Related papers: G\"unter Hellwig (1926-2004) - in memoriam
This is a colloquium talk in CAU, Kiel delivered on June 7, 2024 on the occasion of Walter Bergweiler's retirement. Walter's work on meromorphic functions consists of two parts: generalizations of Picard's theorem to differential…
This expository article explores the vital role of interpolation theory and Lorentz spaces in the rigorous analysis of partial differential equations (PDEs). While classical Lebesgue spaces ($L_{p}$) successfully measure the magnitude of…
This is a slightly modified version of my MSc thesis from 2019. Supervisor was D\"om\"ot\"or P\'alv\"olgyi.
These lecture notes grew out of notes for courses around Integrable PDEs and the KdV equation given by the authors during the past five years at the University of Antwerp (Belgium). Comments and suggestions are welcome.
We report on a recent implementation of Giesbrecht's algorithm for factoring polynomials in a skew-polynomial ring. We also discuss the equivalence between factoring polynomials in a skew-polynomial ring and decomposing $p^s$-polynomials…
We prove an index theorem for Toeplitz operators on the quarter-plane using the index theory for generalized Toeplitz operators introduced by G. J. Murphy. To prove this index theorem we construct an indicial triple on the tensor product of…
In 1989 H.Karcher rewrote the theory of elliptic functions through an approach that is much more geometrical than analytical. Therewith he obtained an optimal control over the behaviour and image values of these functions, which allowed for…
The history of astronomy in Odessa is briefly discussed with a special emphasis on the scientific school of variable star researches founded by Prof. V.P.Tsesevich.
The subject of our discussion is the theory of differential equations as set out in two classical Euler's textbooks "Institutiones Calculi Differentialis" and "Institutiones Calculi Integralis".
A focused modernization of Sophus Lie's brilliant writings about the foundations of geometry that every contemporary geometer should have at least once a look at. Translated, updated, commented.
A working mathematician's summary of many results on the derived category, perverse sheaves, and vanishing cycles. This is the August 2025 version, with a completely revised section on vanishing cycles.
In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential…
We survey a vast array of known results and techniques in the area of polynomial identities in pointed Hopf algebras. Some new results are proven in the setting of Hopf algebras that appeared in papers of D. Radford and N. Andruskiewitsch -…
Steven Weinberg was a giant of late 20th Century physics on whose shoulders we stand while groping for the science of the 21st Century. This article provides a too-brief summary of a selection of his many achievements -- eight decades of…
David Brink was one of the leading theoretical nuclear physicists of his generation. He made major contributions to the study of all aspects of nuclear physics embracing nuclear structure, nuclear scattering, and nuclear instability. His…
The algebra of quantum differential operators on graded algebras was introduced by V. Lunts and A. Rosenberg. D. Jordan, T. McCune and the second author have identified this algebra of quantum differential operators on the polynomial…
After some brief biographical notes, Wolfgang Pauli's main contributions to general relativity, quantum theory, quantum field theory, and elementary particle physics are reviewed. A detailed description is given how Pauli descovered -…
An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space, X. The main result is…
The purpose of these lectures is to introduce the notion of a Stokes-perverse sheaf as a receptacle for the Riemann-Hilbert correspondence for holonomic D-modules. They develop the original idea of P. Deligne in dimension one, and make it…
Wolfgang Priester was one of Germany's most versatile and quixotic astrophysicists, re-inventing himself successively as a radio astronomer, space physicist and cosmologist, and making a lasting impact on each field. We focus in this…