Kant noted the importance of spatial and temporal intuitions (synthetics) in geometric reasoning, but intuitions lend themselves to different interpretations and a more solid grounding may be sought in formality. In mathematics David Hilbert defended formality, while L. E. J. Brouwer cited intuitions that remain unencompassed by formality. In this paper, the conflict between formality and intui...

Contextuality is a foundational phenomenon underlying key differences between quantum theory and classical realistic descriptions of the world. Here we propose an experimental test which is capable of revealing contextuality in all qutrit systems, except the completely mixed state, provided we choose the measurement basis appropriately. The 3-level system is furnished by the polarization and sp...

Researching second screen interactions that form a social soundtrack concerning a major broadcast media event, we perform statistical analysis on more than 800 K postings and 50 K blogs of Super Bowl XLIX on Instagram and Tumblr respectively for three categories (commercials, music and game) during three phrases (Pre, During, and Post) identifying the influence of different social soundtrack fe...

Contextuality is a natural generalization of nonlocality which does not need composite systems or spacelike separation and offers a wider spectrum of interesting phenomena. Most notably, in quantum mechanics there exist scenarios where the contextual behavior is independent of the quantum state. We show that the quest for an optimal inequality separating quantum from classical noncontextual cor...

Using a single trapped ion, we have experimentally demonstrated state-independent violation of a recent version of the Kochen-Specker inequality in a three-level system (qutrit) that is intrinsically indivisible. Three ground states of the (171)Yb(+) ion representing a qutrit are manipulated with high fidelity through microwaves and detected with high efficiency through a two-step quantum jump ...

Let M g,l be the moduli space of stable algebraic curves of genus g with l marked points. With the operations which relate the different moduli spaces identifying marked points, the family (M g,l) g,l is a modular operad of projective smooth Deligne-Mumford stacks, M. In this paper we prove that the modular operad of singular chains C * (M; Q) is formal; so it is weakly equivalent to the modula...

Let Mg,l be the moduli space of stable algebraic curves of genus g with l marked points. With the operations that relate the different moduli spaces identifying marked points, the family (Mg,l)g,l is a modular operad of projective smooth Deligne-Mumford stacksM. In this paper, we prove that the modular operad of singular chains S∗(M;Q) is formal, so it is weakly equivalent to the modular operad...

We introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist (rather than sets) measurements and outcomes, thereby generalizes nonsignaling distributions distributions, which are modeled by sets. Using this formalism we present topologi...

In these notes, we present Kontsevich’s theorem on the deformation quantization of Poisson manifolds, his formality theorem and Tamarkin’s algebraic version of the formality theorem. We also introduce the necessary material from deformation theory.