Events

This workshop encompasses three major aspects of computation within Representation Theory and Algebraic Combinatorics. One concerns the development of efficient algorithms to compute important quantities in order to understand and classify them better. This is closely related to understanding what optimality we could expect and in particular the computational complexity aspects of those problems. Their computational complexity class can also be used to understand the existence of combinatorial interpretations, in particular for major structure constants lacking positive formulas like Kronecker and plethysm coefficients. On the other hand, representation theory has seen important applications within computational complexity theory, in the context of Geometric Complexity Theory and Quantum Information Theory. Last, but not least, we will discuss the collection of “experimental” data, which helps formulate conjectures, find counterexamples and understand the behavior for some of the problems listed above.

How to “visualize” the shape of a manifold? More technically, how can one describe the topological and geometric structures of manifolds in a quantitative way? In modern differential geometry, a fundamental strategy is to appropriately “normalize” the shape by canonical metrics — the Riemannian metrics that satisfy certain nonlinear partial differential equations. The seminar will be devoted to investigating canonical metrics and address several basic questions, such as: regularity theory — how well do the canonical metrics perform; degeneration theory: which kinds of complications may appear; moduli space theory — what does the space of all canonical metrics look like? The lectures will focus on degenerations and moduli space of Einstein metrics, global structures and compactifications of moduli space, moduli space and global topological invariants, etc. Deadline for application: 15 September 2025

Webs are diagrammatic tools for representing complex calculations graphically. These diagrams first arose from the representation theory of classical groups, and they have since become important in disparate areas of mathematics. The goal of this workshop is thus to bring together experts from these communities and cross-fertilize these diverse subjects by spreading knowledge of recent developments and perspectives on our shared interest in webs. This workshop will also provide an opportunity for distinct research groups to share current code functionality as well as future needs and desires, with an aim towards building collaborative and open-source computing capabilities.

This program bring together researchers working in Bayesian nonparametric inference (BNP), including computation, foundations, methodology and application of BNP methods, with the goal of identifying newly emerging computational strategies and inference approaches. The program and invited talks are planned to balance theoretical expertise, interest and prowess in computational methods, and exposure to selected substantial application areas. The intended nature of the program as identifying synergies of different approaches and potentially new research directions naturally leads to favoring breath over depth, with more emphasis on covering diverse areas rather than on in-depth discussions of a single specific theme.

The main goal of this program is to advance foundational research in stochastic and randomized methods for scientific computing and optimization, enabling their effective and widespread use in challenging applications. This includes the development of new mathematical approaches, convergence results, next-generation hardware, statistical guarantees, and error bounds, as well as the integration of these tools in scientific applications at scale. We also aim to create research and mentorship opportunities for researchers at all levels, including advanced undergraduate students, graduate students, postdocs, and senior scientists.

The program will unite researchers from a number of areas: algebraic and complex geometry, arithmetic geometry, Hodge theory, and mathematical physics. It will bring theoretically and computationally oriented researchers together, expecting that computations will illuminate conjectures made by the theorists and that theory will enlarge the range of what can be computed. We intend to develop databases of certain types of K3 surfaces for the L-Functions and Modular Forms Database and promote the development of software for computations on K3 surfaces in Magma, SageMath, or other systems for public release.