Related papers: Introduction to evolution equations in geometry
These are lecture notes of a course taken in Leipzig 2023, spring semester. It deals with extremal combinatorics, algebraic methods and combinatorial geometry. These are not meant to be exhaustive, and do not contain many proofs that were…
This evocative essay focuses on mathematical activities witnessed by the author along 1962-64 at IMPA. The list of research problems proposed in September 1962 by Mauricio Peixoto at the Seminar on the Qualitative Theory of Differential…
We sketch an assortment of problems that were posed -- and not yet solved -- during problem sessions at the conference ``Approximation Theory and Numerical Analysis meet Algebra, Geometry, and Topology'', which was held at the Palazzone…
Recently, computational modelling became a very important research tool that enables us to study problems that for decades evaded scientific analysis. Evolutionary systems are certainly examples of such problems: they are composed of many…
These are the lecture notes for a short course on geometric quantization given by the author at the XVIII Modave Summer School on Mathematical Physics, Sep 5 - Sep 9.
These lecture notes provide an introduction to logarithmic geometry with a view towards recent applications in the desingularization theory.
We discuss Einstein's knowledge of projective geometry. We show that two pages of Einstein's Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his…
Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…
These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…
We prove that any evolution equation admitting a potential symmetry can always be reduced to another evolution equation such that the potential symmetry in question maps into the group of its contact symmetries. Based on this fact is out…
This is an outline of my Gibbs Lecture to the American Mathematical Society in January 1994; it is essentially a sign-posted guide to a still-developing literature.
Studies of galaxy evolution at optical and near-infrared wavelengths have reached an interesting point in their historical development and the arrival of a new millenium provides an appropriate occasion to review the overall direction in…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
This is lecture notes for a course given at the PCMI Summer School "Quantum Field Theory and Manifold Invariants" (July 1 -- July 5, 2019). I describe basics of gauge-theoretic approach to construction of invariants of manifolds. The main…
There is an abundance of empirical evidence in the numerical relativity literature that the form in which the Einstein evolution equations are written plays a significant role in the lifetime of numerical simulations. This paper attempts to…
In this paper we study subalgebras of complex finite dimensional evolution algebras. We obtain the classification of nilpotent evolution algebras whose any subalgebra is an evolution subalgebra with a basis which can be extended to a…
These notes are intended to be an introduction to shifted symplectic geometry, targeted to Poisson geometers with a serious background in homological algebra. They are extracted from a mini-course given by the first author at the Poisson…
In the lecture notes, the author will survey the development of conformal geometry on four dimensional manifolds. The topic she chooses is one on which she has been involved in the past twenty or more years: the study of the integral…
Evolutionary Computation is a branch of computer science with which, traditionally, High Energy Physics has fewer connections. Its methods were investigated in this field, mainly for data analysis tasks. These methods and studies are,…
The theory of evolution equations has been applied in various ways in general relativity. Following some general considerations about this, some illustrative examples of the use of ordinary differential equations in general relativity are…