Talk About Your Thesis

The Radcliffe Science Library invites science and medicine postgraduates to give a short, engaging 5–7 minute talk on their research. It’s a great chance to practice explaining your work clearly and succinctly - perfect preparation for the DPhil transfer or upcoming conferences - and to connect with other researchers in a relaxed setting. A complimentary pizza lunch will follow the talks.

Radcliffe Science Library , Friday 20 March 2026, 12:00–13:00 followed by lunch.

Fri, 23 Jan 2026
13:00
L6

Latschev’s theorem in persistent homotopy theory

Lukas Waas
(Oxford University)
Abstract
A central question in topological data analysis is whether the sublevel-set persistent homology of a function from a sufficiently regular metric space can be recovered from a finite point sample. A natural approach is to equip the Vietoris–Rips complex of the sample, at a fixed scale, with an appropriate filtration function and to compute persistent homology of the resulting filtered complex.
 
Despite its appeal, this approach has so far lacked theoretical guarantees. Existing results instead rely on image persistence, computing the image of transition morphisms between Rips homology at two different scales. By contrast, Latschev’s theorem in metric inference shows that, under suitable regularity and sampling assumptions, the Vietoris–Rips complex of the sample at a single scale is already homotopy equivalent to the underlying space.
 
In this talk, I will explain how tools from persistent homotopy theory yield a persistent version of Latschev’s theorem, which in particular resolves this classical question of estimating persistent homology at the level of persistent homotopy types.
Tue, 10 Feb 2026
13:00
L2

Dynamics of the Fermion-Rotor System

Vazha Loladze
(Oxford )
Abstract

In this talk, I will examine the dynamics of the fermion–rotor system, originally introduced by Polchinski as a toy model for monopole–fermion scattering. Despite its simplicity, the system is surprisingly subtle, with ingoing and outgoing fermion fields carrying different quantum numbers. I will show that the rotor acts as a twist operator in the low-energy theory, changing the quantum numbers of excitations that have previously passed through the origin to ensure scattering consistent with all symmetries, thereby resolving the long-standing Unitarity puzzle. I will then discuss generalizations of this setup with multiple rotors and unequal charges, and demonstrate how the system can be viewed as a UV-completion of boundary states for chiral theories, establishing a connection to the proposed resolution of the puzzle using boundary conformal field theory.

The Mathematics of Shuffling

Massada Public Seminar @Worcester College 

Itay Glazer (Technion, Israeli Institute of Technology)  -  The Mathematics of Shuffling

Mon 9 Feb 2026 5:15 - 7:00 pm, Sultan Nazrin Shah Centre, Worcester College

Book here

Thu, 15 Jan 2026
14:00
C1

Igusa stacks and the cohomology of Shimura varieties

Pol van Hoften
(Zhejiang University)
Abstract
Associated to a modular form $f$ is a two-dimensional Galois representation whose Frobenius eigenvalues can be expressed in terms of the Fourier coefficients of $f$, using a formula known as the Eichler--Shimura congruence relation. This relation was proved by Eichler--Shimura and Deligne by analyzing the mod p (bad) reduction of the modular curve of level $\Gamma_0(p)$. In this talk, I will discuss joint work with Patrick Daniels, Dongryul Kim and Mingjia Zhang, where we give a new proof of this congruence relation that happens "entirely on the rigid generic fibre". More precisely, we prove a compatibility result between the cohomology of Shimura varieties of abelian type and the Fargues--Scholze semisimple local Langlands correspondence, generalizing the Eichler--Shimura relation of Blasius--Rogawski. Our proof makes crucial use of the Igusa stacks that we construct, generalizing earlier work of Zhang, ourselves, and Kim.
 
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