101 results
Search Results
Now showing 1 - 10 of 101
- ItemComputational Inverse Problems for Partial Differential Equations (hybrid meeting)(Zürich : EMS Publ. House, 2020) Hohage, Thorsten; Kaltenbacher, BarbaraInverse problems in partial differential equations (PDEs) consist in reconstructing some part of a PDE such as a coefficient, a boundary condition, an initial condition, the shape of a domain, or a singularity from partial knowledge of solutions to the PDE. This has numerous applications in nondestructive testing, medical imaging, seismology, and optical imaging. Whereas classically mostly boundary or far field data of solutions to deterministic PDEs were considered, more recently also statistical properties of solutions to random PDEs have been studied. The study of numerical reconstruction methods of inverse problems in PDEs is at the interface of numerical analysis, PDE theory, functional analysis, statistics, optimization, and differential geometry. This workshop has mainly addressed five related topics of current interest: model reduction, control-based techniques in inverse problems, imaging with correlation data of waves, fractional diffusion, and model-based approaches using machine learning.
- ItemStatistics of Stochastic Differential Equations on Manifolds and Stratified Spaces (hybrid meeting)(Zürich : EMS Publ. House, 2021) Li, Xue-Mei; Pokern, Yvo; Sturm, AnjaStatistics for stochastic differential equations (SDEs) attempts to use SDEs as statistical models for real-world phenomena. This involves an understanding of qualitative properties of this class of stochastic processes which includes Brownian motion as well as estimation of parameters in the SDE or a nonparametric estimation of drift and diffusivity fields from observations. Observations can be in continuous time, in high frequency discrete time considering the limit of small inter-observation times or in discrete time with constant inter-obseration times. Application areas of SDEs where state spaces are naturally viewed as manifolds or stratified spaces include multivariate stochastic volatility models, stochastic evolution of shapes (e.g. of biological cells), time-varying image deformations for video analysis and phylogenetic trees.
- ItemDynamische Systeme (hybrid meeting)(Zürich : EMS Publ. House, 2021) Hofer, Helmut; Hutchings, Michael; Kaloshin, VadimThis workshop continued a biannual series of workshops at Oberwolfach on dynamical systems that started with a meeting organized by Moser and Zehnder in 1981. Workshops in this series focus on new results and developments in dynamical systems and related areas of mathematics, with symplectic geometry playing an important role in recent years in connection with Hamiltonian dynamics. In this year special emphasis was placed on various kinds of spectra (in contact geometry, in Riemannian geometry, in dynamical systems and in symplectic topology) and their applications to dynamics.
- ItemHomotopic and Geometric Galois Theory (online meeting)(Zürich : EMS Publ. House, 2021) Dèbes, Pierre; Nakamura, Hiroaki; Stix, JakobIn his "Letter to Faltings'', Grothendieck lays the foundation of what will become part of his multi-faceted legacy to arithmetic geometry. This includes the following three branches discussed in the workshop: the arithmetic of Galois covers, the theory of motives and the theory of anabelian Galois representations. Their geometrical paradigms endow similar but complementary arithmetic insights for the study of the absolute Galois group $\mathrm{G}_{\mathbb{Q}}$ of the field of rational numbers that initially crystallized into a functorially group-theoretic unifying approach. Recent years have seen some new enrichments based on modern geometrical constructions - e.g. simplicial homotopy, Tannaka perversity, automorphic forms - that endow some higher considerations and outline new geometric principles. This workshop brought together an international panel of young and senior experts of arithmetic geometry who sketched the future desire paths of homotopic and geometric Galois theory.
- ItemMini-Workshop: Three Facets of R-Matrices (hybrid meeting)(Zürich : EMS Publ. House, 2021) Smirnov, Andrey; Wendlandt, Curtis; Yamazaki, MasahitoBy definition, an $R$-matrix with spectral parameter is a solution to the Yang-Baxter equation, introduced in the 1970's by C.N. Yang and R.J. Baxter. Such a matrix encodes the Boltzmann weights of a lattice model of statistical mechanics, and the Yang-Baxter equation appears naturally as a sufficient condition for its solvability. In the last decade, several mathematical and physical theories have led to seemingly different constructions of $R$-matrices. The theme of this workshop was the interaction of three such approaches, each of which has independently proven to be valuable: the geometric, analytic and gauge-theoretic constructions of $R$-matrices. Its aim was to bring together leading experts and researchers from each school of thought, whose recent works have given novel interpretations to this nearly classical topic.
- ItemGeometric Numerical Integration (hybrid meeting)(Zürich : EMS Publ. House, 2021) Lubich, Christian; McLachlan, Robert; Sanz-Serna, Jesús MaríaThe topics of the workshop included interactions between geometric numerical integration and numerical partial differential equations; geometric aspects of stochastic differential equations; interaction with optimisation and machine learning; new applications of geometric integration in physics; problems of discrete geometry, integrability, and algebraic aspects.
- ItemRepresentation Theory of Quivers and Finite Dimensional Algebras(Zürich : EMS Publ. House, 2020) Crawley-Boevey, William; Iyama, Osamu; Krause, HenningMethods and results from the representation theory of quivers and finite dimensional algebras have led to many interactions with other areas of mathematics. Such areas include the theory of Lie algebras and quantum groups, commutative algebra, algebraic geometry and topology, and in particular the theory of cluster algebras. The aim of this workshop was to further develop such interactions and to stimulate progress in the representation theory of algebras.
- ItemApplied Harmonic Analysis and Data Science (hybrid meeting)(Zürich : EMS Publ. House, 2021) Kutyniok, Gitta; Rauhut, Holger; Strohmer, ThomasData science has become a field of major importance for science and technology nowadays and poses a large variety of challenging mathematical questions. The area of applied harmonic analysis has a significant impact on such problems by providing methodologies both for theoretical questions and for a wide range of applications in signal and image processing and machine learning. Building on the success of three previous workshops on applied harmonic analysis in 2012, 2015 and 2018, this workshop focused on several exciting novel directions such as mathematical theory of deep learning, but also reported progress on long-standing open problems in the field.
- ItemEnveloping Algebras and Geometric Representation Theory (hybrid meeting)(Zürich : EMS Publ. House, 2021) Leclerc, Bernard; Varagnolo, MichaelaThe workshop brought together experts investigating algebraic Lie theory from the geometric and categorical viewpoints.
- ItemCombinatorics(Zürich : EMS Publ. House, 2020) Steger, Angelika; Sudakov, BennyCombinatorics is a fundamental mathematical discipline that focuses on the study of discrete objects and their properties. The present workshop featured research in such diverse areas as Extremal, Probabilistic and Algebraic Combinatorics, Graph Theory, Discrete Geometry, Combinatorial Optimization, Theory of Computation and Statistical Mechanics. It provided current accounts of exciting developments and challenges in these fields and a stimulating venue for a variety of fruitful interactions. This is a report on the meeting, containing extended abstracts of the presentations and a summary of the problem session.