Oberwolfach Reports最新文献

{"title":"MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties","authors":"Gunnar Fløystad, S. Murai, C. Riener, Kohji Yanagawa","doi":"10.4171/owr/2021/43","DOIUrl":"https://doi.org/10.4171/owr/2021/43","url":null,"abstract":"The study of symmetry as a structural property of algebraic objects is one of the fundamental pillows of the developments of modern mathematics, most prominently beginning with the work of Abel and Galois. The focus of the workshop was on permutation actions of the symmetric group on polynomial rings and algebraic and semi-algebraic sets. More concretely, it was centered around recent developments in the asymptotic setup of symmetric ideals in the polynomial ring in infinitely many variables. Mathematics Subject Classification (2010): 13A99, 13F20, 13P10,20B30. Introduction by the Organizers The MFO-RIMS Tandem Workshop Symmetries on Polynomial Ideals and Varieties organised by Gunnar Fløystad (Bergen), Satoshi Murai (Tokyo), Cordian Riener (Tromsø), and Kohji Yanagawa (Osaka) took place between September 5– 11 2021 as a joint hybrid workshop hosted at the Mathematical Research Institute Oberwolfach and the Research Institute for Mathematical Sciences in Kyoto. Unfortunately, the ongoing Covid-19 pandemic made it impossible to have a physical meeting in Kyoto and the workshop was therefore attended by 14 participants physically at MFO and another 24 participants who joint in virtually. The main focus of the workshop was on the study of properties of ideals in the infinite polynomial ring which are invariant with respect to actions of the 2 Oberwolfach Report 43/2021 symmetric group. As has been observed by various authors, many properties of classical commutative algebra, which fail for the infinite polynomial ring, can be restored when considered in an equivariant setup, up to symmetry. Most notably, it had been already observed by Cohn in the 1980s that although the infinite polynomial ring is not Noetherian symmetric, ideals can always be generated by finitely many orbits of polynomials. In recent years renewed motivation to study such ideals stemmed from the observation that one can view such ideals as limits of sequences of algebraic objects which arise in the area of algebraic statistics and algebraic chemistry. One main goal of the joint workshop between the two research institutes was to bring together different mathematicians working on various aspects of this thematic area and, in particular, build new research connections between Europe and Asia around this topic. The technical facilities in the lecture halls allowed recording of the talks and interactions between remote participants. We would say this worked well, with some minor technical problems. On the Japanese side they had the disadvantage that each participant was in their home or office, so all interaction was digital. Nevertheless, questions after talks, and problem discussions worked well interactively. Also, the time difference between the two groups of participants made it necessary to distinguish between talks, which could followed by all participants live and talks which were recorded because their time slot was falling into very early hours in Europe or very late hours ","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121905520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Arbeitsgemeinschaft: Derived Galois Deformation Rings and Cohomology of Arithmetic Groups","authors":"Frank Calegari, Søren Galatius, Akshay Venkatesh","doi":"10.4171/owr/2021/18","DOIUrl":"https://doi.org/10.4171/owr/2021/18","url":null,"abstract":"","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128044377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles","authors":"K. Chemla, Vincenzo De Risi, A. Malet","doi":"10.4171/owr/2021/26","DOIUrl":"https://doi.org/10.4171/owr/2021/26","url":null,"abstract":"","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126134542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis, Geometry and Topology of Singular PDE","authors":"C. Debord, R. Mazzeo, P. Piazza, Boris Vertman","doi":"10.4171/owr/2021/27","DOIUrl":"https://doi.org/10.4171/owr/2021/27","url":null,"abstract":"","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129008927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical Methods for Fully Nonlinear and Related PDEs","authors":"S. Bartels, S. C. Brenner, Xiaobing H. Feng, M. Neilan","doi":"10.4171/owr/2021/31","DOIUrl":"https://doi.org/10.4171/owr/2021/31","url":null,"abstract":"","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128578887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mini-Workshop: Analysis of Data-driven Optimal Control","authors":"Lars Grüne, K. Morris","doi":"10.4171/owr/2021/23","DOIUrl":"https://doi.org/10.4171/owr/2021/23","url":null,"abstract":". This hybrid mini-workshop discussed recent mathematical methods for analyzing the opportunities and limitations of data-driven and ma-chine-learning approaches to optimal feedback control. The analysis con-cerned all aspects of such approaches, ranging from approximation theory particularly for high-dimensional problems via complexity analysis of algorithms to robustness issues.","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"188 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133782384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Small Collaboration: Modeling Phenomena from Nature by Hyperbolic Partial Differential Equations","authors":"C. Klingenberg, Qin Li, M. Pirner","doi":"10.4171/owr/2021/19","DOIUrl":"https://doi.org/10.4171/owr/2021/19","url":null,"abstract":"Nonlinear hyperbolic partial differential equations constitute a plethora of models from physics, biology, engineering, etc. In this workshop we cover the range from modeling, mathematical questions of well-posedness, numerical discretization and numerical simulations to compare with the phenomenon from nature that was modeled in the first place. Both kinetic and fluid models were discussed. Mathematics Subject Classification (2010): 35B40, 35L65, 35Q20, 35R30, 65M06, 76W05, 82C40. Introduction by the Organizers The workshop (held in a hybrid format) titled Modeling Phenomena from Nature by Hyperbolic Partial Differential Equations, organized by Christian Klingenberg (Würzburg, Germany), Qin Li (Madison, Wisc., USA) and Marlies Pirner (Würzburg, Germany) was attended by 18 participants, 9 of which were female. Nonlinear hyperbolic systems of time-dependent partial differential equations are important mathematical models for a large number of complex natural systems of fundamental interest. The governing equations can be derived from first principles. In applications these models are used with great success. In this workshop we spanned the gamut from modeling physical phenomena by hyperbolic partial differential equations, discussing questions of existence, uniqueness and well-posedness, their numerical discretization and related numerical analysis and numerical implementation questions to numerical simulations in order to ascertain how this matches the physical phenomenon at hand. 2 Oberwolfach Report 19/2021 Depending on the time scale and spatial scale in the application at hand, the models may be either microscopic kinetic equations or a macroscopic fluid equations. Both types of models were discussed. Next we list some of those topics. Kinetic models Here we take an atomistic view of the flow. Considering density distributuons of these micrsoscopically interacting particles, we obtain Boltzmann-type equations consisting of a first order transport operator for the density distribution of the particles which are set equal to a zeroth order term describing the interaction between the particles. As reported on by Marlies Pirner, she models gas mixtures in this way, see e.g. [1], and proves that this model satisfies physical properties. The numerical implementation of this new model needs to be found. Seok-Bae Yun and Gi-Chan Bae reported on theoretical aspects of certain kinetic models, which lend itself to efficient numerical simulations, while still modeling the physics appropriately. For a kinetic model of plasma, the Vlasov-Poisson model, enhanced by a BGK relaxation term, aspects of Landau damping were discussed by Lena Baumann. The study of uncertainty quantification for kinetic models was discussed, see here [2]. But uncertainty quantification does not always represent the viewpoint of the experimentalists. Instead they want to determine the uncertain coefficient in a PDE by measuring the solution at the parts of the boundary, given data o","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116615451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Enumerative Geometry of Surfaces","authors":"G. Borot, S. Grushevsky, Martin Möller","doi":"10.4171/owr/2021/28","DOIUrl":"https://doi.org/10.4171/owr/2021/28","url":null,"abstract":"","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"1999 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131083611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mini-Workshop: Mathematics of Dissipation – Dynamics, Data and Control","authors":"S. Grundel, V. Mehrmann, J. Scherpen, Felix L. Schwenninger","doi":"10.4171/owr/2021/24","DOIUrl":"https://doi.org/10.4171/owr/2021/24","url":null,"abstract":"","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125193473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Foundations of Bayesian Inference for Complex Statistical Models","authors":"Richard Nickl, J. Rousseau, A. van der Vaart","doi":"10.4171/owr/2021/22","DOIUrl":"https://doi.org/10.4171/owr/2021/22","url":null,"abstract":". In this virtual workshop a variety of recent developments in Bayesian high-dimensional and nonparametric statistics were discussed in depth. There were 12 in depth talks delivered via zoom in the afternoons (to allow for US attendance), and several informal evening time meetings on wonder.me, where follow up discussions of the most important mathematical developments took place.","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125325383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}