HKIAS International Conference on Mathematical Analysis and its Applications 2026

About

Background and objectives of the Conference

This workshop is organized to address the critical need for advanced methodologies in multi-agent systems and AI. As modern challenges grow in scale and complexity, tools are required to analyze and design the intricate interactions within large populations of intelligent agents. The conference brings together experts in AI and multi-agent systems—a framework for modeling decentralized decision-making, learning, and coordination—to apply these cutting-edge techniques to complex challenges across various domains, such as coordination, optimization, and emergent behavior.

The primary objective is to create a dedicated forum where leading experts in mathematics and machine learning can converge to explore the application of multi-agent systems theory to real world AI challenges. The deliverable will be a focused three-day workshop featuring invited presentations, aimed at seeding new research collaborations and culminating in a special journal issue to disseminate the findings.

Organizing Committee

Pierre-Louis Lions

Collège de France, France

Professor · Organizing Committee

Charles Bertucci

Université Paris Dauphine-PSL, France

CNRS Researcher · Organizing Committee

Chenchen Mou

City University of Hong Kong

Associate Professor · Organizing Committee

Mathieu Lauriere

NYU Shanghai, China

Assistant Professor · Organizing Committee

Speakers & Abstracts

Pierre-Louis Lions

Collège de France, France

Professor · Organizing Committee

Title: Remarks on Maths and AI

Abstract: In this talk, we will provide a brief overview of some of the key connections between mathematics and artificial intelligence. It will also highlight the main themes and lectures presented at the Conference.

Professor
Collège de France, France

Pierre-Louis Lions is a French mathematician known for his groundbreaking contributions to partial differential equations, mean field games, and stochastic analysis. He is a Professor at the Collège de France, holding the chair of Partial Differential Equations and Applications. He was awarded the Fields Medal in 1994 for his work on nonlinear partial differential equations, viscosity solutions of Hamilton–Jacobi equations, and the Boltzmann equation. His research has profoundly influenced modern analysis, probability theory, and their applications in economics and finance. He is a member of the French Academy of Sciences and several other national academies. His more recent work includes the development of mean field game theory with Jean-Michel Lasry, which has become a fundamental framework for modeling large populations of interacting agents. Professor Pierre-Louis Lions is one of the most prominent experts, worldwide, of the theory of nonlinear partial differential equations. He is a Professor at the prestigious Collège de France in Paris, where he holds the Chair of "Partial Differential Equations and Applications" since 1992. He has made profound and lasting contributions to the mathematical analysis of the Boltzmann equation, the compressible Navier-Stokes equations, the Hamilton-Jacobi equations, the Hartree-Fock equation, image processing, viscosity solutions, concentration compactness, mean field games, and stochastic partial differential equations. He is Commandeur in the National Order of the Legion of Honor in France. He is a member of the French Academy of Sciences, of the Accademia dei Lincei, of the Academies of Sciences of Argentina, Chile, and Brazil, of the Academia Europaea, of the Istituto Lombardo, of the Accademia di Napoli, of the French Academy of Technologies, of the World Academy of Sciences (TWAS), and of the Royal Academy of Belgium. Professor Lions has received numerous awards, including the prestigious Fields Medal in 1994, the Grand Prize Ampère from the French Academy of Sciences, the Grand Prize from the INRIA, France, the IBM Prize, and the Philip Morris Prize. He is "Doctor Honoris Causa" at Heriot-Watt University, at City University of Hong Kong, at the Ecole Polytechnique Fédérale de Lausanne, at Bucharest University, and at Narvik University. He is listed as an ISI highly cited researcher.

Title: Remarks on Maths and AI

Yali Du

King's College London, UK

Associate Professor

Title: Towards Trustworthy Cooperative AI: Simulating, Aligning, and Governing Multi-Agent Systems

Associate Professor in AI
King's College London, UK
The Alan Turing Institute

Dr Yali Du is an Associate Professor in AI at King's College London and a Turing Fellow at The Alan Turing Institute. She leads the Cooperative AI Lab. Her research aims to build cooperative, safe, and human-aligned AI agents for complex decision-making tasks, with a focus on multi-agent cooperation, human-AI coordination, reinforcement learning, and value alignment. She received the AAAI New Faculty Highlights Award in 2023 and was named a Rising Star in AI (KAUST). She received Responsible AI UK Best Research Paper Awards in 2026. She has delivered tutorials on cooperative multi-agent learning at ACML 2022 and AAAI 2023. She serves as an Associate Editor for the Journal of AAMAS and IEEE Transactions on AI, and has served as an Area Chair for NeurIPS/ICML/ICLR/IJCAI and as a Senior Area Chair for AAMAS 2026-2027, NACCL2027. She has also served on the organising committees of DAI 2025, NeurIPS 2024 and AAMAS 2023&2027.

Title: Towards Trustworthy Cooperative AI: Simulating, Aligning, and Governing Multi-Agent Systems

Abstract: As AI systems increasingly operate as autonomous agents, intelligence is becoming inherently social. Future AI systems will not act in isolation, but will learn, coordinate, communicate, and make decisions alongside humans and other agents in open-ended environments. This shift raises fundamental challenges: How can agents acquire cooperative behaviours? How can they adapt to human preferences and evolving social norms? And how can we ensure safety when intelligent agents interact at scale? In this talk, we present a framework to ground cooperative AI in real-world human contexts. We will explore how to resolve the computational limits of complex social simulation, transition from hand-crafted rewards to dynamic value alignment via mixed-quality human feedback, and replace inflexible numerical costs with intuitive natural language safety boundaries. Together, these interconnected works outline a cohesive pathway for building cooperative AI that is highly scalable and deeply aligned with human intent. Finally, I will outline a research agenda for building trustworthy agent societies where learning, coordination and safety continue beyond deployment.

Mathieu Lauriere

NYU Shanghai, China

Assistant Professor

Title: Clustering in Deep Stochastic Transformers

Assistant Professor of Mathematics and Data Science
NYU Shanghai, China

Mathieu Lauriere is currently an assistant professor of Mathematics and Data Science at NYU Shanghai. He obtained his MS from University Paris 6 and ENS Cachan, and his PhD from University Paris 7. He was a Postdoctoral Fellow at the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai and a Postdoctoral Research Associate at Princeton University, in the Operations Research and Financial Engineering (ORFE) department. Prior to his current position NYU Shanghai, he was a Visiting Faculty Researcher at Google Research, in the Brain Team (Paris).

Title: Clustering in Deep Stochastic Transformers

Abstract: Transformers have revolutionized deep learning across various domains but understanding the precise token dynamics remains a theoretical challenge. Existing theories of deep Transformers with layer normalization typically predict that tokens cluster to a single point; however, these results rely on deterministic weight assumptions, which fail to capture the standard initialization scheme in Transformers. In this work, we show that accounting for the intrinsic stochasticity of random initialization alters this picture. More precisely, we analyze deep Transformers where noise arises from the random initialization of value matrices. Under diffusion scaling and token-wise RMS normalization, we prove that, as the number of Transformer layers goes to infinity, the discrete token dynamics converge to an interacting-particle system on the sphere where tokens are driven by a common matrix-valued Brownian noise. In this limit, we show that initialization noise prevents the collapse to a single cluster predicted by deterministic models. For two tokens, we prove a phase transition governed by the interaction strength and the token dimension: unlike deterministic attention flows, antipodal configurations become attracting with positive probability. Numerical experiments confirm the predicted transition, reveal that antipodal formations persist for more than two tokens, and demonstrate that suppressing the intrinsic noise degrades accuracy. Joint work with Lev Fedorov, Michaël E. Sander, Romuald Elie, and Pierre Marion.

Chenchen Mou

City University of Hong Kong, Hong Kong SAR

Associate Professor

Title: Master Equations of Mean Field Games of Controls

Abstract: In this manuscript, we establish the global well-posedness for master equations of mean field games of controls, where the interaction is through the joint law of the state and control. Our results are proved under two different conditions: the Lasry-Lions monotonicity and the displacement λ-monotonicity, both considered in their integral forms.

Tianyang Nie

Shandong University, China

Professor

Title: Indefinite Linear–Quadratic Mean-Field Game and Optimal Control Problem with Partial Information

Professor
Shandong University, China
Director, CSIAM Activity Group on Intelligent Control and Game Theory
Director, Shandong Provincial Key Laboratory of Stochastic System Control and Scientific Computing

Dr. Tianyang Nie has published more than 30 papers in the journals of the fields in stochastic analysis, control theory and mathematical finance, including SIAM J. Control Optim., Math. Finance, Finance Stoch. and Math. Oper. Res. He has conducted research on stochastic analysis and control theory of forward-backward stochastic systems as well as their application in contract pricing problems in nonlinear markets. He proposed methods including control projection, adjoint operator, dynamic programming principle with stopping time, to solve the constrained stochastic optimal control problems of forward-backward systems. He proposed discounting method for mean-field backward stochastic differential equations and established the wellposdness of such equations, he also established the wellposdness of fractional backward stochastic differential equation by introducing fractional norm. Moreover, he also established the unilateral pricing theory to solve the open problem of pricing the contracts in nonlinear markets. He serves as the Director of CSIAM Activity Group on Intelligent Control and Game Theory, and as the Director of the Shandong Provincial Key Laboratory of Stochastic System Control and Scientific Computing, and as an editorial board member of the journal Applied Mathematics and Computation.

Title: Indefinite Linear–Quadratic Mean-Field Game and Optimal Control Problem with Partial Information

Abstract: We investigate an indefinite linear-quadratic partially observed mean field game with common noise, incorporating both state-average and control-average effects. In our model, each agent's state is observed through both individual and public observations. It is noteworthy that the weighting matrices in both the cost functional are allowed to be indefinite. We derive the optimal decentralized strategies using the Hamiltonian approach and establish the well-posedness of the resulting Hamiltonian system by employing a relaxed compensator. The associated consistency condition and the feedback representation of decentralized strategies are also established, and we demonstrate that the set of decentralized strategies forms an ε-Nash equilibrium. We also investigate mean-field linear-quadratic optimal control problem in the indefinite case with partial information. By employing the backward separation approach, we derive the optimal control from a Hamiltonian system without requiring a monotonicity condition. The feedback representation of optimal control is provided by the indefinite Riccati equations. As an application, we solve a mean variance portfolio selection problem. The talk is based on the joint work with Dr. Tian Chen, Prof. Guangchen Wang, Prof. Zhen Wu and Mr. Weiye Wu.

Shanjian Tang

Fudan University, China

Professor

Title: Newton Algorithm of Backward Stochastic Riccati Differential Equation

Abstract: The Bellman equation for optimal control of non-Markovian stochastic differential equations is known to display as a fully nonlinear backward stochastic partial differential equation. In the Linear quadratic optimal control problem with random coefficients, it is reduced to a backward stochastic Riccati Equation (SRDE).

Peng Wang

University of Macau, Macau SAR

Assistant Professor

Title: Understanding Distribution Learning of Diffusion Models from a Low-Dimensional Perspective

Assistant Professor
University of Macau, Macau SAR
Department of Artificial Intelligence and Department of Computer Science

Dr. Peng Wang is an Assistant Professor in the Department of Artificial Intelligence and the Department of Computer Science at the University of Macau. Previously, he was a postdoctoral research fellow at the University of Michigan. He received his Ph.D. from the Department of Systems Engineering and Engineering Management at The Chinese University of Hong Kong. His research lies at the intersection of optimization, machine learning, and artificial intelligence, with current focus on the mathematical and optimization foundations of deep learning and generative AI models. He received a Best Paper Runner-up Award at the ICML 2026 Workshop on Foundations of Deep Generative Models and a Rising Star Award at the 2024 Conference on Parsimony and Learning.

Title: Understanding Distribution Learning of Diffusion Models from a Low-Dimensional Perspective

Abstract: Despite their empirical success across a wide range of generative tasks, the fundamental principles underlying the ability of diffusion models to learn data distributions are poorly understood. In this work, we develop a new mathematical framework that explains how diffusion models can effectively learn low-dimensional distributions from a finite number of training samples without suffering from the curse of dimensionality. Specifically, motivated by the intrinsic low-dimensional structure of image data, we theoretically analyze a setting in which the data distribution is modeled as a mixture of low-rank Gaussians. Under a suitable network parameterization, we show that optimizing the training objective of diffusion models is equivalent to solving the canonical subspace clustering problem over the training samples, where each subspace basis corresponds to the low-rank covariance of a Gaussian component. This equivalence allows us to show that the sample complexity for learning the underlying distribution scales linearly with the intrinsic dimension of the data, rather than exponentially with the ambient dimension. Moreover, we establish a correspondence between the learned subspace bases and semantic attributes of image data, providing a principled foundation for controllable image generation.

Zhen Wu

Shandong University, China

Executive Vice President

Title: Mean Field Games and Control via Forward Backward Stochastic Differential Equations

Executive Vice President
Shandong University, China

Wu Zhen serves as the Executive Vice President of Shandong University. He is a Distinguished Professor of the Changjiang Scholars Program of the Ministry of Education and a recipient of the National Outstanding Youth Science Fund. He currently holds the positions of Vice President of the Chinese Mathematical Society, Deputy Director of the National Key Laboratory of Cryptography and Digital Economy Security, Chairman of the Shandong Mathematical Society, member of the Expert Advisory Committee of the Department of Mathematical Sciences of the National Natural Science Foundation of China (NSFC), and Deputy Head of the Academic Steering Group of the NSFC's Mathematics Tianyuan Fund (10th term). He previously served as an editorial board member of the premier control theory journal SIAM Journal on Control and Optimization, and currently serves on the editorial boards of the NSFC's English-language academic journal Fundamental Research as well as several SCI-indexed journals. He has received the Shiing-Shen Chern Mathematics Award and the First Prize of the Shandong Provincial Natural Science Award. Wu Zhen's research focuses on forward-backward stochastic differential equations (FBSDEs) and their applications in stochastic optimal control and financial mathematics. He has systematically investigated three progressively interrelated fundamental theoretical topics: the solvability of FBSDEs and related stochastic partial differential equations (SPDEs), optimal control under complete information, and optimal control under partial information. He creatively proposed three original universal theories and methods—the monotone framework, control embedding, and the backward separation principle—which have overcome several key limitations of classical theory. His work has resolved multiple open problems posed by internationally renowned scholars, including Fields Medalist Professor P.-L. Lions, U.S. National Academy of Sciences member Professor R. E. Kalman, and Academician of the Chinese Academy of Sciences Professor Peng Shige. He has progressively established a research system for stochastic optimal control characterized by FBSDE theory, providing an important theoretical foundation and mathematical tools for the analysis and optimization of complex stochastic systems as well as the measurement and control of financial risks. His related results have been extensively cited by more than 20 academicians from various countries and invited speakers of the International Congress of Mathematicians (ICM), with over 1,700 SCI non-self-citations.

Wu Zhen has served as the principal investigator for major research projects including the NSFC Innovative Research Group Project (Category A) and the National Key Research and Development Program of China. His related results have contributed to the robust operation and multi-resource coordinated dispatch of smart grids, providing important theoretical support for China's green and low-carbon development strategy. They have also made significant academic contributions to the A+ rating of Shandong University's mathematics discipline and the recognition of the School of Mathematics as a "National Advanced Collective in the Education System."

Title: Mean Field Games and Control via Forward Backward Stochastic Differential Equations

Abstract: Mean field theory provides a powerful framework for analyzing large-scale interacting particle systems, with broad applications in game and control theory. In such system, competitive optimization by individual particles leads to N-particle games, while cooperative optimization yields social optima problems. Due to the high dimensionality and coupling among particles, direct analysis of such systems is often intractable. A common approach is to consider the limit behavior of a representative particle, leading to mean field game and mean field control problems. These limiting problems are typically characterized by infinite-dimensional partial differential equations such as the master equation and the Hamilton–Jacobi equation. Two main approaches are used to study their well-posedness: the probabilistic method and the analytical PDE approach. This talk focuses on the probabilistic method, utilizing the theory of forward backward stochastic differential equations (FBSDEs) to address linear-quadratic mean field games with non-monotone data and linear-quadratic mean field control problems with non-convex data. It can be shown that the corresponding master equation and the Hamilton–Jacobi equation admit unique classical solution. The propagation of chaos property for the related trajectories can also be proved.

Xianjin Yang

CUHK Shenzhen, China

Assistant Professor

Title: Kernel Methods for PDEs: From Finite to Infinite Dimensions

Abstract: This talk presents Gaussian process and kernel methods for solving partial differential equations (PDEs), from finite-dimensional domains to infinite-dimensional problems including functional PDEs and PDEs on spaces of probability measures.

Jianfeng Zhang

University of Southern California, USA

Professor

Title: On Monotonicity Conditions and Global Well-posedness of Mean Field Game Master Equations: A Unified Approach

Abstract: In this talk, we present a unified framework for establishing the global well-posedness of general mean field game master equations. The central idea is to introduce a new notion of M-monotonicity condition, which is an essentially sharp condition that guarantees the a priori Lipschitz continuity of the value function in the measure variable.

Xiang Zhou

City University of Hong Kong, Hong Kong SAR

Associate Professor

Title: Probability Flow Equivalence and Score-Based Generative Modelling for Lévy Processes

Abstract: In this talk, I will demonstrate how score-based generative modelling inspires the key perspective of probability flow equivalence and offers a new approach to handling non-Gaussian Lévy noise beyond the classical Gaussian diffusion setting. We introduce the Lévy score function, a non-local analogue of the Stein score for Gaussian diffusions, and show (1) how to solve and sample the non-Gaussian Lévy–Itô SDE via this Lévy score function through a transport-based particle algorithm; (2) how to harness Lévy jump processes to improve sampling quality while following the same principles as score-based diffusion modelling; and (3) how a flow-based generative method solves the gradient flow of a general free energy in Wasserstein space by means of the geometric Dawson–Gärtner action. The technique of probability flow equivalence is further demonstrated by our derivation of the second law and fluctuation relations in the stochastic thermodynamics of non-Gaussian active matter. This talk is mainly based on joint works with Yuanfei Huang and Chengyu Liu.

Venue

Interdisciplinary Multi-function Room (AE-040)

LG/F Academic Exchange Building

City University of Hong Kong

The conference will be held at the Interdisciplinary Multi-function Room (AE-040), LG/F Academic Exchange Building, City University of Hong Kong.

Get directions to CityUHK

Program

HKIAS International Conference on Multi-Agent Systems and AI 2026

21 October 2026 (Wednesday)

08:40–09:00

Registration

09:00–09:10

Opening Ceremony

09:10–09:55

Newton Algorithm of Backward Stochastic Riccati Differential Equation

Prof. Shanjian TANG (Fudan University, China)

09:55–10:40

On Monotonicity Conditions and Global Well-posedness of Mean Field Game Master Equations: A Unified Approach

Prof. Jianfeng ZHANG (University of Southern California, USA)

10:40–11:00

Photo-taking and Coffee Break

11:00–11:45

Towards Trusthworthy Cooperative AI: Simulating, Aligning, and Governing Multi-Agent Systems

Prof. Yali DU (King's College London, UK)

11:45–12:30

Probability Flow Equivalence and Score-Based Generative Modelling for Lévy Processes

Prof. Xiang ZHOU (City University of Hong Kong)

12:30–14:00

Lunch Break

14:00–15:30

Discussion

15:30–17:30

Welcome Reception (HKIAS Lounge, LG/F, Academic Exchange Building, City University of Hong Kong) (Invited guests only)

22 October 2026 (Thursday)

09:00–09:10

Registration

09:10–09:55

Mean Field Games and Control via Forward Backward Stochastic Differential Equations

Prof. Zhen WU (Shandong University, China)

09:55–10:40

Indefinite linear–quadratic mean-field game and optimal control problem with partial information

Prof. Tianyang NIE (Shandong University, China)

10:40–11:00

Coffee Break

11:00–11:45

Master Equations of Mean Field Games of Controls

Prof. Chenchen MOU (City University of Hong Kong)

11:45–12:30

Kernel Methods for PDEs: From Finite to Infinite Dimensions

Prof. Xianjin YANG (Chinese University of Hong Kong, Shenzhen, China)

12:30–14:00

Lunch Break

14:00–16:00

Discussion

16:00–16:30

Coffee Break

18:00–20:30

Conference Dinner (Invited guests only)

23 October 2026 (Friday)

09:00–09:10

Registration

09:10–09:55

Understanding Distribution Learning of Diffusion Models from a Low-Dimensional

Prof. Peng WANG (University of Macau, China)

09:55–10:40

Clustering in Deep Stochastic Transformers

Prof. Mathieu LAURIERE (NYU Shanghai, China)

10:40–11:00

Coffee Break

11:00–12:00

Remarks on Maths and AI

Prof. Pierre-Louis LIONS (Collège de France, France)

12:00–14:00

Lunch Break

14:00–16:00

Discussion

16:00–16:30

Coffee Break

Photos

Photos from the conference will be available here after the event.

Accommodations

Recommended accommodation options for conference participants.

CityU Lodge

Academic Exchange Building, 81 Tat Chee Avenue (facing To Yuen Street), Kowloon, Hong Kong

+852 3442 3600

+852 3442 3700

info@lodge.cityu.edu.hk

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Email: hkias@cityu.edu.hk

Tel: +852 3442 6611

HKIAS International Conference on Multi-Agent Systems and AI

Conference Registration

About

Organizing Committee

Pierre-Louis Lions

Charles Bertucci

Chenchen Mou

Mathieu Lauriere

Speakers & Abstracts

Pierre-Louis Lions

Yali Du

Mathieu Lauriere

Chenchen Mou

Tianyang Nie

Shanjian Tang

Peng Wang

Zhen Wu

Xianjin Yang

Jianfeng Zhang

Xiang Zhou

Venue

Interdisciplinary Multi-function Room (AE-040)

Program

Photos

Accommodations

CityU Lodge

Contact Us