Related papers: Sasakian Geometry: The Recent Work of Krzysztof Ga…
These are lecture notes for the course "MATS4120 Geometry of geodesics" given at the University of Jyv\"askyl\"a in Spring 2020. Basic differential geometry or Riemannian geometry is useful background but is not strictly necessary. Exercise…
We introduce and study a notion of `Sasaki with torsion structure' (ST) as an odd-dimensional analogue of K\"ahler with torsion geometry (KT). These are normal almost contact metric manifolds that admit a unique compatible connection with…
We present a review of recent work on the mathematical aspects of the BCS gap equation, covering our results of [arXiv:0801.4159] as well our recent joint work with Hamza and Solovej [arXiv:math-ph/0703086] and with Frank and Naboko…
We give a pedagogical review of the localization of supersymmetric gauge theory on 5d toric Sasaki-Einstein manifolds. We construct the cohomological complex resulting from supersymmetry and consider its natural toric deformations with all…
In this expository note, we give a self-contained introduction to some modern incarnations of Hamiltonian reduction. Particular emphasis is placed on applications to symplectic geometry and geometric representation theory. We thereby…
These are lecture notes focusing on recent progress towards Bourgain's slicing problem and the isoperimetric conjecture proposed by Kannan, Lovasz and Simonovits (KLS).
The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.
This paper is a survey of finiteness results in hyperk\"ahler geometry. We review some classical theorems by Sullivan, Koll\'ar-Matsusaka, Huybrechts, as well as theorems in the recent literature by Charles, Sawon, and joint results of the…
In a recent preprint, we discussed geometric lifts, and in particular the notion of St\"ackel lift. In this note, we wish to clarify several aspects raised in the comment arXiv:2511.05765.
Several recent SIGGRAPH papers on surface simplification are described.
This is an intrusion in the life and the mathematics of Norbert A'Campo, intended to be a tribute to him and an acknowledgement of his impact on those who know him and his work. The final version of this paper appears in the book ``Essays…
The exposition has been significantly altered, hopefully improved.
This is an introductory text to differential geometry (written in Polish) aimed for high-school students.
We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.
This paper was written as part of a book entitled: "Questions of Modern Cosmology - Galileo's Legacy" which is a celebrative book dedicated to Galileo Galilei. The book is published in 2009, the International Year of Astronomy, since it is…
Quasi contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of the contact metric manifolds. Weak almost contact metric manifolds, i.e., the linear complex structure on the contact…
This is a point of view of the work of Herbert Busemann (1905-1994), seen as a return to the geometry of Ancient Greece. The importance of this work, its recognition and its relation with other works are discussed. The final version of this…
This article is a survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory (GCT). It is written to be accessible to graduate students. Numerous open questions in…
This is a report of the author's talk at Kinosaki Algebraic Geometry Symposium 2018. We discuss some recent progress on the geometry of thin exceptional sets in Manin's Conjecture.
These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.