Veranstaltungen

In this talk, I will discuss work in progress, joint with Kai Hugtenburg, on defining open Gromov-Witten invariants (in genus zero) for embedded relatively spin Lagrangians in general closed symplectic manifolds. Our definition rests on the construction of a global Kuranishi chart for the relevant moduli spaces and is an invariant of the almost complex structure. We prove a relation between the invariants of Lagrangians related a Lagrangian cobordism. Time permitting, I will also discuss some results in higher genus.

This will describe joint work with Decio, Engelstein, Mayboroda, Michetti, with help of Filoche. The main question is the boundary behavior of harmonic functions on a domain in Euclidean space, subject to a Robin condition on the boundary $\frac{\partial u}{\partial n} + a u = f$, where $a > 0$ is a positive parameter and $f$ is the data, and measured by the Robin analogue of the harmonic measure on the boundary. For the Dirichlet condition $u = f$ on the boundary, we get the usual harmonic measure and it is known that its absolute continuity with respect to surface measure is a subtle issue. For the Robin condition, it turns out that the situation is much simpler, even on domains with a fractal boundary.

Toroidal compactifications and their cone stacks

The waist inequality for the sphere by Gromov is wonderful result of geometric measure theory. Formulated appropriately for families of spaces, a (uniform) waist inequality for a family of Riemannian manifolds is the Riemannian analog of higher dimensional expanders. We formulate a conjectural picture for locally symmetric spaces. Finally, we show that the Kazhdan property alone gives rise not only to expanders, which is classical, but also to 2-dimensional expanders. An extra dimension for free! This is joint work with Uri Bader.

The goal of this talk is to provide a brief overview of the interactions between hyperbolic surfaces and certain combinatorial objects. Specifically, we will explore Brock's combinatorial approach to understanding the coarse geometry of Teichmüller space equipped with the Weil-Petersson metric. This approach revolves around using the pants graph as a combinatorial tool for navigating Teichmüller space. Along the way, we will also encounter the hexagons graph and other related questions.

Calderon's inverse problem asks whether one can determine the conductivity of a medium by making voltage and current measurements at the boundary. This question arises in several areas of applications including medical imaging and geophysics. I will report on some of the progress that has been made on this problem since Calderon proposed it in 1980, including recent developments on similar problems for nonlinear equations and nonlocal operators. We will also discuss several open problems.

This talk is about asymptotic formulas for the number of rational points of bounded (or large) height on Hirzebruch-Kleinschmidt varieties over global fields. These varieties are realizations of split toric varieties with Picard rank 2, and their explicit models enable computations that go beyond the general expectation of the Manin-Peyre conjecture. This is joint work with Tobías Martínez (University of El Salvador) and Pedro Montero (UTFSM, Chile).

Simulation studies are widely used in methodological research fields such as statistics, psychometrics, bioinformatics, ecology, econometrics, or machine learning. They generate artificial data sets under specified mechanisms and compare the performance of data analysis methods under different conditions. Careful design, analysis, and reporting of simulation studies is important because they often provide the basis for data analysis decisions in scientific and medical practice. Problems with the reporting of simulation studies were first described nearly half a century ago. Recent attention to reproducibility issues in the biomedical and social sciences has led to more critical reflection on simulation studies and new proposals for improving them. In this talk, I will provide an overview of these recent meta-scientific developments. I will also discuss how questionable research practices (QRPs), such as cherry-picking of favorable results, can affect the validity of simulation studies. To illustrate this point, I present a simulation study of a novel prediction method with no expected performance gain, and show how easy it is to make the method appear superior to well-established competing methods when QRPs are employed. I also discuss approaches for addressing QRPs, and present a newly developed template for preregistration of simulation studies. References: - Pawel, S., Kook, L., Reeve, K. (2024). Pitfalls and potentials in simulation studies: Questionable research practices in comparative simulation studies allow for spurious claims of superiority of any method. Biometrical Journal. https://doi.org/10.1002/bimj.202200091 - Siepe, B.S., Bartos, F., Morris, T.P., Boulesteix, A.-L., Heck, D.W., Pawel, S. (2024). Simulation Studies for Methodological Research in Psychology: A Standardized Template for Planning, Preregistration, and Reporting. Psychological Methods (to appear). https://doi.org/10.31234/osf.io/ufgy6