Date/Time : 16 Dec 2025 14:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Yongchun Li, The Chinese University of Hong Kong

The low-rank constrained optimization arises in various machine learning and operations research problems. It minimizes a linear objective function subject to multiple two-sided linear inequalities and a low-rank domain set. Although the low-rank constrained optimization is generally NP-hard, a viable approach is to convexify the domain set (i.e., replace the domain set with its convex hull), known as “partial convexification.” Partial convexification often leads to a tractable convex relaxation; however, its solution quality lacks theoretical guarantees. To fill this gap, (i) we establish the necessary and sufficient condition under which the partial convexification matches the original low-rank constrained optimization; and (ii) we derive an upper bound on the minimum rank among all the optimal solutions of the partial convexification and prove its tightness. To efficiently solve the partial convexification, we develop a column generation algorithm combined with a rank-reduction algorithm. This combination ensures that the output solution satisfies the theoretical guarantees. Finally, our numerical experiments validate the strength of the partial convexification and the effectiveness of the proposed algorithms.

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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 : 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 : 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 : 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 09:30
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Various speakers,

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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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Date/Time : 08 Dec 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Yuta Takaya, Tokyo University

The relation between period integrals and L-functions, studied since the work of Hecke and Tate, has recently been reformulated by Ben-Zvi–Sakellaridis–Venkatesh as relative Langlands duality. In this talk, I will present a version of this duality, the normalized period conjecture, in the framework of the categorical local Langlands correspondence à la Fargues-Scholze. I will describe computations for the Iwasawa-Tate and Hecke periods that support this conjecture, and discuss how it leads to a relation between distinguished representations and distinguished L-parameters. This talk is based on joint work with Milton Lin.

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Date/Time : 03 Dec 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Jose Carrillo, University of Oxford

Many phenomena in the life sciences, ranging from the microscopic to macroscopic level, exhibit surprisingly similar structures. Behaviour at the microscopic level, including ion channel transport, chemotaxis, and angiogenesis, and behaviour at the macroscopic level, including herding of animal populations, motion of human crowds, and bacteria orientation, are both largely driven by long-range attractive forces, due to electrical, chemical or social interactions, and short-range repulsion, due to dissipation or finite size effects. Various modelling approaches at the agent-based level, from cellular automata to Brownian particles, have been used to describe these phenomena. An alternative way to pass from microscopic models to continuum descriptions requires the analysis of the mean-field limit, as the number of agents becomes large. All these approaches lead to a continuum kinematic equation for the evolution of the density of individuals known as the aggregation-diffusion equation. This equation models the evolution of the density of individuals of a population, that move driven by the balances of forces: on one hand, the diffusive term models diffusion of the population, where individuals escape high concentration of individuals, and on the other hand, the aggregation forces due to the drifts modelling attraction/repulsion at a distance. The aggregation-diffusion equation can also be understood as the steepest-descent curve (gradient flow) of free energies coming from statistical physics. Significant effort has been devoted to the subtle mechanism of balance between aggregation and diffusion. In some extreme cases, the minimisation of the free energy leads to partial concentration of the mass. Aggregation-diffusion equations are present in a wealth of applications across science and engineering. Of particular relevance is mathematical biology, with an emphasis on cell population models. The aggregation terms, either in scalar or in system form, is often used to model the motion of cells as they concentrate or separate from a target or interact through chemical cues. The diffusion effects described above are consistent with population pressure effects, whereby groups of cells naturally spread away from areas of high concentration. This talk will give an overview of the state of the art in the understanding of aggregation-diffusion equations, and their applications in mathematical biology and machine learning.

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