The UK-Japan Winter Schools have been held since 1999, held at both countries. For 20 years, the school brought together Japanese and UK scientists, in particular also young researchers and students from mathematics and mathematical physics, in a relaxing and stimulating atmosphere. Every year the focus was on a special topic.

The celebration workshop, delayed due to the pandemic, will expose the latest research developments and open topics in the area of the speakers and their wider impact. There will be also talks highlighting work of young researchers from both countries. 

Organisers: Jürgen Berndt – John Bolton – David Elworthy – Martin Guest – Xue-Mei Li – Yoshiaki Maeda 

Please follow details on UK-Japan Winter School

All are welcome — there is no registration fee, but please register for catering purpose via UK-Japan Winter School website

Japan

Abstracts

Monday, 12 September

Kenji Fukaya (Stony-Brook): TBA

Martin Hairer (ICL): TBA

Chris Budd (Bristol): The mathematics of climate change
Climate change is important, controversial, and the subject of huge debate. Much of our understanding of the future climate comes from the use of complex climate models based on mathematical and physical ideas.
In this talk, I will describe how these models work and the assumptions that go into them. I will discuss how reliable our predictions of climate change are, and show how mathematicians can give us insights into both past and future.

Yoshiaki Maeda (Tohoku/Keio): Geometry of Loop space and the fundamental group of contact manifolds
We study the diffeomorphism and isometry groups of manifolds Mp, p 2 Z, which are circle bundles over a closed 4n-dimensional integral symplectic manifold. Equivalently, Mp is a compact (4n+1)-dimensional contact manifold with closed Reeb orbits. We use Wodzicki-Chern-Simons forms to prove that 1(Diff(Mp) and 1(Isom(Mp)) are innite for jpj 0: For the Kodaira-Thurston manifold, we explicitly compute that this result holds for all p. We also give the rest examples of nonvanishing Wodzicki-Pontryagin forms.”


Tuesday, 12 September

Darryl Holm (ICL): A Stochastic Climate Change Model
A generic approach to stochastic climate modelling is developed for the example of an idealized Atmosphere-Ocean model that rests upon Hasselmann’s paradigm for stochas- tic climate models. Namely, stochasticity is incorporated into the fast moving atmo- spheric component of an idealised coupled model by means of stochastic Lie transport, while the slow moving ocean model remains deterministic. This is joint work with D Crisan and P Korn. A remarkable property of the model is that the dynamics of its higher moments are governed by deterministic equations obtained by replacing the drift velocity of the stochastic Lie transport vector field by its expected value.

Takashi Sakajo (kyoto): Topological flow data analysis – theory and applications
We construct a mathematical theory classifying topological structures of orbits gener- ated by structurally stable Hamiltonian vector fields, which is a model of two-dimensional incompressible fluid flows. Based on the classification theory, we can show that struc- turally stable Hamiltonian flows are in one-to-one correspondence with Reeb graphs, and their symbolic expressions, named COT representations. By using this theory, we then develop a new way of topological data analysis, which we call Topological Flow Data Analysis (TFDA). In the present talk, after the classification theory is presented, I will talk about the recent applications of TFDA to geophysical data in atmospheric sci- ence and oceanography. The talk is based on the joint works with T. Yokoyama (Gigu U), T. Uda (Tohoku U), M. Inatsu (Hokkaido U), S. Oishi (RIKEN) and K. Koga (Kyoto U).

Graeme Segal (Oxford): TBA
Hiroshi Iritani (Tokyo): TBA
Yota Samoto (Waseda):TBA


Wednesday, 14 September

Peter Topping (Warwick): TBA

Jonathan Fraser (St Andrews): Dimension interpolation in conformal dynamics
Dimension interpolation’ is the idea that by viewing two distinct notions of fractal di- mension (e.g. Hausdorff and box-counting dimension) as extremes in a carefully defined ’continua of dimensions’, one may gain a more nuanced understanding of the fractal ob- jects at hand. I will review recent developments in this area in the context of conformal dynamics.

Ben Lambert: TBA


Thursday, 15 September

Takashi Kumagai (Waseda): Anomalous diffusions and time fractional differential equations
Time fractional diffusion equations have been widely used to model anomalous diffu- sions exhibiting sub-diffusive behavior, due to particle sticking and trapping phenom- ena. In this talk, I will discuss how anomalous sub-diffusions and the corresponding time-fractional differential equations arise naturally as limits of random walks in ran- dom media. I will then present some results on the probabilistic representation to the solutions of time fractional Poisson equations and estimates of their fundamental solu- tions. This talk is based on joint works with Z.-Q. Chen (Washington), P. Kim (Seoul) and J. Wang (Fuzhou).
Roland Bauerschmidt (Cambridge): Log-Sobolev inequalities for Euclidean field theories and spin models
I will present an extension of the Bakry-Emery method for Log-Sobolev inequalities that applies to Euclidean field theories which are invariant measures of singular SPDEs. The method uses as input estimates on the renormalised potential which is the solution to Polchinski’s continuous renormalisation group equation. Examples where this applies include the sine-Gordon model (with mass term) and the ϕ4 models in d < 4 (uniformly in the volume up to the critical point), and also the near-critical Ising model in d > 4. This talk is based on joint works in Thierry Bodineau and Benoit Dagallier.

Seiichiro Kusuoka (kyoto): Construction of a non-Gaussian and rotation-invariant Φ − 4-measure and associ- ated flow on R3 through stochastic quantization
In this talk, we construct the Φ4-measure on R3 by approximations of interactions with localization and regularization. Here, we remark that for approximations, we do not apply scaling of a torus. As an advantage of our approximations, we can prove the rota- tion invariance of the Φ4-measure. To prove the convergence of the approximations, we apply the stochastic quantization and the methods of singular stochastic PDEs. This is a joint work with Sergio Albeverio. Asma Hassannezhad asma.hassannezhad@bristol.ac.uk A tour on Steklov eigenvalue problem We discuss the importance and the beauty of the Steklov eigenvalue problem and its connection to the Laplace eigenvalue problem. The talk will be a brief tour of some classic results and recent developments on the subject.

Terry Lyons (Oxford/Turing institute): TBA

Ajay Chandra (ICL): Paracontrolled calculus and regularity structures
We prove a general equivalence statement between the notions of models and modelled distributions over a regularity structure, and paracontrolled systems indexed by the reg- ularity structure. The construction of a modelled distribution from a paracontrolled system is explicit, and takes a particularly simple form in the case of the regularity structures introduced by Bruned, Hairer and Zambotti for the study of singular stochastic partial differential equations. This talk is based on a joint work with Ismae¨l Bailleul (Universite´ Rennes 1).

Masato Hoshino (Osaka): TBA


Friday, 16 September

Mark Pollicott (Warwick): TBA
Asma Hassannezhad (Bristol): TBA
Adam Harper (Warwick): TBA

Public Lectures at the Embassy of Japan (Entrance strictly by registration)

Martin Hairer (ICL): On Coin Tossing, Atoms and Forest Fires

Hiroshi Ooguri (Caltech and Kavli IPMU):The Science of the Man from the 9 Dimensions