Date/Time : 30 Sep 2022 14:00
Venue : S17 #05-12 (SR4)
Speaker : Chung-Ru Lee, National University of Singapore

Abstract: One of the main application of the Relative Langlands Program is providing a description of distinguished representation, which itself has profuse interpretations. In this talk series I will introduce a method to study such problem through the comparison of relative trace formulae, where the theory of endoscopy plays a significant role. In particular, the study of representations on unitary groups that are distinguished by an orthogonal subgroup remains mysterious due to the presence of a type N-spherical root, which requires extra caution when dealt with.

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Date/Time : 30 Sep 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Huang Fukeng, National University of Singapore

Abstract: Recently it has been observed that when the interfacial tension is lower than normal liquids by two to three orders, the pinch-off dynamics is dominated by bulk diffusion [PRL 123, 134501 (2019)], showing a scaling behavior distinct from that dominated by Stokes flow. We employ the Cahn-Hilliard-Navier-Stokes model to investigate the pinch-off dynamics of a liquid thread surrounded by a viscous external fluid. A characteristic length scale is introduced to measure the competition between diffusion and viscous flow in interfacial motion. The crossover between the Stokes regime and the diffusion-dominated regime is investigated numerically and analytically to reveal how the scaling behaviors of similarity solutions are to be qualitatively changed as the characteristic length scale is accessed by the pinching neck of the interface.

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Date/Time : 30 Sep 2022 14:00
Venue : S17 #04-05 (SR2)
Speaker : Mengdi Wang, Princeton University

Abstract:  Consider the estimation of policy gradient (PG) using data that maybe collected in off-policy manners. The talk presents a Policy Gradient Bellman Equation and shows how to leverage Q function approximator for policy gradient estimation via a double fitted iteration. We show that the double fitted iteration is equivalent to a plug-in estimator. Further, the PG estimation error bound is determined by a restricted chi-square divergence that quantifies the interplay between distribution shift and function approximation. A matching Cramer Rao lower bound is also provided.

Next, we show how to extend policy gradient method to reinforcement learning beyond cumulative rewards. In particular, consider the objective that is a general concave utility function of the state-action occupancy measure, containing as special cases maximal exploration, imitation and safety constrained RL. Such generality invalidates the Bellman equation and Sutton’s Policy Gradient Theorem. We derive a new Variational Policy Gradient Theorem for RL with general utilities, which establishes that the parametrized policy gradient may be obtained as the solution of a stochastic saddle point problem. We also exploit the hidden convexity of the Markov decision process and prove that the variational policy gradient scheme converges globally to the optimal policy for the general objective, though the optimization problem is nonconvex.

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Date/Time : 29 Sep 2022 10:00
Venue : via Zoom
Speaker : He Haiyun, National University of Singapore

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  Using information-theoretic principles, we consider the generalization error (gen-error) of iterative semi-supervised learning (SSL) algorithms that iteratively generate pseudo-labels for a large amount of unlabelled data to progressively refine the model parameters. In contrast to most previous works that bound the gen-error, we provide an exact expression for the gen-error and particularize it to the binary Gaussian mixture model. Our theoretical results suggest that when the class conditional variances are not too large, the gen-error decreases with the number of iterations, but quickly saturates. On the flip side, if the class conditional variances (and so amount of overlap between the classes) are large, the gen- error increases with the number of iterations. To mitigate this undesirable effect, we show that regularization can reduce the gen-error. The theoretical results are corroborated by extensive experiments on the MNIST and CIFAR datasets in which we notice that for easy- to-distinguish classes, the gen-error improves after several pseudo-labelling iterations, but saturates afterwards, and for more difficult-to-distinguish classes, regularization improves the generalization performance.

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Date/Time : 28 Sep 2022 15:00
Venue : via Zoom
Speaker : István Tomon, Umeå University

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https://nus-sg.zoom.us/j/88686191741?pwd=ZHVWbmcvejludWpPRmRLUlBjZ00yQT09

Meeting ID: 886 8619 1741
Passcode: 23571113

Abstract:  At least how many hyperplanes are needed to cover the finite space $\mathbb{F}_p^{n}$ if we require that the normal vectors of the hyperplanes span the whole space, and none of the hyperplanes is redundant? This question is related to a number of long-standing conjectures in linear algebra and group theory, such as the Alon-Jaeger-Tarsi conjecture on non-vanishing linear maps, the Additive Basis conjecture, and a conjecture of Pyber about irredundant coset covers. I will talk about some progress on this question, which in particular leads to a solution of the first conjecture in a strong form, makes substantial progress on the second conjecture, and fully resolves the third conjecture. This is based on a joint work with Janos Nagy and Peter Pal Pach.

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Date/Time : 23 Sep 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Nurul Huda binti Mohammad Ramli, Universiti Brunei Darussalam

Abstract: In this talk, I will discuss the methods of kernel density estimation for the estimation of particle concentrations in Lagrangian SDE trajectory models. We consider a simple two-dimensional Lagrangian model to describe the advection-diffusion flow in a chaotic advection regime. This method is chosen because the implemented numerical method to solve its Eulerian Fokker-Planck Equation provides very accurate solutions for the particle concentration, which can be used to assess our kernel density methods from the trajectory models. Some standard techniques of bandwidth selection are briefly discussed, and then a new approach using Green’s function to construct a more accurate kernel density estimator is proposed.

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Date/Time : 22 Sep 2022 10:00
Venue : S17 #05-11 (SR5)
Speaker : Kengo Kamatani, Institute of Statistical Mathematics

Abstract:  We construct a class of non-reversible Metropolis kernels as a multivariate extension of the guided-walk kernel proposed by Gustafson 1998. The main idea of our method is to introduce a projection that maps a state space to a totally ordered group. By using Haar measure, we construct a novel Markov kernel termed Haar-mixture kernel, which is of interest in its own right. This is achieved by inducing a topological structure to the totally ordered group. Our proposed method, the Delta-guided Metropolis–Haar kernel, is constructed by using the Haar-mixture kernel as a proposal kernel. The proposed non-reversible kernel is at least 10 times better than the random-walk Metropolis kernel and Hamiltonian Monte Carlo kernel for the logistic regression and a discretely observed stochastic process in terms of effective sample size per second.

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Date/Time : 16 Sep 2022 09:00
Venue : via Zoom
Speaker : Yusheng Luo, Stony Brook University

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https://nus-sg.zoom.us/j/88075038959?pwd=cDAyUWMwMDVrd1lwZDQwdXJkbzk3QT09

Meeting ID: 880 7503 8959
Passcode: 384618

Abstract: In 1980s, D. Sullivan formulated a dictionary between discrete subgroups of PSL_2(\C), known as Kleinian groups, and rational maps of \hat \C. The Sullivan dictionary provides a conceptual framework for understanding the connections between these two branches of conformal dynamics.

Around the same time, W. Thurston’s 3-dimensional insights revolutionized the theory of Kleinian groups. He formulated the geometrization conjecture for 3-manifolds, and proved the hyperbolization theorem which implies the conjecture for a large class of 3-manifolds. The keys to the hyperbolization theorem are two bounded results for certain deformation spaces of Kleinian groups.

In 1990s, motivated by Thurston’s boundedness theorem and the Sullivan dictionary, C. McMullen conjectured that certain deformation spaces of hyperbolic rational maps are bounded.

In this talk, I will start with a survey of historical backgrounds, and discuss a general strategy of the proof of Thurston’s boundedness theorem. I will then explain how a similar strategy could work for rational maps, and discuss some recent breakthrough towards McMullen’s boundedness conjecture.

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Date/Time : 16 Sep 2022 14:00
Venue : S17 #05-12 (SR4)
Speaker : Emile Takahiro Okada, National University of Singapore

Abstract: In my talk last year I introduced new methods for computing the wavefront set of depth 0 representations using local wavefront sets. In this series of talks I will begin by briefly recalling the main results from that talk before I go on to outline new results and open questions that have come from these ideas. These will fall into roughly 3 categories: the structure theory of nilpotent orbits, new results on the wavefront set, and finally applications to Arthurs packets.

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