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The Hausdorff Research Institute for Mathematics (HIM)

Analytic questions of a discrete nature are ubiquitous in many areas of mathematics and theoretical computer science. The purpose of this conference is to bring together a diverse group of experts working, broadly, on Discrete Analysis with particular emphasis on questions having a geometric component. The topics will include Boolean analysis, vector-valued harmonic analysis, metric embeddings, geometry of graphs and groups, and aspects of discrete probability and theoretical computer science.

Schloss Dagstuhl – Leibniz-Zentrum für Informatik GmbH

The mathematical study of fundamental objects such as curves, embedded graphs, surfaces, and 3-manifolds has a rich and old history. However, the study of their algorithmic and combinatorial properties and the underlying computational questions is still in its infancy. There is a diverse pool of open problems and unanswered questions from the complexity- theoretic side. Examples include the hardness of realizability, the fine-grained complexity of distance and similarity measure computations, the existence of polynomial-time algorithms for flip distances, or the approximability of such distances. When dealing with polyhedral structures associated with geometric or topological objects, methods from Combinatorics and Algebra come into play to analyze structures such as associahedra, secondary polytopes, and mapping class groups of surfaces. Applied fields such as trajectory analysis and machine learning bring new questions and a fresh perspective to the field. This Dagstuhl Seminar on intractability in discrete geometry and topology will bring together researchers from the fields of computational complexity, computational geometry, topology, discrete geometry, and graph drawing; and will focus on the algorithmic, combinatorial, and computational questions mentioned above.

Wilhelm and Else Heraeus-Foundation

The Heraeus workshop “Topology and geometry: Novel concepts in 3D quantum transport on the mesoscale” explores charge transport in mesoscale systems where conventional Ohmic scaling breaks down. As device dimensions shrink and materials complexity grows, transport becomes governed by a rich interplay of geometry, topology, and many-body interactions. We aim to unify perspectives across three key areas: (1) topological transport shaped by quantum geometry and Berry curvature, (2) semiclassical and quantum transport under high magnetic fields, and (3) strongly correlated electron dynamics including hydrodynamic flow and quantum criticality. Particular emphasis is placed on identifying how disparate length scales—mean free path, magnetic length, and correlation length—conspire to shape transport in modern materials. The workshop will foster cross-disciplinary exchange between condensed matter physics, materials chemistry, and device theory.

Hausdorff School for Mathematics (HSM)

Geometry processing - the acquisition, reconstruction, and manipulation of geometry - is a vibrant research area with novel mathematical models and an increasing impact of machine learning tools. The challenges in these developments include the sheer size of data sets due to advancing acquisition technologies, robustness in the presence of noise and damaged data, the arbitrary topology of surface meshes, as well as the development of structure-preserving discrete algorithms.

Numerische Analysis,    Kurse und Veranstaltungen für Studenten der Mathematik

Hausdorff Center for Mathematics (HCM)

In the spirit of Matthias Lesch’s life’s work, internationally renowned researchers will present recent results from the areas of singular analysis on manifolds, noncommutative geometry and functional analytic methods.

On the occasion of Matthias Lesch's 65 birthday

The Hausdorff Research Institute for Mathematics (HIM)

Kurse und Veranstaltungen für Studenten der Mathematik,    Statistik, Spieltheorie

Hausdorff School for Mathematics (HSM)

The aim of this school is to bring together researchers working in the field of computational topology, particularly in persistence theory and its applications in Topological Data Analysis (TDA), to work together on topics in the field. By fostering collaboration at the intersection of mathematics, data science, and the natural sciences, the school will prepare students at the PhD or postdoc level with a solid background in topology or persistent homology to tackle open problems in TDA. There will be a selection of contributed talks.

Wilhelm and Else Heraeus-Foundation

In topology, properties of a geometric object are identified which remain unchanged under continuous deformations. Those properties are then referred to as topological invariants. This mathematical concept gains ever more importance in many branches of physics, comprising general relativity, quantum field theory, quantum chromodynamics, condensed matter, strongly correlated many-body system, magnetism, soft matter physics, and symmetry classification issues. Topological phases of matter have emerged as a far-reaching scientific breakthrough in the 21st century. The topological states were initially conceived as exotic states that are labeled by topological invariants interpreted as quantum numbers. Furthermore, the exotic transport properties exhibited by topological materials have been harnessed for applications in quantum technologies, making topology a very active research topic in quantum information theory and quantum computing. More recently, topological concepts have been studied in an increasingly diverse list of disciplines, also including applications in classical physics such as mechanics of elastic and deformable bodies, nonlinear dynamics, and biophysics. There are also considerable activites in mathematical physics.