=ay9nT0hzR2ROeUs4U3d5dTBoMGNBdz09

Meeting ID: 859 1006 5038
Password: 753065

Abstract: Finding latent structures in networks is an important task in many fields of science and engineering.  For a variety of problems, the task can be formulated as inferring a latent permutation of vertices of a network from noisy data. Problems in this class are often computationally infeasible in the worst case due to the combinatorial nature of permutations, so statistical methods are essential for inference in large-scale networks. This talk will provide an overview of two problems: ranking items from comparisons and matching correlated networks. For each problem, I will introduce an average-case model and the associated task of learning a latent permutation. Then I will discuss recent development of efficient algorithms that come with theoretical guarantees.

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Date/Time : 11 Jan 2022 15:00
Venue : via Zoom
Speaker : Lee Si Ying, Harvard University

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https://nus-sg.zoom.us/j/88612905478?pwd=cjlrSTRiT3MvYmE5WmlNNGJKdERHQT09

Meeting ID: 886 1290 5478
Passcode: 587672

Abstract: The well-known classical Eichler-Shimura relation for modular curves asserts that the Hecke operator $T_p$ is equal, as an algebraic correspondence over the special fiber, to the sum of Frobenius and Verschiebung. Blasius and Rogawski proposed a generalization of this result for Shimura varieties with good reduction at $p$, and conjectured that the Frobenius satisfies a certain Hecke polynomial. I will talk about a recent proof of this conjecture for a large class of Shimura varieties of abelian type, and how this proves semisimplicity of cohomology for some Shimura varieties.

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Date/Time : 10 Jan 2022 13:00
Venue : via Zoom
Speaker : Hadi Daneshmand, Princeton University

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https://nus-sg.zoom.us/j/83955852990?pwd=VUpkT1o2M2pzN01YWWxVTTJ1QmpLQT09

Meeting ID: : 839 5585 2990
Passcode: 158210

Abstract:  Deep neural networks have achieved incredible performance in various domains by automatizing feature extraction with less need for conventional feature engineering. When neurons are well-connected and optimized, their performance goes beyond the human level for image processing. Yet, wiring and optimizing many neurons is a cumbersome engineering task. Over 70 years of research and optimization breakthroughs have advanced the training of deep networks. In this talk, we will cover the main outcomes of these breakthroughs. The talk presents recent studies on batch normalization, the fundamental building of deep neural networks. Leveraging tools from Markov chain theory, we will shed light on the inner workings of batch normalization for deep learning. Then, we will review escaping challenging attractors for neural learning with first-order optimization methods.

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Date/Time : 07 Jan 2022 10:00
Venue : via Zoom
Speaker : Pavitra Krishnaswamy, I2R, A*STAR

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https://nus-sg.zoom.us/j/89775139658?pwd=b3VxL0pDT0ZNTnIrUUV6MWNZK28xQT09

Meeting ID: 897 7513 9658
Passcode: 238865

Abstract:  Real-world health data from clinical records, disease registries, consumer health devices, and mobile applications offer great potential for a number of health intelligence applications. However, effectively learning from these observational datasets remains challenging as they lack detailed annotations, exhibit significant irregularities, and are often of variable quality. In this talk, I will discuss our research efforts in developing machine learning capabilities to address these challenges for targeted screening, allied health and clinical decision support applications.

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Date/Time : 05 Jan 2022 09:00
Venue : via Zoom
Speaker : Pan Wenyu, University of Chicago

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https://nus-sg.zoom.us/j/84440678768?pwd=RUZ3Y2RCTTB3SStuQWtuOWE0YlNDQT09

Meeting ID: 844 4067 8768
Passcode: 224158

Abstract:  Let $\Gamma$ be a Zariski dense Kleinian Schottky subgroup of $\operatorname{PSL}_2(\mathbb{C})$. Let $\Lambda_{\Gamma}\subset \mathbb{C}$ be its limit set, endowed with a Patterson-Sullivan measure $\mu$. I will present the joint work with Jialun Li and Frédéric Naud in which we showed that the Fourier transform of $\mu$ enjoys polynomial decay.  

For $\operatorname{PSL}_2(\mathbb{R})$, this was proved by Bourgain-Dyatlov.  As a corollary, all limit sets of Zariski dense Kleinian groups have a positive Fourier dimension. Another application is uniform “essential” spectral gap for any finite cover of $\Gamma \backslash \mathbb{H}^3$.  I will outline the main ingredients of the proof and talk about some future problems.

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Date/Time : 22 Dec 2021 09:00
Venue : via Zoom
Speaker : Jiaoyang Huang, New York University

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https://nus-sg.zoom.us/j/86201788855?pwd=ZW9WQ0pmM2RTOS9SbSsrakdIS2FRQT09

Meeting ID: 862 0178 8855
Passcode: 627300

Abstract: The success of random matrices in modeling physical systems lies in the universality phenomenon of their eigenvalue statistics. The general belief is for systems with many strongly interacting components, we expect to see random matrix statistics. The universality is well understood for Wigner matrices, which are dense. In this talk, I will first discuss some results concerning random matrix statistics in sparse systems—the sparse random graphs. Beyond matrix setting, random matrix statistics are conjectured to govern the asymptotic behavior of various random growth models and interacting particle systems. However, this was only proven for some exactly solvable models. I will discuss a general strategy to prove the universality of random matrix statistics, and our recent result proving that for random lozenge tilings of polygons, the scaling limit of the extreme path is given by random matrix statistics.

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