Date/Time : 12 Nov 2021 16:00
Venue : via Zoom
Speaker : Alexandros Beskos, University College of London

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

Meeting ID: 977 560 6531
Passcode: 123321

Abstract: Bayesian inference for nonlinear diffusions, observed at discrete times,is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology – borrowing ideas from statistical physics and computational chemistry – for inferring the posterior distribution of latent diffusion paths and model parameters, given observations of the process. Joint configurations of the underlying process noise and of parameters, mapping onto diffusion paths consistent with observations, form an implicitly defined manifold. Then, by making use of a constrained Hamiltonian Monte Carlo algorithm on the embedded manifold, we are able to perform computationally efficient inference for a class of discretely observed diffusion models. Critically, in contrast with other approaches proposed in the literature, our methodology is highly automated, requiring minimal user intervention and applying alike in a range of settings, including: elliptic or hypo-elliptic systems; observations with or without noise; linear or non-linear observation operators. Exploiting Markovianity, we propose a variant of the method with complexity that scales linearly in the resolution of path discretisation and the number of observation times. Example Python code is given at git.io/m-mcmc.

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Date/Time : 11 Nov 2021 16:00
Venue : via Zoom
Speaker : Ruiwen Shu, University of Oxford

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https://nus-sg.zoom.us/j/82284835444?pwd=ZDFaR1RDeDFWQU1iQmFidHYwbUhCQT09

Meeting ID: 822 8483 5444
Passcode: 965013

Abstract:  Erdős and Turán proved a classical inequality on the distribution of roots for a complex polynomial in 1950, depicting the fundamental interplay between the size of the coefficients of a polynomial and the distribution of its roots on the complex plane. Various results have been dedicated to improving the constant in this inequality, while the optimal constant remains open. In this paper, we give the optimal constant, i.e., prove the sharp Erdős-Turán inequality. To achieve this goal, we reformulate the inequality into an optimization problem, whose equilibriums coincide with a class of energy minimizers with the logarithmic interaction and external potentials. This allows us to study their properties by taking advantage of the recent development of energy minimization and potential theory, and to give explicit constructions via complex analysis. Finally the sharp Erdős-Turán inequality is obtained based on a thorough understanding of these equilibrium distributions.

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Date/Time : 11 Nov 2021 09:00
Venue : via Zoom
Speaker : Yaping Yang, University of Melbourne

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https://nus-sg.zoom.us/j/85407853911?pwd=b3E4ZXNERkFaOGtQalNFKzN4MldrUT09

Meeting ID: 854 0785 3911
Passcode: 295101

Abstract:  In this talk, I will explain a connection between stable homotopy theory and representation theory. I will focus on one application of this idea to a problem arising from the modular representation theory. More explicitly, we study a family of new quantum groups labelled by a prime number and a positive integer constructed using the Morava E-theories. Those quantum groups are related to Lusztig’s 2015 reformulation of his conjecture from 1979 on character formulas for algebraic groups over a field of positive characteristic. This talk is based on my joint work with Gufang Zhao.

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Date/Time : 10 Nov 2021 16:00
Venue : via Zoom
Speaker : Maxime Wolff, Sorbonne University

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

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract: In this talk I will present joint works with Kathryn Mann, in which we take advantage of strong rigidity properties of the actions of some Fuchsian groups on the circle. From this, we derive rigidity properties of some larger groups acting on the circle, such as mapping class groups of pointed surfaces, as well as the existence of groups of critical regularity.

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Date/Time : 10 Nov 2021 16:00
Venue : via Zoom
Speaker : Manat Mustafa, Nazarbayev University

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Abstract: The talk employs the punctuality paradigm in the studies of numberings. We consider the punctual numberings, i.e. uniform computations for families of primitive recursive functions. The punctual reducibility between numberings is induced by primitive recursive functions. This approach gives rise to upper semilattices of degrees, which are called Rogers pr-semilattices. The main focus of the talk will be the structural properties of Rogers pr-semilattices. We will show several examples, which highlight further contrasts between the punctual framework and the classical theory of computable numberings.

All results are obtained in joint work with Nikolay Bazhenov and Sergei Ospichev.

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Date/Time : 03 Nov 2021 16:00
Venue : via Zoom
Speaker : Zhong Guolei, National University of Singapore

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

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract:  We consider a projective klt pair (X,D) of arbitrary dimension with the anti-log canonical divisor -(K+D) being strictly nef. In this talk, I will first show that such X is rationally connected. In particular, when X is a threefold, we show that -(K+D) is indeed ample, which gives a positive answer to the singular version of Campana-Peternell’s conjecture (for the threefold case). Finally, we extend our first result to the (relative) fibration case and study the geometric structure of this fibration. This is a joint work with Jie Liu, Wenhao Ou, Juanyong Wang and Xiaokui Yang.

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Date/Time : 03 Nov 2021 16:00
Venue : via Zoom
Speaker : Wu Guohua, Nanyang Technological University

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Abstract:   Domain theory was contrived by Dana Scott in 1969 as a theory of approximating computations. This topic was also raised by Ershov independently. In this talk, I will give a brief introduction of domain theory first, hopefully, from the beginning, and then move to the comparison of various substitutions of Hausdorff property, including sobriety, well-filteredness and monotone convergence.

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Date/Time : 01 Nov 2021 10:00
Venue : via Zoom
Speaker : Yingzhou Li, Fudan University

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https://nus-sg.zoom.us/j/86776918257?pwd=cHJ3eDZNclUweWhBaitPZFRieGtNQT09

Meeting ID: 867 7691 8257
Passcode: 061477

Abstract: Coordinate descent methods are considered for eigenvalue problems based on a reformulation of the leading eigenvalue problem as a nonconvex optimization problem. The convergence of several deterministic coordinate methods is analyzed and compared. We also analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes. Under generic assumptions, we prove that the algorithm iterate will almost surely escape strict saddle points of the objective function. As a result, the algorithm is guaranteed to converge to local minima if all saddle points are strict. Numerical examples of applications to quantum many-body problems demonstrate the efficiency and provide benchmarks of the proposed coordinate descent methods.

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Date/Time : 29 Oct 2021 09:00
Venue : via Zoom
Speaker : Luca Spolaor, University of California San Diego

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https://nus-sg.zoom.us/j/86945333380?pwd=Q0VEM2drc0YrKzFUc3VHbFVqNjRCQT09

Meeting ID: 869 4533 3380
Passcode: 583463

Abstract:  In this talk I will discuss some results about isolated singularities of minimal surfaces arising from minimization and Min-Max. In particular, I will focus on the local description of minimal surfaces at such singularities and on their generic behavior with respect to a change in the ambient metric.

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