Related papers: Nature's Greatest Puzzles
Galaxy clusters are the largest structures in Universe. They are very important as both cosmological probes and astrophysical laboratories. Several methods have been developed to detect galaxy clusters with different techniques (optical,…
This is a brief review paper summarizing talks at the NATO school on Complexity and Large Deviations in Geilo, Norway, 2001.
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…
This is an extended abstract of my talk at the Oberwolfach Workshop ''Cluster Algebras and Related Topics'' (December 8 - 14, 2013). It is based on a joint work with A. Zelevinsky (arXiv:1306.3495).
This is a survey paper on the space of symplectic structures on closed 4-manifolds, for the Proceedings ICCM 2004
A pedagogical introduction to Wilson loops, lattice gauge theory and the 1/N-expansion of QCD is presented. The three introductory lectures were given at the 37th ITEP Winter School of Physics, Moscow, February 9-16, 2009.
Lecture given at BW2003 Workshop "Mathematical, Theoretical and Phenomenological Challenges Beyond Standard Model" 29 August-02 September, 2003 Vrnjacka Banja, Serbia
We propose an explanatory and computational theory of transformative discoveries in science. The theory is derived from a recurring theme found in a diverse range of scientific change, scientific discovery, and knowledge diffusion theories…
This paper serves as the announcement of my program---a joke version of the Langlands Program. In connection with this program, I discuss an old hat puzzle, introduce a new hat puzzle, and offer a puzzle for the reader.
Developing a better understanding of surprising or counterintuitive phenomena has constituted a significant portion of deep learning research in recent years. These include double descent, grokking, and the lottery ticket hypothesis --…
Lectures presented at the 42nd Scottish Universities Summer School in Physics, St. Andrews, Scotland, August 1993.
The Art, Astronomy, Technology and Society (AATS) project is an artscience collaboration which dwells in the inbetweenness layer of scientific understanding of the origins of planets and the embodied, intuited ways of knowing. One of the…
The Explorations in Statistics Research workshop is a one-week NSF-funded summer program that introduces undergraduate students to current research problems in applied statistics. The goal of the workshop is to expose students to exciting,…
We survey some of the philosophical challenges and pitfalls within origins research. Several of these challenges exhibit circularities, paradoxes, or anthropic biases. We present origins approaches in terms of three broad categories:…
In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…
In this article, we shall describe some of the most interesting topics in the subject of Complexity Science for a general audience. Anyone with a solid foundation in high school mathematics (with some calculus) and an elementary…
Ecology studies biodiversity in its variety and complexity. It describes how species distribute and perform in response to environmental changes. Ecological processes and structures are highly complex and adaptive. In order to quantify…
This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.
This is the written version of the opening talk at the symposium "Expectations of a Final Theory," at Trinity College, Cambridge, on September 2, 2005. It is to be published in Universe or Multiverse?, ed. B. Carr (Cambridge University…
We present a number of questions in commutative algebra posed on the problem solving seminar in algebra at Stockholm University during the period Fall 2014 - Spring 2017.