{"title":"Mini-Workshop: Mathematics of Many-body Fermionic Systems","authors":"Nikolai Leopold, P. T. Nam, C. Saffirio","doi":"10.4171/owr/2023/49","DOIUrl":"https://doi.org/10.4171/owr/2023/49","url":null,"abstract":"","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"76 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141810521","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}
Carlo Bellingeri, Y. Bruned, Ilya Chevyrev, Rosa Preiß
{"title":"Mini-Workshop: Combinatorial and Algebraic Structures in Rough Analysis and Related Fields","authors":"Carlo Bellingeri, Y. Bruned, Ilya Chevyrev, Rosa Preiß","doi":"10.4171/owr/2023/54","DOIUrl":"https://doi.org/10.4171/owr/2023/54","url":null,"abstract":"","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"131 43","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141811239","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: Positivity and Inequalities in Convex and Complex Geometry","authors":"Andreas Bernig, Julius Ross, Thomas Wannerer","doi":"10.4171/owr/2023/51","DOIUrl":"https://doi.org/10.4171/owr/2023/51","url":null,"abstract":"","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"90 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141812920","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}
Maria Stella Adamo, Gandalf Lechner, Roberto Longo, K. Neeb
{"title":"Mini-Workshop: Standard Subspaces in Quantum Field Theory and Representation Theory","authors":"Maria Stella Adamo, Gandalf Lechner, Roberto Longo, K. Neeb","doi":"10.4171/owr/2023/50","DOIUrl":"https://doi.org/10.4171/owr/2023/50","url":null,"abstract":"","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141810483","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}
S. Buss, Rosalie Iemhoff, U. Kohlenbach, Michael Rathjen
The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of current mathematics, constructive mathematics and logical aspects of computational complexity. Mathematics Subject Classification (2010): 03Fxx. Introduction by the Organisers The workshop Mathematical Logic: Proof Theory, Constructive Mathematics was held November 16-22, 2014 and included two tutorials: (1) Thierry Coquand: Univalent Foundation and Constructive Mathematics (2 times 1 hour), (2) Ulrich Kohlenbach, Daniel Körnlein, Angeliki Koutsoukou-Argyraki, Laureņtiu Leu̧stean: Proof-Theoretic Methods in Nonlinear Analysis (2 times 50 min plus 2 times 30). Coquand’s tutorial gave a general introduction on the univalent foundation program of Voevodsky and discussed the construction of the cubical set model of type theory in a constructive metatheory. This model satisfies the computation rules for equality introduced by P. Martin-Löf as judgemental equality. The second tutorial developed the proof-theoretic framework for the unwinding of proofs in nonlinear analysis and outlined recent applications to: image recovery problems (Part I, Kohlenbach), fixed point theory of pseudocontractive mappings 2934 Oberwolfach Report 52/2014 (Part II, Körnlein), convex optimization (Part III, Leu̧stean) and abstract Cauchyproblems given by accretive operators (Part IV, Koutsoukou-Argyraki). In addition to these tutorials, 29 talks of mostly 25 minutes were given aiming: To promote the interaction of proof theory and computability theory with core areas of mathematics as well as computer science via the use of proof interpretations. J. Avigad’s talk studied the amount of algorithmic randomness needed in Weyl’s theorem on uniform distributions. H. Towsner showed how to arrive at Tao’s version of Szemerédi’s regularity lemma as the functional interpretation of a measure-theoretic Π3-statement. H. Schwichtenberg reported on a machine extracted program from the Nash-Williams minimal bad sequence argument for Higman’s lemma. V. Brattka introduced a concept of Las Vegas computable functions to calibrate the computational power of randomized computations on real numbers. A. Weiermann described a general formula for the computation of the maximal order types for well quasi orders arising in the combinatorics of finite multisets. P. Schuster showed how a reformulation of transfinite methods in algebra as admissible rules can be used to eliminate uses of such methods from proofs of sufficiently simple statements in abstract algebra. On the side of applications to concrete applications in computer science, M. Seisenberger reported on applications of logic to the verification of railway control systems and U. Berger developed a proposal to optimize programs extracted by proof-theoretic methods to be able to e.g. control their complexity, allow for partial data and to override data that are no longer used. To further develop foundational aspects of proof
{"title":"Mathematical Logic: Proof Theory, Constructive Mathematics","authors":"S. Buss, Rosalie Iemhoff, U. Kohlenbach, Michael Rathjen","doi":"10.4171/owr/2014/52","DOIUrl":"https://doi.org/10.4171/owr/2014/52","url":null,"abstract":"The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of current mathematics, constructive mathematics and logical aspects of computational complexity. Mathematics Subject Classification (2010): 03Fxx. Introduction by the Organisers The workshop Mathematical Logic: Proof Theory, Constructive Mathematics was held November 16-22, 2014 and included two tutorials: (1) Thierry Coquand: Univalent Foundation and Constructive Mathematics (2 times 1 hour), (2) Ulrich Kohlenbach, Daniel Körnlein, Angeliki Koutsoukou-Argyraki, Laureņtiu Leu̧stean: Proof-Theoretic Methods in Nonlinear Analysis (2 times 50 min plus 2 times 30). Coquand’s tutorial gave a general introduction on the univalent foundation program of Voevodsky and discussed the construction of the cubical set model of type theory in a constructive metatheory. This model satisfies the computation rules for equality introduced by P. Martin-Löf as judgemental equality. The second tutorial developed the proof-theoretic framework for the unwinding of proofs in nonlinear analysis and outlined recent applications to: image recovery problems (Part I, Kohlenbach), fixed point theory of pseudocontractive mappings 2934 Oberwolfach Report 52/2014 (Part II, Körnlein), convex optimization (Part III, Leu̧stean) and abstract Cauchyproblems given by accretive operators (Part IV, Koutsoukou-Argyraki). In addition to these tutorials, 29 talks of mostly 25 minutes were given aiming: To promote the interaction of proof theory and computability theory with core areas of mathematics as well as computer science via the use of proof interpretations. J. Avigad’s talk studied the amount of algorithmic randomness needed in Weyl’s theorem on uniform distributions. H. Towsner showed how to arrive at Tao’s version of Szemerédi’s regularity lemma as the functional interpretation of a measure-theoretic Π3-statement. H. Schwichtenberg reported on a machine extracted program from the Nash-Williams minimal bad sequence argument for Higman’s lemma. V. Brattka introduced a concept of Las Vegas computable functions to calibrate the computational power of randomized computations on real numbers. A. Weiermann described a general formula for the computation of the maximal order types for well quasi orders arising in the combinatorics of finite multisets. P. Schuster showed how a reformulation of transfinite methods in algebra as admissible rules can be used to eliminate uses of such methods from proofs of sufficiently simple statements in abstract algebra. On the side of applications to concrete applications in computer science, M. Seisenberger reported on applications of logic to the verification of railway control systems and U. Berger developed a proposal to optimize programs extracted by proof-theoretic methods to be able to e.g. control their complexity, allow for partial data and to override data that are no longer used. To further develop foundational aspects of proof ","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"125 42","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141811364","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: Felix Klein’s Foreign Students: Opening Up the Way for Transnational Mathematics","authors":"Danuta Ciesielska, Renate Tobies","doi":"10.4171/owr/2023/47","DOIUrl":"https://doi.org/10.4171/owr/2023/47","url":null,"abstract":"","PeriodicalId":436142,"journal":{"name":"Oberwolfach Reports","volume":"84 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141812887","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}
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