相关论文: The Future of Set Theory

In this paper, I develop a novel version of the multiverse theory of sets called hierarchical pluralism by introducing the notion of `degrees of intentionality' of theories. The presented view is articulated for the purpose of reconciling…

In these lectures I start by briefly reviewing the status of the electroweak theory, in the Standard Model and beyond. I then discuss the motivation and the possible avenues for new physics, on the brink of the LHC start.

These lecture notes in the De Rham-Hodge theory are designed for a 1-semester undergraduate course (in mathematics, physics, engineering, chemistry or biology). This landmark theory of the 20th Century mathematics gives a rigorous…

Metaphysical interpretations of set theory are either inconsistent or incoherent. The uses of sets in mathematics actually involve three distinct kinds of collections (surveyable, definite, and heuristic), which are governed by three…

Nobody knows what one's do in the future and everyone will have had a different answer to the question : how do you see yourself in five years after your current job/diploma? In this paper we introduce concepts, large categories of fields…

This short position paper is intended to provide a critique of current approaches to dialogue, as well as a roadmap for collaborative dialogue research. It is unapologetically opinionated, but informed by 40 years of dialogue re-search. No…

This article is the written version of the closing talk presented at the conference `A Century of Cosmology' held at San Servolo, Italy, in August 2007. I focus on the prospects of constraining fundamental physics from cosmological…

The art of the scientific presentation -- much like the art of the perfect plot, the art of the compelling proposal, and the art of the killer job application -- is generally not something we're taught in school. Therefore, in classic…

I present a highly biased and skewed summary of IAU Symposium 314, "Young Stars and Planets Near the Sun," held in Atlanta. This summary includes takeaway thoughts about the rapidly evolving state of the field, as well as crowd-sourced…

Here I indulge in wide-ranging speculations on the shape of physics, and technology closely related to physics, over the next one hundred years. Themes include the many faces of unification, the re-imagining of quantum theory, and new forms…

To predict what someone will say is to model how they think. We study this through next-turn dialogue prediction: given a conversation, predict the next utterance produced by a person. We compare learning approaches along two dimensions:…

What should these lectures be? The subject assigned to us is so broad that many books can be written about it. So, in planning these lectures I had several options. One would be to focus on a narrow subset of topics and to cover them in…

The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…

These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…

Previous approaches to turn-taking and response generation in conversational systems have treated it as a two-stage process: First, the end of a turn is detected (based on conversation history), then the system generates an appropriate…

Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…

Cosmology seems extremely remote from everyday human practice and experience. It is usually taken for granted that cosmological data cannot rationally influence our beliefs about the fate of humanity -- and possible other intelligent…

The purpose of the conference (the fourth in the series of Vaxjo conferences) was to bring together scientists (physicists, mathematicians and philosophers) who are interested in foundations of quantum physics. An emphasis was made on both…

The purpose of this lecture is to describe the KAM theorem in its most basic form and to give a complete and detailed proof. This proof essentially follows the traditional lines laid out by the inventors of this theory, and the emphasis is…

When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…