Date/Time : 12 Dec 2025 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Su Chunmei, Tsinghua University

The quality of the mesh is crucial for simulating curvature flows, as standard approaches may fail due to mesh distortion. We first present a series of high-order parametric finite element methods based on the BGN formulation for solving various types of flows involving curves and surfaces. Extensive numerical experiments demonstrate the anticipated high-order accuracy while maintaining favorable mesh quality throughout the evolution process. Secondly, for flows involving multiple geometric structures, such as surface diffusion—which reduces area while preserving volume—we propose a type of structure-preserving method that incorporates two scalar Lagrange multipliers along with two evolution equations related to area and volume, respectively. These schemes effectively preserve the geometric structure at a fully discrete level. Comprehensive numerical experiments illustrate that our methods achieve the desired temporal accuracy, while simultaneously preserving the geometric structure of the surface diffusion.

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Date/Time : 12 Dec 2025 15:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Yun GAO, Shanghai University

The Galilean conformal algebra is an infinite-dimensional extension of the finite-dimensional Galilean conformal algebra in (d+1) dimensional space-time. We use simple modules over the finite-dimensional solvable Lie algebras to construct many simple restricted modules.

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Date/Time : 11 Dec 2025 15:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Guillaume Bal, University of Chicago

A seemingly widely accepted conjecture in the physical literature states that classical wave-fields propagating in random media over large distances eventually follow a complex circular Gaussian distribution. In this limit, the wave intensity becomes exponentially distributed, which corroborates the speckle patterns of, e.g., laser light observed in experiments. This talk reports on a recent result settling the conjecture in the weak-coupling, paraxial regime of wave propagation, which is accurate and routinely used in the application of laser light propagation in turbulent atmospheres. The limiting macroscopic Gaussian wave-field is fully characterized by a correlation function that satisfies an anomalous diffusion equation. Numerical simulations illustrate the theoretical findings.

This is joint work with Anjali Nair.

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Date/Time : 11 Dec 2025 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ivan Fesenko, Westlake University, China

Zeta functions are the central object in number theory.

Iwasawa and Tate independently described how using adelic structures from class field theory one can obtain an integral presentation for zeta functions of number fields and prove their key properties (except the generalised Riemann hypothesis). They used Haar measure on abelian locally compact groups and associated harmonic analysis.

Modern number theory often works with two-dimensional objects such as elliptic curves over number fields and their proper regular models. Associated 2d local and adelic structures are far from locally compact. It was an open problem to produce a 2d version of the Iwasawa-Tate theory. The speaker introduced higher Haar measure and integration on 2d local and adelic objects and used them to establish such a 2d generalisation. This talk will briefly present this 2d theory and how it further leads to a new approach to the Birch and Swinnerton-Dyer conjecture.

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Date/Time : 10 Dec 2025 15:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Heikki Kälviäinen, Lappeenranta-Lahti University of Technology

The presentation considers computer vision and machine learning in plankton image recognition and animal re-identification, especially from a point of view of applications. Digital image processing and analysis with machine learning methods could enable efficient solutions for various areas of useful data-centric engineering applications. Challenges with imbalance of datasets, domain adaptation, active learning, open set classification, and metric learning of similarities are considered and related examples are given in plankton recognition and animal re-identification, based on the research of LUT Computer Vision and Pattern Recognition Laboratory (CVPRL).

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