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Meeting 37

23 April 2025 (Sheffield)

Hosted by the School of Mathematics and Statistics of the University of Sheffield.
Supported by LMS.
If you will arrive by train, can either walk from the station or take the tram.  Here are some directions.

Please register by using this link, by 12:00 noon (UK time) on Friday 18th April 2025. This will help the organisers planning the coffee breaks, and will also facilitate the completion of the final report for the London Mathematical Society.

All talks will happen in the Hicks building (Lecture Theatre 05 on the E Floor, one up from the entrance). Coffee breaks will be served in the Common Room I15.

Speakers

Schedule

  • 13:00 — 14:00 Mehrnoosh Sadrzadeh (University College London).
  • 14:00 — 14:30 Coffee break.
  • 14:30 — 15:30 Michael Ching (Amherst College, USA).
  • 15:30 — 16:00 Coffee break.
  • 16:00 — 17:00 Jonathan Sterling (Cambridge).
  • 17:00 — 20:00 Informal discussions / pub / dinner.

 

Titles and Abstracts

  • Mehrnoosh Sadrzadeh
    • Title: Quantum machine learning for natural language processing
    • Abstract: In the 1930's, logicians observed that natural language obeys rules similar to rational numbers and developed the first logical model of language. In 1958, a decision procedure for this logic was proposed and led to one of the first automatic parsers. More than half a century later, in 2010, my colleagues and I showed that this logic also relates to real numbers and developed a vector space semantics for it, using the theory of compact closec categories.

      A defining feature all along has been the use of higher order tensors. Tensors are natural inhabitants of quantum systems and they are more efficiently learnt via quantum simulations. Since realising this, we have trained our models by machine learning on quantum computers, obtained manifold improvements, many publications and awards. In this talk, I will introduce our framework, go over its related learning algorithms, and present our recent results on a mainstream linguistic challenge.

  • Michael Ching
    • Title: Differential bundles in Goodwillie calculus
    • Abstract: In joint work with Kristine Bauer and Matthew Burke, we have formalized the analogy between Goodwillie's functor calculus and the ordinary differential calculus of smooth manifolds. Both are examples of a tangent $\infty-$category. That abstract structure, introduced by Rosický in the 1-categorical setting and developed in more detail by Cockett and Cruttwell, is based on categorical properties of the tangent bundle functor in differential geometry. I will describe how we generalize their work to $\infty$-categories and how Goodwillie's theory fits into this framework. Our main result is that Goodwillie's Taylor tower can be completely recovered from a certain tangent $(\infty,2)$-category of $\infty$-categories.

      This work makes it possible to investigate analogues in Goodwillie calculus of various aspects of ordinary differential geometry, and I will describe joint work in progress with Kaya Arro, where we identify the notions corresponding to smooth vector bundles. These turn out to be, more-or-less, cartesian and cocartesian fibrations of ∞-categories for which all the fibres are stable.

  • Jonathan Sterling.
    • Title: When is the partial map classifier a Sierpiński cone?
    • Abstract: The idea of synthetic domain theory is to work in the internal language of a topos containing an interval object that forms a dominance and satisfies a few other axioms, such as Phoa’s principle. Then, not all objects deserve to be called “predomains”, but the ones that do invariably arise within full internal reflective subcategories defined by simple orthogonality laws stated in terms of the interval’s geometry. It so happens that some of these orthogonality laws are also of use in defining synthetic ∞-categories à la Riehl and Shulman.

      I will outline some recent results in synthetic (higher) domain theory obtained with my former Masters student Leoni Pugh concerning partial map classifiers, including (1) the closure of synthetic $\infty$-categories under partial map classifiers, and (2) the discovery of a strengthening of the Segal completeness law that, amongst synthetic partial orders, causes the partial map classifier to coincide with the Sierpiński cone.