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 : 26 Nov 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Bjoern Bringmann, Princeton University

Gibbs measures were first introduced in statistical mechanics, where they have been used to describe statistical equilibria of physical systems. Over the last decades, Gibbs measures have also become central objects in probability theory, partial differential equations, and mathematical physics. In this talk, we are interested in the heat, wave, and Schrödinger dynamics corresponding to Gibbs measures. In the first part of the talk, we discuss the invariance of the $\Phi^4_3$-measure under the three-dimensional cubic nonlinear wave equation. In the second part, we then discuss the global well-posedness of the stochastic Abelian-Higgs model, which is the Langevin equation for the Abelian-Higgs measure.

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Date/Time : 08 Oct 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Peter Markowich, King Abdullah University of Science and Technology

We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problems by taking the continuum limits of both network width and depth. The proposed model captures the complex interactions among hidden nodes, overcoming limitations of traditional discrete and ordinary differential equation (ODE)-based models. We explore the well-posedness of the forward propagation problem, analyze the existence and properties of minimizers for the learning task, and provide a detailed examination of necessary and sufficient conditions for the existence of critical points. Controllability and optimality conditions for the learning task with its associated PDE forward problem are established using variational calculus, the Pontryagin Maximum Principle, and the Hamilton-Jacobi-Bellman equation, framing the deep learning process as a PDE-constrained optimization problem. In this context, we prove the existence of viscosity solutions for the latter and we establish optimal feedback controls based on the value functional. This approach facilitates the development of new network architectures and numerical methods that improve
upon traditional layer-by-layer gradient descent techniques. The paper provides a mathematical foundation for connecting neural networks, PDE theory, variational analysis, and optimal control. By integrating these fields, we offer a robust framework that enhances deep learning models’ stability, efficiency, and interpretability.

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Date/Time : 25 Sep 2025 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Keiji Oguiso, The University of Tokyo

My talk is based on my joint work with Professor Koji Fujiwara (Kyoto University) and Professor Xun Yu (Tianjin University).

Main result of my talk is the finiteness of the Neron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic under the assumption that the Picard number greater than or equal to 6 (which is optimal to ensure the finiteness). In this talk, after recalling the notion of hyperbolicity of group due to Gromov and its importance in mathematics, I would like to explain first why the non-elementary hyperbolicity of K3 surface automorphism group is the problem of the Neron-Severi lattices and next how one can deduce the above-mentioned finiteness, via the study of genus one fibrations on K3 surfaces and recent work of Kikuta and Takatsu on geometrically finiteness.

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Date/Time : 25 Sep 2025 15:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Lars Nerger, Alfred Wegener Institute

Data assimilation is used to estimate the state in components of Earth system models, and to estimate parameters that control processes in these models. The estimate is computed by combining the model state with real observations, like the temperature of the ocean surface or winds in the atmosphere, accounting for the uncertainties in both the model and the observations. The observations are characterized by significant uncertainties and by extreme sparseness. For example, for the ocean satellites can only observe the surface while measurements inside the ocean can only be done by ships or autonomous instruments, of which only a few thousand are distributed over the world ocean. Skillful data assimilation methods have been developed to utilize the sparse observational information with complex models used on supercomputers. Here, ensemble simulations provide uncertainty estimates, but multiply the modeling cost. In addition, the model nonlinearity induces challenges because common methods like ensemble Kalman filters assume Gaussian error distributions. This presentation will discuss the computational, algorithmic, and practical challenges and recent developments in these complex applications of data assimilation.

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Date/Time : 24 Sep 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Shuichiro Takeda, The University of Osaka

Let V be a quadratic space over a nonarchimedean local field of characteristic 0. The orthogonal group O(V) and the special orthogonal group SO(V) have a unique nontrivial GL_1 -extension called GPin(V) and GSpin(V), respectively. Let W\subseteq V be a subspace of codimension 1. Then there are natural inclusions GPin(W)\subseteq
GPin(V) and GSpin(W)\subseteq GSpin(V). One can then consider the Gan-Gross-Prasad (GGP) periods for GPin and GSpin. In this talk, I will talk about the multiplicity-at-most-one theorem for the local GGP periods for GPin and GSpin. This is a joint work with Melissa Emory.

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Date/Time : 19 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

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Date/Time : 18 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

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Date/Time : 17 Sep 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Luo Tao, Shanghai Jiao Tong University

Artificial Intelligence for Mathematics (AI4Math) is a rapidly advancing field with significant implications for both academic research and industrial applications. In this talk, we will review the evolution of AI-driven mathematical reasoning, tracing the transition from intuitive, natural language-based approaches to the rigorous, verifiable proofs enabled by formal languages. After providing a foundational overview, we conduct a technical survey of three key research frontiers within the formal systems: Automated Theorem Proving, Autoformalization, and Automated Semantic Evaluation. The primary focus is placed on our contributions to the latter two areas, which are crucial for bridging the gap between human mathematical knowledge and machine-verifiable logic.

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