Mathematical Institute

Fri, 13 Mar 2026
12:00

Classical conformal blocks as generating functions

Harini Desiraju

(The Mathematical Institute, Oxford)

Abstract

In this talk, I will consider a CFT on a four punctured sphere. I will first gather three known results in the literature about the role classical (c-> infinity) conformal blocks play as generating functions for: accessory parameters, monodromy coordinates, and the connection constant of Heun equations. Secondly, I will outline analogous results for the one-point torus and provide a road-map to proving these results rigorously using probability techniques. Finally, I will discuss potential challenges in rigorous proofs for conformal blocks on any other geometry.

Fri, 06 Mar 2026
12:00

From strong couping amplitudes to Hitchin moduli spaces via twistors

Lionel Mason

(Oxford )

Abstract

Alday & Maldacena conjectured an equivalence between string amplitudes in AdS5 ×S5 and null polygonal Wilson loops and a duality with amplitudes for planar N = 4 super-Yang-Mills (SYM). At strong coupling this identifies SYM amplitudes with (regularized) areas of minimal surfaces in AdS. They reformulated the problem as a Hitchin system and in collaboration with Gaiotto, Sever & Vieira they introduced a Y-system and a thermodynamic Bethe ansatze (TBA) expressing the complete integrability that could in principle be used to solve for the amplitude. This lecture will review the parts of this material that we need and use them to identify new geometric structures on the spaces of kinematics for super Yang-Mills amplitudes/null polygonal Wilson loops. In AdS3, we find that the nontrivial part of these amplitudes at strong coupling, the remainder function, is the (pseudo-)K ̈ahler scalar for a (pseudo-)hyper-Kaher geometry. It satisfies an integrable system and we give its its Lax form. The result follows from a new perspective on Y-systems more generally as defining the natural twistor space associated to the hyperkahler geometry of the Hitchin moduli space for these minimal surfaces. These connections in particular allows us to prove that the amplitude at strong coupling satisfies the Plebanski equations for a hyperKahler scalar for these pseudo-hyperk ̈ahler and related geometries. These hyperkahler geometries go beyond the semiflat examples with a nontrivial TBA. These new structures underpinning the N=4 SYM amplitudes will be important beyond strong coupling.

Mon, 02 Mar 2026
16:00

Vanishing sums of matrix products

Noah Kravitz

((Mathematical Institute University of Oxford))

Abstract

Any two 1 by 1 real matrices commute. This is in general not the case for 2 by 2 real matrices. However, if A, B, C, and D are any 2 by 2 real matrices, then ABCD - ABDC - ACBD + ACDB + ADBC - ADCB - BACD + BADC + BCAD - BCDA - BDAC + BDCA + CABD - CADB - CBAD + CBDA + CDAB - CDBA - DABC + DACB + DBAC - DBCA - DCAB + DCBA = 0. This identity is the first instance of a general result of Amitsur and Levitski; I will explain a simple graph-theoretic proof due to Swan.

North meets South

Today, 4 pm, L1 as below (n.b. the free pizza)

Fri, 27 Feb 2026
04:00

Lecture Theatre 1, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG

North South Colloquium

William Hart and Giovanni Italiano

Abstract

Fully funded 4-year PhD position in Theoretical Physics

The University of Galway invite applications for a fully funded 4-year PhD position in Theoretical High-Energy Physics, funded by the Research Ireland Pathway grant “Integrability in Non-Lorentzian Holography” led by Andrea Fontanella, starting in September 2026.

The main focus of the PhD project is to further develop the recently discovered non-relativistic and Carrollian holography, to construct integrability techniques for non-Lorentzian theories, and to explore applications of non-Lorentzian holography to flat space holography.