Related papers: Arp's Indomitable Universe
Are P and NP provably inseparable ? Take a look at some unorthodox, guilty mentioned folklore and related unpublished results.
Arb is a C library for arbitrary-precision interval arithmetic using the midpoint-radius representation, also known as ball arithmetic. It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many…
In memoria of Vladimir Naumovich Gribov
Work in progress concerning alternative formalizations of arithmetic.
This year is the 100th birth anniversary of Richard Philips Feynman. This article commemorates his scientific contributions and lasting legacy.
Homotopy coherence has a considerable history, albeit also by other names. We provide a brief semi-historical survey providing some links that may not be common knowledge.
It is shown that the recent observations of NASA's explorer mission "Wilkinson Microwave Anisotropy Probe" (WMAP) hint that our Universe may possess a non-trivial topology. As an example we discuss the Picard space which is stretched out…
The life and accomplishments of Grete Hermann are described. During the early twentieth century, she worked in physics, mathematics, philosophy and education. Her most notable accomplishments in physics were in the interpretation of quantum…
In \cite[\S1.3]{Br2}, some unitary representations of ${\rm GL}_2(\mathbf{Q}_p)$ on $p$-adic Banach spaces are associated to 2-dimensional irreducible crystalline representations of ${\rm Gal}(\bar{\mathbf{Q}}_p)/\mathbf{Q}_p)$. Some…
We study the Hp-Lq boundedness of certain integral operators of fractional type.
We present a simple alternative viewpoint on Hodge-Newton indecomposability, illustrating its explanatory value through a uniform proof of a combinatorial identity arising from affine Deligne-Lusztig varieties with finite Coxeter part.
We give an analysis over a variation of causal sets where the light cone of an event is represented by finitely branching trees with respect to any given arbitrary dynamics. We argue through basic topological properties of Cantor space that…
On Saturday 26 September, around 4am, John Barrow died aged 67, with his wife Elizabeth and son Roger at his side. From a scientific perspective, it is hard to conceive a more premature end. During lockdown alone, whilst undergoing…
This article is a contribution to a Festschrift for S. Helgason. After a biographical sketch, we survey some of his research on several topics in geometric and harmonic analysis during his long and influential career. While not an…
Contemporary concerns over the governance of technological systems often run up against narratives about the technical infeasibility of designing mechanisms for accountability. While in recent AI ethics literature these concerns have been…
There has been significant interest of late in generating behavior of agents that is interpretable to the human (observer) in the loop. However, the work in this area has typically lacked coherence on the topic, with proposed solutions for…
Some reflections on the role in the development of Mathematics of our unconscious perception of the world and just as unconscious organizing pulsions for those perceptions.
Our understanding of the processes that are relevant to the formation and maintenance of habitable planetary systems is advancing at a rapid pace, both from observation and theory. The present review focuses on recent research that bears on…
This paper offers a synthesis of the positions in the literature regarding controversies about the multiverse. After reviewing some simple elements of modern cosmology and its observational limitations, we will present the history of the…
This paper explores the evolution of the so called "anthropic reasoning" in a historical perspective. It takes under scrutiny the appearance of "anthropic" considerations in various stages of modern cosmology, focusing also on some very…