Related papers: SPM Bulletin 26
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
These reports present the results of the 2013 Community Summer Study of the APS Division of Particles and Fields ("Snowmass 2013") on the future program of particle physics in the U.S. Chapter 1 contains the Executive Summary and the…
In this paper we introduce public announcement logic in different geometric frameworks. First, we consider topological models, and then extend our discussion to a more expressive model, namely, subset space models. Furthermore, we prove the…
To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.
In this survey article, we summarize some recent progress and problems on the symplectomorphism groups, with an emphasis on the connection to the space of ball-packings.
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
This is a review article for The Review of Particle Physics 2026 (aka the Particle Data Book), appearing as Chapter 23. It forms a compact review of our understanding of cosmological inflation near the end of 2025. Topics included are…
This contribution to the concluding session at IAU Symposium 205 offered comments on some current controversies, including the scientific status of the ''multiverse'' concept and on the prospects for cosmology in the coming decade.
The simple realistic model of the tippe top is considered. An averaged system of equations of motion is obtained in special evolutionary variables. Through the qualitative analysis of this system the general features of the motion of the…
This special issue is dedicated to starshades: science, engineering, technology and programmatics. Our reasons for organizing this special issue are several fold. First as a new technology and with research accomplished in many…
These are lecture notes expanding upon a set of lectures given by G.M. at the TASI 2023 School. Part I is an introduction to topological field theory, including extended topological field theory. Part II is an introduction to generalized…
Science opportunities and recommendations concerning optical/infrared polarimetry for the upcoming decade in the field of Galactic science. Community-based White Paper to Astro2010 in response to the call for such papers.
We consider an N-level non-Hermitian Hamiltonian with an exceptional point of order N. We define adiabatic equivalence in such systems and explore topological phase. We show that the topological exceptional states appear at the interface of…
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical…
This white paper briefly summarized key conclusions of the recent US Community Study on the Future of Particle Physics (Snowmass 2021) workshop on Software and Computing for Small High Energy Physics Experiments.
This set of five lectures provides an introduction to regularity structures and their use for the study of singular stochastic partial differential equations. Two appendices provide some additional informations that enter in the main text…
Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six particular topics related to inscribable polytopes. Along…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…