相关论文: Hans Duistermaat's contributions to Poisson geomet…
We describe the development of the mathematics of Helmut R. Salzmann (3. 11. 1930 -- 8. 3. 2022) and the main difficulties he was facing, documenting his lifelong productivity and his far reaching influence. We include a comprehensive…
This is a former PhD student's take on his teacher's scientific philosophy. I describe a set of 'principles' that I believe are conducive to good applied mathematics, and that I have learnt myself from observing Hans van Duijn in action.
On a foliated manifold equipped with an action of a compact Lie group $G$, we study a class of almost-coupling Poisson and Dirac structures, in the context of deformation theory and the method of averaging.
Some simple observations concerning certain kappa-deformations in the framework of 2D dilaton gravity formulated as Poisson-sigma models are discussed, and the question of (non-)triviality is addressed.
Patrick Moss (1947--2024) had two distinct lives as a mathematician. The first was as a ring theorist in the late 1970s, in which he worked with Ginn and Lenagan as a student. After a long career as an inspirational mathematics teacher,…
C.S. Seshadri passed away in July 2020. The first part of this article contains some reminiscences from the early 1980s, when as a graduate student in the Tata Institute of Fundamental Research (TIFR), Mumbai, I had the good fortune to…
These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…
We study $\mathbb Z_2$-graded Poisson structures defined on $\mathbb Z_2$-graded commutative polynomial algebras. In small dimensional cases, we exhibit classifications of such Poisson structures, obtain the associated Poisson $\mathbb…
We extend the correspondence between Poisson maps and actions of symplectic groupoids, which generalizes the one between momentum maps and hamiltonian actions, to the realm of Dirac geometry. As an example, we show how hamiltonian…
These are notes based on a series of talks that the author gave at the "Interactions between hyperbolic geometry and quantum groups" conference held at Columbia University in June of 2009.
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…
These notes are a part of my lectures on representations of adelic groups attached to two-dimensional schemes. They contain a study of the one-dimensional case as a preliminary step to the case of dimension two. We consider the following…
This is a slightly edited translation of a paper in Dutch which appeared in Nieuw Archief voor Wiskunde (5) 25 (2024), No.2, 87-90 on the occasion of I.G. Macdonald's death in 2023, and aimed at a very broad mathematical audience. First we…
We prove that the space of shifted Poisson structures on a derived scheme $X$ locally of finite presentation is equivalent to the space of shifted Lagrangian thickenings out $X$, solving a conjecture in shifted Poisson geometry. As a…
In this paper, we study obstructed and unobstructed (holomorphic) Poisson deformations with classical examples in deformation theory.
These notes originated in a series of lectures I gave in Marseille in May, 2013. I was invited to give an introduction to the isomorphism theorems, originating with Dynkin, which connect Markov local times and Gaussian processes. This is an…
The purpose of this paper is to investigate shifted $(+1)$ Poisson structures in context of differential geometry. The relevant notion is shifted $(+1)$ Poisson structures on differentiable stacks. More precisely, we develop the notion of…
Robert F. Coleman, a highly original mathematician who has had a profound influence on modern number theory and arithmetic geometry, passed away on March 24, 2014. We give an overview of his life and career, including some of his major…
The paper has been withdrawn by the author.
These notes provide an account on four lectures given by Adrian Ioana at the Institut Henri Poincare in May 2011, regarding a number of "uniqueness of Cartan" type results obtained in a recent series of papers by Chifan-Peterson and…