Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Analytic Number Theory
No full textAnalytic number theory has flourished over the past few years, and this workshop brought together world leaders and young talent to discuss developments in various branches of the subjec
Fourier-Mukai transform on Weierstrass cubics and commuting differential operators
No full textResearch in Pairs 2015In this article, we describe the spectral sheaves of algebras of commuting differential operators of genus one and rank two with singular spectral curve, solving a problem posed by Previato and Wilson. We also classify all indecomposable semi-stable sheaves of slope one and ranks two or three on a cuspidal Weierstraß cubic
Combinatorics and Probability
No full textFor the past few decades, Combinatorics and Probability Theory have had a fruitful symbiosis, each benefitting from and influencing developments in the other. Thus to prove the existence of designs, probabilistic methods are used, algorithms to factorize integers need combinatorics and probability theory (in addition to number theory), and the study of random matrices needs combinatorics. In the workshop a great variety of topics exemplifying this interaction were considered, including problems concerning designs, Cayley graphs, additive number theory, multiplicative number theory, noise sensitivity, random graphs, extremal graphs and random matrices
Diophantische Approximationen
No full textThis number theoretic conference was focused on a broad variety of subjects in (or closely related to) Diophantine approximation, including the following: metric Diophantine approximation, Mahler’s method in transcendence, geometry of numbers, theory of heights, arithmetic dynamics, function fields arithmetic
Algebraic Cobordism and Projective Homogeneous Varieties
No full textThe aim of this workshop was to bring together researchers in the theory of projective homogeneous varieties with researchers working on cohomology theories of algebraic varieties, so that the latter can learn about the needs in an area of successful applications of these abstract theories and the former can see the latest tools
Mini-Workshop: Topological Complexity and Related Topics
No full textTopological complexity is a numerical homotopy invariant of topological spaces, of Lusternik-Schnirelmann type, introduced by Farber and motivated by the motion planning problem from topological robotics. This mini-workshop assembled researchers interested in calculating the topological complexity and its many variants, with the aim of providing a snapshot of the current state of knowledge, and shaping directions of future research
Topologie
No full textThe Oberwolfach conference “Topologie” is one of only a few opportunities for researchers from many different areas in algebraic and geometric topology to meet and exchange ideas. This year we emphasized two topics of recent interest: representation stability and motivic homotopy theory, with their respective applications to arithmetic, classical homotopy theory as well as algebraic geometry. Double lectures on each topic where given by Benson Farb and Dan Isaksen. The rest of the program spanned a wide range of topics ranging from topological Hochschild homology to obstruction theory of positive scalar curvature, via, to name a few, -theory of -algebras, modular characteristic classes, Goodwillie calculus, 2-Segal spaces and deformation quantization
Recent Mathematical Developments in Quantum Field Theory
No full textThis workshop has focused on three areas in mathematical quantum field theory and their interrelations: 1) conformal field theory, 2) constructions of interacting models of quantum field theory by various methods, and 3) several approaches studying the interplay of quantum field theory and gravity
Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry
No full textWhile arrangements of hyperplanes have been studied in algebra, combinatorics and geometry for a long time, recent discoveries suggest that they (and more generally arrangements of nonlinear subvarieties) play an even more fundamental role in major problems in algebraic geometry than has yet been understood. The workshop brought into contact experts from commutative algebra and algebraic geometry working on these problems – it provided opportunities to get updated on the latest developments through talks of the participants, but also reserved time for working groups in which participants brainstormed ideas and insights in the context of high-intensity discussions aimed at initiating immediate progress on proposed problems, thereby setting the stage for on-going collaborations after the workshop