Date/Time : 22 Nov 2022 10:00
Venue : S17 #04-06 (SR1)
Speaker : Carsten Chong, Columbia University

In recent years, there has been substantive empirical evidence that stochastic volatility is rough. In other words, the local behaviour of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian motion with Hurst parameter H<0.5. In this paper, we derive a consistent and asymptotically mixed normal estimator of H based on high-frequency price observations. In contrast to previous works, we work in a semiparametric setting and do not assume any a priori relationship between volatility estimators and true volatility. Furthermore, our estimator attains a rate of convergence that is known to be optimal in a minimax sense in parametric rough volatility models.

This talk is based on joined work with Marc Hoffmann (Paris Dauphine), Yanghui Liu (Baruch College), Mathieu Rosenbaum and Grégoire Szymanski (both Ecole Polytechnique).

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Date/Time : 18 Nov 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Hoang-Hung Vo, Saigon University

In this talk, I will present some recent advances for the qualitative properties of the principal eigenvalue of nonlocal operators, which arise from many natural phenomena, especially in ecology and population dynamics. I shall first introduce several notions of generalized principal eigenvalue in the sense of Berestycki-Nirenberg-Varadhan and then employ them to investigate the qualitative properties of the principal eigenvalue the asymptotic behavior with respect to the dispersal range and dispersal rate. Different limits are obtained and linked to different phenomena in ecology. We also obtain the long time dynamics of nonlocal Fisher-KPP equation assuming that the environment is unfavorable far away. By taking into account on the seasonal effect on the population, the qualitative properties of the principal eigenvalue of time-periodic nonlocal operators are also discussed, new limiting properties of the principal eigenvalue and long time dynamics nonlocal Fisher-KPP equation with time periodic coefficients are further investigated.

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Date/Time : 17 Nov 2022 15:30
Venue : S17 #04-04 (SR3)
Speaker : Renaud Leplaideur, University of New Caledonia

This is a joined work with A. Baraviera from UFRGS (Brazil). We introduce a notion of substitution on the colored binary trees.

In the first step I will present the motivtions for this work. Strangely (perhaps), they come from questions in ergodic theory and thermodynamic formalism.

In the second step I will present how we define these substreetutions, and then present one example.

The main result is that the associated “attractor” is minimal and non-periodic. I will also present many open questions about these objects.

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Date/Time : 16 Nov 2022 16:00
Venue : S15 #03-15 (Seminar Room L3)
Speaker : Cristian Calude, University of Auckland

Abstract: We construct a class of 3-dimensional photonic quantum random number generators and prove that each generates maximally unpredictable digits via measurements that are robust to errors. In particular, every sequence generated is strongly incomputable; hence its quality is provable better than that of every pseudo-random sequence. We also briefly contrast 2-dimensional and 3-dimensional quantum random number generators, discuss photonic implementations and show the superiority of the latter ones. These results suggest that incomputability in physics is real and practically useful.

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Date/Time : 15 Nov 2022 15:00
Venue : S17 #04-04 (SR3)
Speaker : Timo Takala, Aalto University

The John-Nirenberg space JNp is a space of functions with bounded oscillation depending on a parameter p. It is a generalization of the space of bounded mean oscillation BMO. The most profound result on JNp functions is probably the John-Nirenberg inequality, which shows that the space JNp is embedded in the weak Lp space. In this talk I will present the space JNp and some of its fundamental properties. I will also show my recent results on weak Lp type integrals of JNp functions.

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Date/Time : 11 Nov 2022 16:00
Venue : via Zoom
Speaker : David Hilditch, The University of Lisbon

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https://nus-sg.zoom.us/j/84455764091?pwd=WDF6dWJFVHVFNHZSWHY3VlNWM0xodz09

Meeting ID: 844 5576 4091
Passcode: 171086

In my talk I will consider the initial value problem in general relativity, with smooth initial data tuned to the threshold of black hole formation. Starting in the early 1990s with the work of Choptuik such setups have been studied numerically with various simplifying assumptions. For instance spherical symmetry has often been assumed and combined with a scalar field matter model to drive the dynamics. In that context a remarkably simple phenomenology manifests near the threshold of collapse, with a naked singularity appearing in the limit of perfect tuning. I will review recent progress in the more subtle setting in which symmetry assumptions are dropped, so as to include the fundamental case of pure gravitational waves collapsing under their own self-gravity.

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Date/Time : 11 Nov 2022 14:00
Venue : via Zoom
Speaker : Liping Li, Hunan Normal University

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https://nus-sg.zoom.us/j/85349169300?pwd=bE9Ed2ZLelNHdVpjSFV5YnEwdlJpUT09

Meeting ID: 853 4916 9300
Passcode: 176749

Abstract: In this talk we describe an approach to classify irreducible discrete representations of infinite linear groups, based on Artin’s theorem connecting discrete representations of topological groups and sheaves of modules over atomic sites as well as some recent development in representation stability theory.

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Date/Time : 10 Nov 2022 15:30
Venue : S17 #05-11 (SR5)
Speaker : Fabrizio Bianchi, University of Lille

Abstract:  We discuss the stability of holomorphic dynamical systems under perturbation. In dimension 1, the theory is now classical and is based on works by Lyubich, Mané-Sad-Sullivan and DeMarco. I will review this theory and present a recent generalisation valid in any dimension. Since classical 1-dimensional techniques no longer apply in higher dimensions, our approach is based on ergodic and pluripotential methods.

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Date/Time : 10 Nov 2022 10:00
Venue : via Zoom
Speaker : Yoonsang Lee, Darthmouth College

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

Meeting ID: 977 560 6531
Passcode: 123321

We propose a neural network-based approach to the homogenization of multiscale problems. The proposed method uses a derivative-free formulation of a training loss, which incorporates Brownian walkers to find the macroscopic description of a multiscale PDE solution. Compared with other network-based approaches for multiscale problems, the proposed method is free from the design of hand-crafted neural network architecture and the cell problem to calculate the homogenization coefficient. The exploration neighborhood of the Brownian walkers affects the overall learning trajectory. We determine the bounds of micro- and macro-time steps that capture the local heterogeneous and global homogeneous solution behaviors, respectively, through a neural network. The bounds imply that the computational cost of the proposed method is independent of the microscale periodic structure for the standard periodic problems. We validate the efficiency and robustness of the proposed method through a suite of linear and nonlinear multiscale problems with periodic and random field coefficients.

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