Oberwolfach Reports (OWR)
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- ItemInterfaces, Free Boundaries and Geometric Partial Differential Equations(Zürich : EMS Publ. House, 2024) Elliott, Charles M.; Garcke, Harald; Niethammer, Barbara; Simonett, GieriPartial differential equations arising in the context of interfaces and free boundaries encompass a flourishing area of research. The workshop focused on new developments and emerging new themes. At the same time also new interesting results on more traditional areas like, e.g. regularity theory and classical numerical approaches have been addressed. By convening experts from various disciplines related to modeling, analysis, and numerical methods concerning interfaces and free boundaries, the workshop facilitated progress on longstanding open questions and paved the way for novel research directions.
- ItemDiscrete Geometry(Zürich : EMS Publ. House, 2024) Adiprasito, Karim; Goaoc, Xavier; Patáková, ZuzanaA number of important recent developments in various branches of discrete geometry were presented at the workshop. The presentations illustrated both the diversity of the area and its strong connections to other fields of mathematics such as convex geometry, combinatorics, or topology. Two open problem sessions highlighted the abundance of open questions and many of the results presented were obtained by young researchers, confirming the vitality of the field.
- ItemMini-Worskhop: Artin Groups meet Triangulated Categories(Zürich : EMS Publ. House, 2024) Boyd, Rachael; Heng, Edmund; Ozornova, ViktoriyaArtin and Coxeter groups are naturally occurring generalisations of the braid and symmetric groups respectively. However, unlike for Coxeter groups, many basic group theoretic questions remain unanswered for general Artin groups – most notably the K(π,1)-conjecture for Artin groups remains open except for certain special families of Artin groups. Recently, Artin groups have also appeared as groups acting on triangulated categories, where the associated spaces of Bridgeland's stability conditions provide new realisations of the corresponding K(π,1) spaces. The aim of the workshop is to bring together experts and early career researchers from two seemingly different areas of research: (i) geometric and combinatorial group theory and topology, and (ii) triangulated categories and stability conditions, to explore their intersection via the K(π,1)-conjecture.
- ItemMini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations(Zürich : EMS Publ. House, 2024) Carnovale, Giovanna; Heckenberger, István; Vendramin, LeandroNichols algebras are graded Hopf algebra objects in braided tensor categories. They appeared first in a paper by Nichols in 1978 in the search for new examples of Hopf algebras. Rediscovered later several times, they also provide a conceptual explanation of the construction of quantum groups. The aim of the workshop is to review recent developments in the field, initiate collaborations, and discuss new approaches to open problems.
- ItemMini-Workshop: Permutation Patterns(Zürich : EMS Publ. House, 2024) Bóna, Miklós; Bouvel, Mathilde; Brignall, Robert; Pantone, JayThe study of permutation patterns has recently seen several surprising results, and the purpose of this mini-workshop was to bring together researchers from across the field to focus on four hot topics related to these recent developments. The topics covered the nature of generating functions that enumerate permutation classes, the structure of permutation classes and the impact this has on their growth rates, and the study of permutons, which lies at the interface of permutation patterns and discrete probability. The workshop offered an opportunity for knowledge exchange, but also time and space to initiate group collaborations on open problems related to these topics.