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Autumn Semester 2026

Date / Time Speaker Title Location
* 22 October 2026
15:00-15:45 		Gioele Zardini
MIT
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Talks in Mathematical Physics

Title Compositional Design and Operation of Autonomous Multi-Agent Systems
Speaker, Affiliation Gioele Zardini, MIT
Date, Time 22 October 2026, 15:00-15:45
Location Y35 F 32
Abstract Complex engineered systems can no longer be designed by optimizing components in isolation. In domains such as autonomy, mobility, and other society-critical infrastructures, system-level performance emerges from tightly coupled choices across hardware, software, control, operations, infrastructure, and policy. Moreover, these choices are distributed across abstraction levels and stakeholders, and the same subsystem is often both a system in its own right and a component of a larger one. This calls for a compositional approach to design: one that can represent interdependence, capture trade-offs across scales and disciplines, and remain computationally tractable. In this talk, I will present a framework for the compositional co-design of complex systems, drawing on optimization, control, and applied category theory. The central idea is to model components and their interconnections in a modular way, so that large design problems can be assembled, queried, and solved systematically from smaller ones. This perspective gives rise to a new class of compositional optimization problems, in which design trade-offs are expressed structurally and solved through algorithms that exploit interconnection and feedback, rather than collapsing everything into a monolithic formulation. I will illustrate the framework through examples spanning autonomous systems and future mobility, showing how it supports task-driven design across levels: from the choice of algorithms and components in autonomous vehicles to the co-design of services, operations, infrastructure, and policies in intermodal mobility systems. These examples highlight how compositional design can unify heterogeneous models and objectives, enable collaboration across disciplines, and provide quantitative tools to reason about the societal impact of emerging technologies. I will conclude by outlining ongoing efforts that extend this framework toward uncertainty-aware and adaptive design, including distributional formulations of co-design problems, online learning with embedded black-box components, and broader questions at the intersection of compositional optimization, strategic interaction, and multi-stakeholder system design.
Compositional Design and Operation of Autonomous Multi-Agent Systemsread_more
Y35 F 32
* 22 October 2026
16:00-16:45 		Paolo Perrone
Oxford
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Talks in Mathematical Physics

Title Markov Categories and Entropy 
Speaker, Affiliation Paolo Perrone, Oxford
Date, Time 22 October 2026, 16:00-16:45
Location Y35 F 32
Abstract Markov categories are a new mathematical framework designed to deal with problems in probability and information theory, using a higher abstraction layer. For an analogy, high-level programming languages (such as Python) allow the user to write code without worrying about lower-level issues such as memory allocation. Similarly, Markov categories allow the user to write rigorous mathematics, possibly involving continuous sample spaces and singularities, without having to know any measure theory. Moreover, they come equipped with a graphical formalism which faithfully reflects the information flow and the stochastic dependencies, and so they give a very general theory of graphical models. In this talk we will also see that several quantitative aspects of information theory can be captured by an enriched version of Markov categories, where the spaces of morphisms are equipped with a divergence or even a metric. For instance, we can define entropy exactly by measuring how far a source or channel is from being deterministic in the Markov category sense. This recovers the Shannon and Rényi entropies, as well as the Gini-Simpson coefficient used in ecology to quantify diversity in an ecosystem, and it can be used to give a conceptual definition of generalized entropy. Relevant paper: Paolo Perrone, "Markov Categories and Entropy", IEEE Transactions on Information Theory 70(3), 2024. (arXiv:2212.11719)
Markov Categories and Entropy read_more
Y35 F 32
26 October 2026
13:30-14:30 		Xiao Han
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Talks in Mathematical Physics

Title Braided Hopf algebroids and Lie algebroids
Speaker, Affiliation Xiao Han,
Date, Time 26 October 2026, 13:30-14:30
Location Y27 H 25
Abstract We construct braided Hopf algebroids in a braided monoidal category over a field $k$ and study its properties using graphical representation. Then we study Ehresmann-Schauenburg Hopf algebroids assocaited to braided Hopf Galois extensions. We introduce braided Lie-Rinehart algebras which generalize the definition in \cite{ALP24, ALP23, ALP25} and study its universal enveloping algebra under symmetric condition. In particular, we introduce Lie-Rinehart algebras (braided Lie-algebroids) associated with braided Hopf algebroids in the category of the module of a triangular Hopf algebra. We then focus on the case for braided Ehresmann-Schauenburg Hopf algebroids and study their right invariant vector fields, which turn out to be isomorphic to the $H$-equivariant vector fields on the quantum principal bundle (Hopf Galois extension) as Lie-Rinehart algebras. Finally, we introduce braided jet Hopf algebroids associate to braided Hopf algebroids in the case that the source and target subalgebra belong to the braided center. Moreover, we show there is a dual pairing between the $k$-order universal enveloping algebra of the braided right invariant vector fields and the $k$-th jet space of a braided Hopf algebroid and further more a skew pairing between the universal enveloping algebra of its braided right invariant vector fields and its jet Hopf algebroid under a finiteness condition.
Braided Hopf algebroids and Lie algebroidsread_more
Y27 H 25
9 November 2026
13:30-14:30 		Arthemy Kiselev
University of Groningen
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Talks in Mathematical Physics

Title Title T.B.A.
Speaker, Affiliation Arthemy Kiselev, University of Groningen
Date, Time 9 November 2026, 13:30-14:30
Location Y27 H 25
Title T.B.A.
Y27 H 25

Notes: the highlighted event marks the next occurring event and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

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