Related papers: On the work of Peter Scholze
Researchers and students face an explosion of newly published papers which may be relevant to their work. This led to a trend of sharing human summaries of scientific papers. We analyze the summaries shared in one of these platforms…
The aim of this paper is to get some results about ruled surfaces which configure a projective theory of scrolls and ruled surfaces. Our ideas follow the viewpoint of Corrado Segre, but we employ the contemporaneous language of locally free…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
We revisit congruence zeta functions of smooth projective varieties over finite fields in the framework of Scholze's Berkovich motives. Via this formalism and categorical traces, we construct a new zeta function, and show that it agree with…
In this expository paper, we provide the readers with an overview of Dennis Sullivan's major contributions to the area of Dynamical Systems.
A shortcoming in the authors' interpretation of this beautiful new experiment is pointed out and briefly discussed.
This paper has been withdrawn by the author, due to a recent article by Kriete and Moorhouse (Linear relations in the Calkin algebra for composition operators, Trans. AMS, 359 (2007), 2915-2944) which includes more general results.
In the last decade, an explosive attention has been paid to piezoelectric harvesters due to their flexibility in design and increasing need to small-scale energy generation. As a result, various energy review papers have been presented by…
In this paper, we give a survey on the history and recent developments on the DDVV-type inequalities.
The article presents an overview of current specialized ontology engineering tools, as well as texts' annotation tools based on ontologies. The main functions and features of these tools, their advantages and disadvantages are discussed. A…
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
This is an extended version of my 2018 Heinemann prize lecture describing the work for which I got the prize. The citation is very broad so this describes virtually all my work prior to 1995 and some afterwards. It discusses work in…
I attempted to write the full translation of this article to make the remarkable proof of Pierre Deligne available to a greater number of people. Overviews of the proofs can be found elsewhere. I especially recommend the notes of James…
A collection of short expository essays by the author on various topics in quantum mechanics, quantum cosmology, and physics in general.
This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…
This short note provides an overview of some theorems and conjectures obtained by the author and his collaborators. It is an extended abstract for the Oberwolfach workshop "New Trends in Teichm\"uller Theory and Mapping Class Groups", 2…
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
A brief account of K-theory written in honour of Friedrich Hirzebruch
We consider the space of all musical scales with the ambition to systematize it. To do this, we pursue the idea to view certain scales as basic constituents and to "mix" all remaining scales from these. The German version of this article…