Generative modeling has emerged as a powerful tool for molecular design and structure prediction, offering the ability for molecular discovery. However, challenges such as synthetic feasibility, novelty, diversity of generated molecules, and generalization remain critical for real-world applications, particularly in drug discovery. In this presentation, we provide a comprehensive overview of state-of-the-art generative models, including graph-based methods, generative flow networks, and diffusion methods, all aimed at addressing these challenges. First, we focus on strategies that improve molecular structural optimzation using geometric deep learning methods. Second, we show how generative modeling can be applied to design novel molecules with desired properties such as drug potency, binding affinities to a specific target protein. Third, we will consider synthesizability of generated molecules by incorporating chemical reaction templates, enabling the generation of novel compounds that are not only drug-like but also synthetically accessible. Moreover, advanced sampling techniques and adaptive learning allow these models to explore diverse molecular structures, including those composed of previously unseen building blocks, while optimizing for key properties such as binding affinity and drug-likeness. Through case studies in drug design and broader molecular applications, we demonstrate how these generative modeling can help accelerate molecular discovery, offering a pathway to more practical and innovative solutions across diverse chemistry domains.

Reinforcement learning (RL) focuses on achieving efficient learning and optimal decision-making from available trials. Recent breakthroughs such as ChatGPT, robotics, autonomous driving, and recommendation systems owe much to advancements in reinforcement learning. Reinforcement learning is often framed as the ‘exploration vs. exploitation’ dilemma. In each trial, the learning agent must decide between ‘exploring’ to discover new possible outcomes or ‘exploiting’ by choosing familiar actions that yield reliable rewards. Effective exploration is crucial to enabling the agent to understand its environment with fewer trials, thereby saving trial opportunities for exploitation, which ultimately maximizes cumulative reward. In this talk, we will delve into a deeper understanding of efficient exploration through two RL variants: the bandit problem and best-arm identification. Throughout the series of new results, we will discuss how to address the two key aspects of exploration research: the design of experiments and the stopping condition for exploration.

In quantum many-body systems, complexity arises not from randomness alone, but from the rich interplay of interactions and entanglement. These systems often exhibit emergent behavior, where global coherence emerges in ways that are absent in single- or few-body descriptions. While most many-body systems are governed by short-range interactions, we explore how strong correlations can arise even between spatially distant degrees of freedom by introducing the concept of multifractality in wave functions. In this talk, we present new perspectives on how quantum many-body systems can exhibit long-range and effectively all-to-all coupling, despite being governed by local Hamiltonians. We highlight key examples where multifractal wave functions naturally appear, such as in quasiperiodic systems, systems with mobility edges, and near localization–delocalization transitions. These critical states possess spatially inhomogeneous amplitude distributions that mediate strong, non-local entanglement and random long-distance couplings, offering a novel route toward engineering globally connected quantum systems.

Stochastic Volterra equations (SVEs for short) are useful to model dynamics with hereditary properties, memory effects and roughness of the path, which cannot be described by standard SDEs. However, the analysis of SVEs is much more difficult than the SDEs case since the solutions are no longer Markovian or semimartingales in general. In this talk, we introduce an infinite dimensional framework which captures Markov and semimartingale structures behind SVEs. We show that an SVE can be “lifted” to an infinite dimensional stochastic evolution equation (SEE for short) and that the solution of the SEE becomes a Markov process on a Hilbert space. Furthermore, we establish asymptotic properties and well-posedness results for lifted SEEs, and then apply them to the original SVEs.