Lewis De Felice (University of Melbourne, Australia)
Optimal strategies for the decumulation of retirement savings under differing appetites for liquidity and investment risks
11:00 • EPF Lausanne, Extranef 126
Jürgen Dölz (University of Bonn)
Abstract:
We consider generalized symmetric operator eigenvalue problems with random symmetric perturbations of the operators. This implies that the eigenpairs of the eigenvalue problem are also random. We investigate stochastic quantities of interest of eigenpairs of higher but finite multiplicity and discuss why for multiplicity larger than one, only the stochastic quantities of interest of the eigenspaces are meaningful. To do so, we characterize the Fréchet derivatives of the eigenpairs with respect to the perturbation and provide a new linear characterization for eigenpairs of higher multiplicity. As a side result, we prove local analyticity of the eigenspaces. Based on the Fréchet derivatives of the eigenpairs we discuss a meaningful Monte Carlo sampling strategy for multiple eigenvalues and develop an uncertainty quantification perturbation approach. We present numerical examples to illustrate the theoretical results. For further information about the seminar, please visit this webpage .
11:00 • Universität Basel, DMI, Spiegelgasse 5, 4051 Basel Seminarraum 05.001
Dr. Francesco Zerman (UniDistance Suisse)
Heegner points on Pizer curves abstract
Abstract:
Let $E/\\mathbb{Q}$ be an elliptic curve of conductor $N$ and let $K$ be an imaginary quadratic field. Assume that $N=N^+ N^-$ with $N^+$ split in $K$ and $N^-$ squarefree and inert in $K$. Under this "generalised" Heegner hypothesis, in the last thirty years there have been many works building $K$-Heegner points on $E$ by studying the arithmetic of Eichler orders of level $N^+$ inside the quaternion algebra of discriminant $N^-$ over $\\mathbb{Q}$. The existence of nontrivial systems of Heegner points has always deep consequences, leading to rank one results for $E(K)$ and to control on the arithmetic of $E$ over anticyclotomic $p$-extensions of $K$. Much less is known when $N^-$ is not squarefree. In this talk, I will explain how one can use the arithmetic of Pizer orders to build Heegner points in this setting, building on a recent work of Longo, Rotger and de Vera-Piquero. I will then show how their work could be generalized to study other Galois representations, mainly focusing on Hida families of modular forms. This is a joint work with Luca Dall\'Ava.
14:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Gigliola Staffilani (Massachusetts Institute of Technology)
Stable blowup for the higher-dimensional Skyrme model abstract
Abstract:
In this talk we will use the periodic cubic nonlinear Schrödinger equation to present some estimates of the long time dynamics of the energy spectrum, a fundamental object in the study of wave turbulence theory. Going back to Bourgain, one possible way to conduct the analysis is to look at the growth of high Sobolev norms. It turns out that this growth is sensitive to the nature of the space periodicity of the system. I will present a combination of old and very recent results in this direction.
14:15 • EPF Lausanne, MA B1 11
Adam Sykulski (Imperial College London)
Debiasing Welch\'s Method for Spectral Density Estimation
15:15 • EPF Lausanne, CM 1 517
Dr. Sergej Monavari (EPFL)
Tetrahedron instantons in Donaldson-Thomas theory abstract
Abstract:
Tetrahedron instantons were recently introduced by Pomoni-Yan-Zhang in string theory, as a way to describe systems of D0-D6 branes with defects. We propose a rigorous geometric interpretation of their work by the point of view of Donaldson-Thomas theory. We will explain how to naturally construct the moduli space of tetrahedron instantons as a Quot scheme, parametrizing quotients of a torsion sheaf over a certain singular threefold, and how to construct a virtual fundamental class in this setting using quiver representations and the recent machinery of Oh-Thomas (which is in principle designed for moduli spaces of sheaves on Calabi-Yau 4-folds). Furthermore, we will show how to formalize mathematically the invariants considered by Pomoni-Yan-Zhang (initially defined via supersymmetric localization in Physics) and how to rigorously compute them, solving some open conjectures. Joint work with Nadir Fasola.
16:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Fadoua Balabdaoui (ETH Zürich)
Abstract:
Consider the regression problem where the response $Y\\in \\mathbb R$ and the covariate $X\\in \\mathbb R^d $ for $d\\geq 1$ are \\textit{unmatched}. Under this scenario we do not have access to pairs of observations from the distribution of $(X, Y)$, but instead we have separate data sets $\\{Y_i\\}_{i=1}^n$ and $\\{X_j\\}_{j=1}^m$, possibly collected from different sources. We study this problem assuming that the regression function is linear and the noise distribution is known or can be estimated. We introduce an estimator of the regression vector based on deconvolution and demonstrate its consistency and asymptotic normality under an identifiability assumption. In the general case, we show that our estimator (DLSE: Deconvolution Least Squares Estimator) is consistent in terms of an extended $\\ell_2$ norm. Using this observation, we devise a method for semi-supervised learning, i.e., when we have access to a small sample of matched pairs $(X_k, Y_k)$. Several applications with synthetic and real data sets are considered to illustrate the theory.The talk is based on a joint work with Mona Azadkia
16:15 • Universität Bern, IMSV, Alpeneggstrasse 22, 3012 Bern, Hörraum -203