Katrien Antonio (KU Leuven, Belgium)
Torsten Kleinow (University of Amsterdam)
Michel Vellekoop (University of Amsterdam)
Jens Robben (KU Leuven)
Ecole d\'été abstract
Abstract:
HEC welcomes actuaries from around the worldThe 35th International Summer School of the Swiss Association of Actuaries (ASA) will again be held on the campus of the University of Lausanne. Organized by the Department of Actuarial Science (DSA) and Professor Hansjörg Albrecher, more than a hundred actuaries from 25 countries will meet from June 3 to 7, 2024 at HEC. The ASA aims to promote actuarial science and related fields as well as risk management in general. This 35th edition of its summer school is entitled ‘Modelling and quantifying mortality and longevity risk ’.
09:00 • EPF Lausanne, Internef 273
Dr. Severin Schraven (TU Munich)
Two-sided Lieb-Thirring bounds abstract
Abstract:
We discuss upper and lower bounds for the number of eigenvalues of semi-bounded Schrödinger operators in all spatial dimensions. For atomic Hamiltonians with Kato potentials one can strengthen the result to obtain two-sided estimates for the sum of the negative eigenvalues. Instead of being in terms of the potential itself, as in the usual Lieb-Thirring result, the bounds are in terms of the landscape function, also known as the torsion function, which is a solution of $(-\\Delta + V +M)u_M =1$ in $\\mathbb{R}^d$; here $M\\in\\mathbb{R}$ is chosen so that the operator is positive. This talk is based on the preprint \\href{https://arxiv.org/abs/2403.19023}{arXiv:2403.19023} which is joint work with S. Bachmann and R. Froese.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Wenda Fang (RIMS Kyoto)
Generalized AKS Scheme of Integrability Via Vertex Algebra abstract
Abstract:
There is a well-known way to construct integrable systems via Lie algebra called the Adler-Kostant-Symes (AKS) scheme. Let g be a Lie algebra with an invariant, non-degenerate bilinear form ⟨ , ⟩. Let R be a classical Rmatrix of g, this gives a modified Lie algebra gR. Consider the Kirillov-Kostant Poisson structures on the g∗ and g∗R and denote Poisson brackets on g∗ and g∗R by { , } and { , }R, respectively. Then all functions in the Poisson center with respect to { , } are commute with respect to { , }R. In this talk, we define the classical R-matrix for the vertex Lie algebras. We will see that a sufficient condition for an operator on a vertex Lie algebra to be a classical R-matrix is the modified Yang-Baxter equation (mYBE) of vertex Lie algebra which is an analog of the mYBE of Lie algebra. By using this R-matrix of vertex Lie algebra, we give a new scheme of integrability.
15:30 • Université de Genève, Conseil Général 7-9, Room 1-07