Triangle Seminars

Abstract:
AI for Mathematical Sciences (AIMS) seminar series

This talk is a personal account of the changing landscape of mathematics through the lens of one beautiful problem in algebraic geometry: a conjecture of Aluffi, Chen and Marcolli on the real-rootedness of the Poincaré polynomials of the moduli spaces of genus-zero curves. We follow how the search for a solution evolved with the AI tools this year, and how it finally resulted in the refutation of several long-standing conjectures in matroid positivity. This leads us to the unavoidable question of how mathematics is changing. I will argue that mathematics is becoming a humanity, and ask what the mathematician's role is in the new world. Is the AlphaZero moment of mathematics close? And what do we do, in the meantime, about the allocation of grants, positions and publications? I will end with a positive tone: what new problems and challenges we face, including new mathematical questions emerging in interpretability and the mathematics of AI safety.

Please fill in this form https://tally.so/r/zEjXe1 to confirm your attendance at Geordie’s talk
To subscribe to the series, please fill in this form https://applications.lims.ac.uk/subscribe-to-aims

Abstract:
Entanglement bootstrap (EB) aims to uncover the universal data and structural properties of quantum many-body systems from local entanglement properties. In this talk, I will discuss our past progress on EB for 1+1D conformal field theories, including anomalous CFTs that can arise only as boundaries of 2+1D topological quantum field theories. Explicitly, I will discuss a locally checkable condition for 1+1D CFT ground states, as well as the reconstruction of Virasoro generators directly from the wavefunction. This allows us to diagnose if a given state is a CFT ground state or not, and if it is then how to extract CFT data from it.

Although these results are motivated by continuum field theory, they are also applicable to critical lattice systems. This opens the possibility of using entanglement bootstrap as a systematic framework for enumerating and potentially discovering new CFTs

Abstract:
TBA

Abstract:
Since the times of Ludwig Boltzmann, most physicists take it for granted that generic non-integrable closed dynamical systems, whether classical or quantum, thermalize at long times for generic initial conditions. Whether this belief is true or false depends on the type of systems one is willing to consider and the meaning of “generic” and “thermalizes”. In this talk I will discuss two types of many-body dynamical systems where thermalization (i.e. weak convergence to the state of maximal entropy) can be established for a large class of initial states. The first one is a system of an infinite number of spins with evolution generated by a repeated application of a Clifford Cellular Automaton. The second one is its classical counterpart and can be thought of as a mixing automorphism of an infinite-dimensional torus.

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Please register for the event!
https://lims.ac.uk/event/chaos-and-thermalisation-in-many-body-floquet-systems/

Colloquium at 5:00 PM, 11 Nov 2026 at LIMS, 2F of Royal Institution, 21 Albemarle St, W1S4BS, London

Everyone is warmly invited to stay for the reception afterwards, featuring drinks, cheese, refreshments, lively conversations, networking, and music in the evening!

Abstract:
TBD.