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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.
Adrian Miranda (30th of January)
The passage from a monad (A,S) to its category of algebras (resp. category of free algebras) can be seen as a V = Cat weighted limit (resp. colimit) construction [1]. The colimit case also has a description involving maps of the form X -->SY and the so-called Kleisli composition.
When we move to the two-dimensional setting, the 2-category of pseudoalgebras can be seen as a V= Gray enriched weighted limit [2], but neither of the familiar descriptions of the Kleisli category categorify to give a weighted colimit [3]. We give a third, less well-known description of the Kleisli category which does categorify to the pseudomonad setting to give a weighted colimit. We show that comparisons induced by pseudoadjunctions splitting the pseudomonad are biequivalences if and only if their left pseudoadjoints are biessentially surjective on objects. This allows the more familiar Kleisli constructions for pseudomonads to be seen as tricategorical colimits, and for the development of the formal theory of pseudomonads pt. 2.