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In this talk we show that bounded harmonic functions are constant on gradient shrinking Ricci solitons with CSC by frequency function method. As an application, we show that the space of harmonic func...
The motivation to study manifolds with scalar curvature bounded from below comes from Mathematical General Relativity and Riemannian Geometry. In this talk, I'll first briefly introduce some problems ...
Peaked soliton dynamics is one of the most intriguing features of the Camassa-Holm-type integrable equations. In this talk, I will give a review on the issue of the stability of peaked solitons, inclu...
The problem of using covariates to predict shapes of objects in a regression setting is important in many fields. A formal statistical approach, termed geodesic regression model, is commonly used for ...
In this talk, I will majorly focus on the scalar peakon models developed in the last 30 years. Most integrable peakon equations come from the negative order flow in the hierarchy. I will take some exa...
In this talk, I will introduce the precise late-time asymptotics for the scalar field in the interior of a non-static subextreme Kerr black hole, which provides a new proof of the generic $H^1_{loc}$-...
We consider the weakly dissipative and weakly dispersive Burgers-Hopf-Korteweg-de-Vries equation with the diffusion coefficient ε and the dispersion rate δ in the range δ/ε → 0. We study thetravelling...
We perform a comparative Monte Carlo study of the easy-plane deconfined critical point (DCP) action and its short-range counterpart to reveal close similarities between the two models for intermediate...
In this paper, we present a global invariant, called renormal-ized volume, which can be defined for a large class of conformally compact manifolds. We use this definition to show a local volume compa...
This paper is concerned with a Yamabe-type flow for compact Riemannian manifolds with boundary. The convergence of this flow is established if the manifold with boundary satisfies either a generic con...
Distributed functional scalar quantization (DFSQ) theory provides optimality conditions and predicts performance of data acquisition systems in which a computation on acquired data is desired. We addr...
We consider an one-dimensional conservation law with random space-time forcing and calculate using large deviations the exponentially small probabilities of anomalous shock profile displacements. Unde...
We define a new grading, that we call the "level grading", on the algebra of polynomials generated by the derivatives $u_{k+i}=\partial^{k+i}u/\partial x^{k+i}$ over the ring $K^{(k)}$ of $C^{\infty}$...
We consider the dynamics of a massless scalar field with time-dependent sources in the adiabatic limit. This is an example of an adiabatic problem without spectral gap. The main goal of our paper is t...
We consider a natural extension of the Petersson scalar product to the entire space of modular forms of integral weight $k\ge 2$ for a finite index subgroup of the modular group. We show that Hecke op...

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