Mon, 12 May 2025
15:30
L5

Surgery presentations of bordism bicategories

Filippos Sytilidis
(Oxford University)
Abstract

A topological quantum field theory (TQFT) is a functor from a category of bordisms to a category of vector spaces. Classifying low-dimensional TQFTs often involves presenting bordism categories in terms of generators and relations. In this talk, we introduce these concepts and outline a general procedure for obtaining such presentations using Morse–Cerf theory and surgery. We further discuss how this perspective can be extended to yield presentations of bordism bicategories.


 
Wavefront sets of unipotent representations of reductive p-adic groups I
Ciubotaru, D Mason-Brown, L Okada, E American Journal of Mathematics
Wed, 14 May 2025
13:30
L5

q-deformations and (uniqueness of) string amplitudes

Maria Nocchi
Abstract

q-deformations offer a systematic way to generalize familiar mathematical structures, revealing hidden symmetries and richer geometries that collapse back to classical frameworks as the deformation parameter goes to 1. Beyond their mathematical elegance, q-deformations have naturally emerged in diverse areas of theoretical physics, offering fresh perspectives on quantization, regularization, and non-commutative geometry. In this talk, we will explore how q-deformations intersect with the intriguing question of the uniqueness of string scattering amplitudes.

 

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

Turán Problems for Expanded Hypergraphs
Keevash, P Lifshitz, N Long, E Minzer, D Combinatorica volume 45 issue 3 (23 Apr 2025)
tt

Many of the artists that we encounter are completely unaware of the mathematics that bubble beneath their craft, while some consciously use it for inspiration. Our instincts might tell us that these two subjects are incompatible forces with nothing in common, mathematics being the realm of precise logic and art being the realm of emotion and aesthetics. But what if we’re wrong?

Scalar-flat Kähler metrics with SU (2) symmetry
Dancer, A Journal fur die Reine und Angewandte Mathematik issue 479 99-120 (01 Jan 1996)
Nahm data and SU(3) monopoles
Dancer, A Nonlinearity volume 5 issue 6 1355-1373 (01 Dec 1992)
A family of hyperkähler manifolds
Dancer, A Quarterly Journal of Mathematics volume 45 issue 4 463-478 (01 Dec 1994)
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