The completed finite period map and Galois theory of supercongruences

A period is a complex number arising as the integral of a rational function with algebraic number coefficients over a rationally-defined region. Although periods are typically transcendental numbers, there is a conjectural Galois theory of periods coming from the theory of motives. This paper formalizes an analogy between a class of periods called multiple zeta values, and congruences for rational numbers modulo prime powers (called supercongruences). We construct an analogue of the motivic period map in the setting of supercongruences, and use it to define a Galois theory of supercongruences. We describe an algorithm using our period map to find and prove supercongruences, and we provide software implementing the algorithm.Comment: 24 pages. Comments are welcome. Most of the results of this paper were previously part of arXiv:1608.0686

Intersection local times for interlacements

We define renormalized intersection local times for random interlacements of L\'evy processes in R^{d} and prove an isomorphism theorem relating renormalized intersection local times with associated Wick polynomials.Comment: SPA, to appea

Method and means for recording and reconstructing holograms without use of a reference beam Patent

Method and means for recording and reconstructing holograms without use of reference bea

What I make up when I wake up: anti-experience views and narrative fabrication of dreams

I propose a narrative fabrication thesis of dream reports, according to which dream reports are often not accurate representations of experiences that occur during sleep. I begin with an overview of anti-experience theses of Norman Malcolm and Daniel Dennett who reject the received view of dreams, that dreams are experiences we have during sleep which are reported upon waking. Although rejection of the first claim of the received view, that dreams are experiences that occur during sleep, is implausible, I evaluate in more detail the second assumption of the received view, that dream reports are generally accurate. I then propose a “narrative fabrication” view of dreams as an alternative to the received view. Dream reports are often confabulated or fabricated because of poor memory, bizarre dream content, and cognitive deficits. It is well documented that narratives can be altered between initial rapid eye movement sleep awakenings and subsequent reports. I argue that we have reason to suspect that initial reports are prone to inaccuracy. Experiments demonstrate that subjects rationalize strange elements in narratives, leaving out supernatural or bizarre components when reporting waking memories of stories. Inaccuracies in dream reports are exacerbated by rapid memory loss and bizarre dream content. Waking memory is a process of reconstruction and blending of elements, but unlike waking memory, we cannot reality-test for dream memories. Dream experiences involve imaginative elements, and dream content cannot be verified with external evidence. Some dreams may involve wake-like higher cognitive functions, such as lucid dreams. Such dreams are more likely to elicit accurate reports than cognitively deficient dreams. However, dream reports are generally less accurate than waking reports. I then propose methods which could verify the narrative fabrication view, and argue that although the theory cannot be tested with current methods, new techniques and technologies may be able to do so in the future