Hamza Hanbali (University of Melbourne)
Liquidity Shocks, Homeownership, and Income Inequality: Impact of Early Pension Withdrawals and Reduced Deposit abstract
Abstract:
This paper examines the impact of two housing affordability policies (reduced mortgage deposits, and early withdrawal of pension savings) on homeownership and inequality. Both policies are framed as liquidity shocks that ease upfront constraints without increasing household wealth. A lifecycle model is developed to simulate renters’ financial trajectories and housing decisions under each policy. The analysis is powered by an econometric model that captures feedback between household demand and the effect of the housing policy on house prices, with a calibration to Australian data.
11:00 • EPF Lausanne, Extranef 126
Mechthild Thalhammer (Universität Innsbruck)
Recent advances on exponential operator splitting methods for nonlinear evolution equations of Schrödinger and parabolic type abstract
Abstract:
Exponential operator splitting methods constitute a favourable class of time integration methods for various kinds of linear and nonlinear evolution equations.They rely on the presumption that the defining right-hand side comprises two (or more) operators and that the numerical approximation of the associated subproblems is significantly simpler compared to the numerical approximation of the original problem. Under these premises, their excellent behaviour with respect to stability, accuracy, and the preservation of conserved quantities has been confirmed by a remarkable amount of contributions.In my talk, I will review well-known achievements and recent advances on exponential operator splitting methods. As fundamental test problems, I will study Gross-Pitaevskii equations modelling Bose-Einstein condensates, their parabolic counterparts arising in ground and excited state computations, complex Ginzburg-Landau equations having a similar structure, and high-order semilinear parabolic equations describing quasicrystalline patterns. I will contrast standard splitting schemes involving real coefficients with two alternative approaches that are based on the incorporation of complex coefficients or double commutators, respectively. Besides, I will demonstrate that the formal calculus of Lie derivatives provides powerful tools regarding the design and analysis of splitting methods in the context of nonlinear evolution equations.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Lia Gaiur (UniGE)
Motivic Kernels to Algebraic Relations: A Bessel Function Case abstract
Abstract:
I will report on work in progress related to the algebraization of product formulas for the higher Bessel functions introduced by V. Rubtsov, D. van Straten, and myself. Product formulas for higher Bessel functions (and, more generally, for hypergeometric functions) take the form of integral equations that relate products at different points (tensor products) to integrals with parametric kernels. As we have shown, the integral operators that appear in such formulas admit a natural geometric interpretation.I will give a brief overview of this geometric interpretation and its connection to the Givental version of mirror symmetry and averaging formulas. Furthermore, I will demonstrate how this geometric perspective enables the reformulation of Bessel function identities in an algebraic framework. This approach naturally generalizes the product of exponential functions and allows for the introduction of q-analogues of Bessel functions via the Manin q-plane.In the remaining time, I will discuss possible extensions, connections with differential equations and open problems related that may be of interest to the audience.
15:00 • Université de Genève, Conseil Général 7-9, Room 1-07
Aleksandr Trufanov (Montréal)
Gelfand–Tsetlin Bases in Admissible Representations of \\widehat{gl}(n) abstract
Abstract:
The classical Gelfand–Tsetlin (GT) basis provides a convenient indexing of basis vectors in finite-dimensional representations of gl(n) via Gelfand–Tsetlin tableaux, which can be viewed as semi-standard Young tableaux of a fixed shape. In arXiv:0812.4656v4, this construction was extended to integrable modules of the affine Lie algebra \\widehat{gl}(n). In this talk, we further generalize the GT basis construction to admissible representations of \\widehat{gl}(n). This leads to a combinatorial formula for the characters of admissible representations, generalizing the expression of the Schur polynomial as a generating function of semi-standard tableaux. This talk is based on work in progress with M.Bershtein, E.Mukhin, and L.Rybnikov.
16:15 • Université de Genève, Conseil Général 7-9, Room 1-07
Prof. Dr. Alex Wein (UC Davis)
Overcomplete Tensor Decomposition via Koszul-Young Flattenings abstract
Abstract:
An order-3 tensor is an n-by-n-by-n array of real numbers. We considerthe task of decomposing a given tensor as the sum of rank-1 tensors,using the minimal number of terms. This task has various applicationsin statistics and data science, such as learning the latent parametersof certain statistical models from the empirical third moment tensor.Under the standard assumption that the tensor components are"generic," a classical method called simultaneous diagonalization or"Jennrich\'s algorithm" can decompose tensors of rank up to r <= n inpolynomial time. A recent result of Koiran (2024) improves this to r<= 4n/3, and we improve this further to r <= 2n. The algorithm isbased on a non-trivial procedure for "flattening" tensors to matrices.We also give a matching impossibility result, showing that noflattening of the style we consider can surpass 2n. This may suggest afundamental barrier for fast algorithms.
16:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room 19.1