- TS. Trần Thế Dũng (Trường Đại học Khoa học Tự nhiên, Đại học Quốc gia Hà Nội)
Title: Higher-order Riemannian spline interpolation problems: a unified approach via gradient flows and applications
Abstract: This talk addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks, providing a novel framework for tackling these challenges. This method notably extends to the variational spline interpolation problem on Lie groups, which is frequently encountered in mechanical optimal control theory. As a result, our work contributes to both geometric control theory and statistical shape data analysis.
We rigorously prove the existence of global solutions in H\"{o}lder spaces for the gradient flow and demonstrate that the asymptotic limits of these solutions validate the existence of solutions to the variational spline interpolation problem. This constructive proof also offers insights into potential numerical schemes for finding such solutions, reinforcing the practical applicability of our approach.
- TS. Nguyễn Đình Dương (Yonsei University and Chung-Ang University)
Title: Fluid Equations in Scaling-Critical Function Spaces
Abstract: We investigate several partial differential equations arising in fluid dynamics within the framework of scaling-critical function spaces. The natural scaling of these equations plays a decisive role in determining the appropriate analytic setting for well-posedness and regularity. After recalling the classical critical theory for the incompressible Navier–Stokes system, we examine how similar ideas extend to other fluid models, including those with modified dissipation, additional transport structure, or coupled dynamics. Our focus is on identifying functional spaces—typically based on Besov, Sobolev, or Lebesgue scales—that remain invariant under the intrinsic symmetries of the equations, and on understanding how these critical spaces influence questions of existence, uniqueness, and stability of solutions. The discussion highlights both recent progress and open problems in the critical regularity theory of fluid PDEs.
- TS. Hoàng Mạnh Tuấn (Trường Đại học FPT)
Title: Mathematical modeling and efficient numerical methods with applications to infectious diseases
Abstract: In this talk, we summarize our recent results on mathematical modeling and efficient numerical methods with applications to infectious diseases. Some open problems and potential directions for future research are also presented and discussed.
- TS. Đỗ Văn Hoàn (Học viện Kỹ thuật quân sự)
Title: Mapping Tissue Architecture with AI: Scalable Unsupervised and Supervised Models for Spatial Domain & Niche Discovery
Abstract: Spatial transcriptomics and high-complex spatial omics technologies are transforming our ability to map tissue architecture, cellular microenvironments, and disease-associated niches. However, accurately identifying spatial domains across heterogeneous platforms, multiple slices, and multi-modal assays remains a fundamental computational challenge. In this talk, I will introduce three complementary approaches that jointly address the challenge: an unsupervised Bayesian clustering framework, a transformer-based model for spatial representation learning, and a highly scalable supervised prediction method. These correspond to our three methods: GraphBG, GraphGPT, and Coreset-based Logistic Regression.
First, GraphBG integrates spectral graph convolutions with Bayesian mixture modeling to deliver fast and robust unsupervised domain detection, extending naturally to multi-slice and multi-modal datasets. Second, GraphGPT adapts GPT-style transformers for spatial omics, outperforming conventional ML and GNN baselines in domain classification, spatial smoothness, and biological interpretability. Finally, Coreset-based Logistic Regression introduces a coreset-optimized logistic regression method enabling accurate and scalable transfer of tissue niches across large atlases. Together, these methods provide a unified suite for mapping tissue architecture across technologies, conditions, and scales, paving the way toward consistent cross-platform spatial atlasing.