Conjugacy for normal or abnormal linear Bolza problems

AbstractFor certain Bolza problems with linear dynamics, two sets extending the notion of conjugate points in the calculus of variations are introduced. Independently of nonsingularity assumptions, their emptiness, in one case without normality assumptions, is shown to be equivalent to a second order necessary condition. A comparison with other notions available in the literature is given

International Congress of Mathematicians: 2022 July 6–14: Proceedings of the ICM 2022

Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library

Toroidal q-Opers

We define and study the space of $q$-opers associated with Bethe equations for integrable models of XXZ type with quantum toroidal algebra symmetry. Our construction is suggested by the study of the enumerative geometry of cyclic quiver varieties, in particular, the ADHM moduli spaces. We define $(\overline{GL}(\infty),q)$-opers with regular singularities and then, by imposing various analytic conditions on singularities, arrive at the desired Bethe equations for toroidal $q$-opers.Comment: 53 pages, 1 figur

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 04. bis 06.07. 2012, Bauhaus-Universität Weimar

The 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 4th till 6th July 2012. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 04. bis 06.07. 2012, Bauhaus-Universität Weimar

The 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 4th till 6th July 2012. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference