Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Cutoff Phenomenon: Surprising Behaviour in Card Shuffling and other Markov Chains
No full textThis snapshot compares two techniques of shuffling a deck of cards, asking how long it will take to shuffle the cards until a “well-mixed deck” is obtained. Surprisingly, the number of shuffles can be very different for very similar looking shuffling techniques.[Also available in German
Random Graphs: Combinatorics, Complex Networks and Disordered Systems
No full textSince the turn of the millennium the theory of random graphs has advanced by leaps and bounds.
Random graphs have found very many applications, and many unexpected applications, in a remarkable variety of disciplines, and they are nowadays studied by mathematicians with various backgrounds (combinatorialists, probabilists, mathematical physicists), computer scientists and physicists.
While this diversity has led to a proliferation of new models, questions and results, the community also has shattered, and by now different methods, terminologies and research agendas have come to coexist without much interaction.
The workshop brought together distinct communities, who don't typically interact at their own intra-community events, but have each made significant contributions to the recent advancements in the theory. The workshop provided an effective platform for exchanging ideas, sharing insights, and building bridges across their respective domains
Partial Differential Equations
No full textThis workshop focused on nonlinear elliptic and parabolic partial differential equations, touching topics such as geometric flows, geometric variational problems and minimal surfaces, free boundaries, and geometric measure theory
Mini-Workshop: Combinatorial and Algebraic Structures in Rough Analysis and Related Fields
No full textRecent years have seen an explosion of algebraic methods to study singular stochastic
and rough dynamics. These include developments in geometric rough path theory
based on the algebra of words, the introduction of decorated trees in regularity
structures, and the recent approach to singular stochastic partial differential equations
based on multi-indices. These developments have furthermore led to important
links with numerical analysis, machine learning, stochastic quantisation, and the
study of symmetries of physical systems. The aim of this mini-workshop was to bring
together experts working on these fields using algebraic structures that appear in
rough dynamics. The goal was to facilitate the exchange of ideas and encourage further
connections to be established
New Challenges in the Interplay between Finance and Insurance
No full textThe aim of this workshop was to convene experts for fostering the discussion and the development of innovative approaches in insurance and financial mathematics. New challenges like price instability, huge insurance claims and climate change are affecting the markets, while at the same time the possibility of using large volumes of data and continuously increasing computer power as well as recently developed mathematical methods offer new opportunities for modelling and risk assessment.
Here we present an overview of these recent developments by providing the abstracts of the talks that were given during the week, together with a brief summary of the covered topics
Representations of Finite Groups
No full textThe workshop "Representations of Finite Groups" was organised by Olivier Dudas
(Marseille), Meinolf Geck (Stuttgart), Radha Kessar (Manchester), and Gabriel
Navarro (Valencia). It covered a wide variety of aspects of the representation theory
of finite groups and related topics, and showcased several recent breakthrough results
New Directions in Real Algebraic Geometry
No full textThis workshop explored the forefront of connections of real algebraic geometry with convex analysis, combinatorics, and computational complexity. Important aspects have been promising interactions with the fields of quantum information theory, discrete geometry, complex and random algebraic geometry
The Geometry of Fair Division
No full textHow can we fairly divide a necklace with various types of beads? We use this problem as a motivating example to explain how geometry naturally appears in solutions of non-geometric problems. The strategy we develop to solve this problem has been used in several other contexts
Characterizations of intrinsic volumes on convex bodies and convex functions
No full textWenn wir die Größe einer zweidimensionalen Form mittels einer Zahl ausdrücken wollen, dann denken wir gewöhnlich an ihren Flächeninhalt oder ihren Umfang. Aber was macht diese Kennzahlen so besonders? Wir beantworten diese Frage anhand klassischer mathematischer Resultate und werfen einen Blick auf Anwendungen und Verallgemeinerungen dieser Theorie
Komplexe Analysis - Differential and Algebraic methods in Kähler spaces
No full textOur workshop focused on recent results in our main field (complex geometry) and its connection with
other branches of mathematics. The main theme of an important proportion of the talks was Hodge theory, combined with differential-geometric methods in the study of singular spaces. One special lecture was a very comprehensive introduction in Scholze-Clausen's theory of condensed mathematics