果冻传媒

Term 1

• Wednesday 7 October 2026: Jens Marklof (University of Bristol):
  

  Title: Randomness in the spectrum of the Laplacian: from flat tori to hyperbolic surfaces of high genus

  Abstract: I will report on recent progress on influential conjectures from the 1970s and 1980s (Berry-Tabor, Bohigas-Giannoni-Schmit), which suggest that the spectral statistics of the Laplace-Beltrami operator on a given compact Riemannian manifold should be described either by a Poisson point process or by a random matrix ensemble, depending on whether the geodesic flow is integrable or 鈥渃haotic鈥�. This talk will straddle aspects of analysis, geometry, probability, number theory and ergodic theory, and should be accessible to a broad audience. The two most recent results presented in this lecture were obtained in collaboration with Laura Monk and with Wooyeon Kim and Matthew Welsh.

• Friday 16 October 2026: An afternoon event in honor of Peter Swinnerton-Dyer

• Friday 23 October 2026: Ellen Luckins (果冻传媒):

Title: Multiphase porous-media flows: modelling challenges and applications

Abstract: Flows of multiple fluids (eg: a liquid and a gas) within a porous medium occur in many important areas of geoscience and modern industrial processes. However, in general, we do not have accurate, efficient models to study them. In this talk, I will discuss why these flows are such an interesting challenge to model mathematically and give an overview of some different modelling approaches taken in practice. Simplifications can sometimes be exploited to more carefully understand specific flow processes: I鈥檒l discuss work on evaporation of water from stone or soil, salt weathering, mushy freezing of metal alloys or sea ice, and injection problems in manufacturing composite materials.

• Wednesday 28 October 2026: Emma Davis (果冻传媒):
  Title: A different meaning of 鈥渧ector鈥�: Modelling vector-borne disease dynamics at a population scale

  
  Abstract: A vector-borne disease is pathogen that is transmitted indirectly via an intermediate host or organism. This can create complex coupled dynamics between the primary host and the intermediate host - the 鈥渧ector鈥�, which can pose challenges for control, surveillance, and forecasting. I draw on examples from my research to show how mathematical modelling can be used to explore and understanding these systems, demonstrating the importance of considering different scales and sources of heterogeneity.
  
  

• Friday 6 November 2026: Martin Lotz (果冻传媒):
  
  Title: Pfaffian geometry - intersections, incidences and neural networks
  Abstract: Pfaffian functions satisfy triangular systems of first-order partial differential equations with polynomial coefficients. They extend polynomial functions to include transcendental examples such as exp, log and tanh, while retaining effective quantitative bounds on the topological complexity of the sets they define. We give an introduction to the theory and highlight recent applications to seemingly unrelated areas: incidence combinatorics, tubular neighbourhoods and the robustness of neural network classifiers. A central tool is Khovanskii's generalization of Bezout's theorem for the number of solutions of a set of Pfaffian equations. This talk features joint work with Abhiram Natarajan (果冻传媒), Paul Lezeau (Imperial) and Nicolai Vorobjov (Bath)
  
  
• Wednesday 11 November 2026: Gregor Tanner (Nottingham):
  
  
• Friday 20 November 2026: Bruno Nachtergaele (UC Davis):
  Title: Quantum states of matter
  
  

  Abstract: At sufficiently low temperatures many materials enter states of matter with a fundamentally quantum signature. Superfluids and superconductors have been known for a long time and good theoretical descriptions of these intrinsically quantum states of matter have been developed. In the past couple of decades even more exotic states of matter have been discovered. We will review some of the fascinating mathematical theory of quantum many-body systems that describes those.

• Friday 27 November 2026: Ginestra Bianconi (Queen Mary):
• Friday 4 December 2026: Andrew Hazel (University of Manchester):
• Wednesday 9 December 2026: Vadim Kaimanovich (Universit茅 de Rennes)