The 26th Geometry and Physics Colloquia
- Date
- 26 February 2026, 13:30–14:30
- Location
- Ångström Laboratory, Polhemsalen
- Type
- Lecture
- Lecturer
- Chris Hull and Tobias Ekholm
- Organiser
- Centre for Geometry and Physics
- Contact person
- Maxim Zabzine
At this 26:th GP Colloquia we had two distinguished speakers: Prof. Chris Hull (Imperial College London) and Prof. Tobias Ekholm (Uppsala University). The Colloquia aim at increasing the interaction between physics and mathematics.
Due to unforeseen circumstances, Prof. David Witt Nyström was unfortunately not able to participate in the colloquium. Prof. Tobias Ekholm (Uppsala University), Director of the Centre for Geometry and Physics, stepped in at short notice.
Chris Hull and Tobias Ekholm outside the Polhem lecture room during the brake.
Programme
13:30-14:30 Lecture by Prof. Chris Hull (Imperial College, London)
Title: Homotopy Lie Algebras and their Role in String Theory and Field Theory
Abstract: Lie algebras, which are vector spaces equipped with a 2-bracket satisfying the Jacobi identity, play a central role in physics. These have an interesting generalisation to Homotopy Lie Algebras which are graded vector spaces equipped with n-brackets for n=1,2,3,4,… satisfying a generalisation of the Jacobi identities. An important case is the $L_\infty$ algebra which was first discovered in string theory and has been shown to play a central role in all field theories, providing an algebraic formulation that is complementary to the geometric formulation of Batalin and Vilkovisky. In particular, there is a natural $L_\infty$-symmetric action that generalises the Chern-Simons action. In the field theory for strings, the action is of precisely this type and has $L_\infty$ symmetry. Some of the remarkable properties of string theory can be understood as arising from this algebraic structure. This colloquium will provide an introduction to these developments in mathematics and physics.
14:30-15:00 Coffee and tea
15:00-16:00 Lecture by Prof. Tobias Ekholm (Uppsala University):
Title: Skein trace from curve counting
Abstract: If M is a 3-manifold and L is a Lagrangian in the cotangent bundle of M such that the projection of L to M is a branched cover then there is a natural map from the skein of M to the skein of L. Given a link in M, think of it as the boundary of a holomorphic curve in the cotangent bundle and map it to the boundaries of all holomorphic curves with boundary in L that has the given curve with boundary in M as their thick part. When L is a double cover we obtain explicit formulas for the lift by counting Morse flow trees. When M and L are products of surfaces, our results give (skein lifts of) Kontsevich-Soibelman wall crossing formulas, and (HOMFLYPT skein lifts of) the Neitzke-Yan results for lifts of the gl(1) skein to the gl(2) skein. The talk reports on joint work with Longhi, Park, and Shende.
Welcome to join!
This colloquium is organised by the Centre for Geometry and Physics.