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The Topos Institute Colloquium is an expository virtual talk series on topics relevant to the Topos mission and community. We usually meet over Zoom on Thursdays at 17:00 UTC, but this may vary depending on the speaker's time-zone. Talks are recorded, and remain available on our YouTube channel.
If you wish to be subscribed to the mailing list, then simply send an email to seminars+subscribe@topos.institute. For any queries about the colloquium, contact tim+colloquium@topos.institute.
The colloquium centres around following four themes, with many talks fitting multiple themes.
Topos aims to shape technology for public benefit via creating and deploying a new mathematical systems science. What does this mean, and how do we do it? How does technology shape people’s lives today? What are the risks that future technologies may bring? What is the role of mathematicians and computer scientists in shaping how their work has been deployed? What lessons can we learn from the past and present about successes and failures? This theme aims to spark discussion among mathematicians and computer scientists about these questions, and bring them into contact with experts on these subjects.
Thinking clearly about today’s most pressing scientific, technical, and societal questions requires finding the right abstractions. Category theory can help with this by offering design principles for structuring how we account for phenomena in a specific domain, as well as how we translate problems and solutions between different domains. This theme aims to highlight recent developments in applied category theory, in domains such as computation, neuroscience, physics, artificial intelligence, game theory, and robotics.
Like many parts of pure mathematics, results that are initially seen as purely theoretical may not be ripe for application until much later. At Topos we foster the entire pipeline, from the creation of elegant theory to the development of its effective application. The goal of this theme is to foster the pure side of this pipeline, to take in the most beautiful results in category theory, logic, type theory, and related fields, as well as to scout for not-yet-categorical work that appears ripe for "categorification".
Beyond its intrinsic interest, the purpose of applied mathematics is to provide a foundation for new capabilities and technologies that benefit the public. In this theme, we highlight work, at the intersection of research and engineering, that transfers ideas from applied category theory and other parts of mathematics into viable technologies, with an emphasis on software systems and tools. Topics may include scientific modeling, functional programming, differential programming, probabilistic programming, quantum computing, formal verification, and software and systems engineering.
To see the talks from previous years, use the links to the archives at the top of the page.
Inna Zakharevich (29th of January)
[Abstract TBA]
Dan Ghica (5th of February)
For the last five years I have been working as one of the architects of a new programming language called Cangjie (CJ). CJ is part of a new open-source ecosystem for Huawei devices which has the HarmonyOS operating system at its core. I will discuss some of the innovations adopted by CJ such as effect handlers (released) and modal types (work in progress) and comment on my personal experience as a 'theory person' now involved in developing a language for a wide audience, which includes some of the top Chinese tech companies.
Chad Nester (12th of February)
Combinatory logic was introduced more than a century ago in pursuit of logical syntax without bound variables. Its power and simplicity have made it a subject of enduring interest, and it has played a foundational role in logic and computer science. A combinatory algebra is an algebraic model of combinatory logic. Concretely, such an algebra consists of a set equipped with a binary operation satisfying a condition called combinatory completeness. This condition is rather complex, but is equivalent to the existence of elements of the carrier set satisfying certain simple equations.
This talk concerns a more general notion of combinatory completeness relative to a certain well-behaved collections of functions between finite sets, called faithful Cartesian clubs. The classical notion of combinatory completeness corresponds to the club consisting of all such functions. Moreover, the equivalence of combinatory completeness with the existence of elements satisfying simple equations holds in some form for a number instances of the more general notion. These results hold in settings beyond the usual category of sets and functions, and their technical development takes place in a multicategory equipped with an action of the faithful Cartesian club in question. These structured multicategories are a natural setting in which to study (variations of) combinatory algebras.