Schedule and abstracts

Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoffmann-Ostenhof and Nadirashvili proved this to be false by constructing a counterexample in the plane with an unspecified, but large, number of holes and raised the question of the minimum number of holes a counterexample can have. In this talk I will present the construction and verification of a counter example with 6 holes. A large part of the verification is computer assisted and I will discuss how the problem can be reduced to something which can be checked by the computer.

In profile analysis, there exist three tests: test of parallelism, test of levels and test of flatness. In this talk, these tests have been studied. Firstly, a classical setting, where the sample size is greater than the dimension of the parameter space, is considered. The hypotheses have been established and likelihood ratio tests have been derived. The distributions of these test statistics have been given. In the latter stage, all tests have been derived in a high-dimensional setting, where the number of parameters exceeds the number of sample size. Such settings have become more common due to the advances in computer technologies in the last decades. In high-dimensional data analysis, several issues arise with the dimensionality and different techniques have been developed to deal with these issues. We propose a dimension reduction method using scores that was first proposed by Lauter et al. (1996). To be able to find the specific distributions of the test statistics of profile analysis in this context, the properties of spherical distributions are utilized.

Automorphism groups of free groups have long been objects of interest in group theory as well as low dimensional topology. This talk will be about homological stability results for these groups. I will informally explain what these (co)homology groups are and why we care about them, as well as give an overview of what is known about them, specifically in some stable range, i.e. when we let the number of generators of the free group be sufficiently large in comparison to the cohomological degree. The talk will land in my own recent results about stable rational cohomology with certain so called “twisted coefficients”. These cohomology groups assemble into an algebraic object known as a wheeled PROP, and it turns out that this gives them a very simple description.

Snow removal is an inevitable and important problem in some countries like Sweden. A number of streets in a city need to be cleared of snow by a limited number of vehicles. The problem can be formulated as a very large mixed integer programming model, which is practically unsolvable. In order to find a feasible solution, first we break done the work into smaller parts, one for each vehicle. We solve a weighted k-Chinese postman problem to find which streets a vehicle shall take care of. Based on the allocation obtained, we consider snow removal problems for single vehicles, where details such as turning penalties and precedences are included. These problems can be reformulated to asymmetric traveling salesman problems in extended graphs, and we have a heuristic for finding feasible solution of those. Finally, we discuss combined solution approaches and coordination of the vehicles to find a feasible solution for the whole original problem including all details. We use an iterative procedure to combine the tours, based on the tools mentioned above, and a procedure for constructive coordination of the tours. We also have new improvement procedures for the combined solution. We have implemented the methods and applied them to real life city networks. The numerical results show that the methods obtain feasible tours for large problems within a reasonable time.

Finding a directed acyclic graph (DAG) that best encodes the conditional independence statements observable from data is a central question within causality. Algorithms that greedily transform one candidate DAG into another given a fixed set of moves have been particularly successful, for example the GES, GIES, and MMHC algorithms. In 2010, Studen'y, Hemmecke and Lindner introduced the characteristic imset polytope, CIM_p, whose vertices correspond to Markov equivalence classes, as a way of transforming causal discovery into a linear optimization problem. We show that the moves of the aforementioned algorithms are included within classes of edges of CIM_p and that restrictions placed on the skeleton of the candidate DAGs correspond to faces of CIM_p. Thus, we observe that GES, GIES, and MMHC all have geometric realizations as greedy edge-walks along CIM_p. Furthermore, the identified edges of CIM_p strictly generalize the moves of these algorithms.

Ice sheets are melting and seawater is changing. To study the behavior of these physical systems, simulations rely on the solution of the Navier-Stokes equations, which is a a system of partial differential equations. To tackle this infinite-dimensional problem computationally, we need to discretize the domain in smaller chunks and approximate the solutions in some way. Join for a tour of fluid dynamics and of the finite elements methods, where we will discover how we go from the physical problem statement up to the solution methods modern simulation frameworks employ, and where you will get a feel for how different water setups evolve in time.

I will report on recent work about some cohomology groups of configuration spaces. In particular I will show how these groups are related to the Hochschild homology, and that when the configuration spaces are taken over a wedge of spheres then, up to a filtration, they are described by universal "polynomial" coefficients.

Persistent homology is a subject in Topological Data Analysis that takes a filtered topological space and studies how homology changes over the filtration. Given a simple filtration by the real line, the persistent homology of a filtered space is well-studied and can be decomposed into simple so-called bars. However, when the space has multiple filtrations, the theory of persistence becomes much more complex. In this talk I will present a homological algebraic approach to approximating multiparameter persistent homology by well-chosen families of simpler algebraic objects, including generalizations of the one-dimensional bars. I will also show how, under certain conditions, we can effectively compute certain features of this approximations.

16:30 - 16:38: Rigidity of ALF manifolds - Bernardo Hipólito Fernandes

16:40 - 16:48: Benford's Law and Circular Ensembles - Nedialko Bradinoff

16:50 - 16:58: Schramm-Loewner Evolution - a family of scaling limits - Ellen Krusell

17:00 - 17:08: Large Deviations and SLE - Vladislav Guskov

17:10 - 17:18: Noncommutative crepant resolutions and higher preprojective structures - Darius Dramburg

17:20 - 17:28: Introduction to the random lozenge tiling, a playground for all - Wen-Kui Liu

16:30 - 16:38: Multi-marginal optimal transport and its applications - Isabel Haasler

16:40 - 16:48: Optimization Methods for Scheduling in Radiation Therapy - Sara Frimodig

16:50 - 16:58: Optimal selection of points for extrapolation - Joar Bagge

17:00 - 17:08: The Overlap Gap Property: Showing when stable algorithms must fail - Vilhelm Agdur

17:10 - 17:18: Regularity properties of a nonlocal nonlinear operator - Seyed Alireza Tavakoli

17:20 - 17:28: The Triangle Inequality and Musical Harmony - Emanuel Ström