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A unifying principle explaining the numerical bounds of quantum correlations remains elusive despite the efforts devoted to identifying it. Here we show that these bounds are indeed not exclusive to quantum theory: for any abstract…

Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space, preserves the split of systems into quantum and classical degrees of freedom, and preserves probabilities. The evolution law…

It is a well-known result of Etingof, Nikshych and Ostrik that there are finitely many inequivalent integral modular categories of any fixed rank $n$. This follows from a double-exponential bound on the maximal denominator in an Egyptian…

Given two positive integers n and c, we determine an upper bound, as a function of n and c, for the maximum order of a finite nilpotent transitive group of degree n and nilpotency class at most c.

Recently, the number of non-standard percolation models has proliferated. In all these models, there exists a phase transition at which long range connectivity is established, if local connectedness increases through a threshold $p_c$. In…

The subgroup commutativity degree of a group G has been defined in [6] as the probability that two subgroups of G commute, or equivalently that the product of two subgroups is again a subgroup. Problem 4.3 of [6] asks whether there exist…

One of Yakir Aharonov's endlessly captivating physics ideas is the conjecture that two axioms, namely relativistic causality ("no superluminal signalling") and nonlocality, so nearly contradict each other that a unique theory - quantum…

In quantum theory, particles in three spatial dimensions come in two different types: bosons or fermions, which exhibit sharply contrasting behaviours due to their different exchange statistics. Could more general forms of probabilistic…

Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest…

We first prove Bosch-L\"utkebohmert-Raynaud's conjectures on existence of global N\'eron models of not necessarily semi-abelian algebraic groups in the perfect residue fields case. We then give a counterexample to the existence in the…

We give a combinatorial model for the bounded derived category of graded modules over the dual numbers in terms of arcs on the integer line with a point at infinity. Using this model we describe the lattice of thick subcategories of the…

Any account of the emergence of classicality from quantum theory must address the fact that the quantum operators representing positions and momenta do not commute, whereas their classical counterparts suffer no such restrictions. To…

We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the…

Minisuperspace models derived from Kaluza-Klein theories and low energy string theory are studied. They are equivalent to one and two minimally coupled scalar fields. The general classical and quantum solutions are obtained. Gaussian…

Let $\mathcal{F}$ be a family of $k$-sized subsets of $[n]$ that does not contain $s$ pairwise disjoint subsets. The Erd\H{o}s Matching Conjecture, a celebrated and long-standing open problem in extremal combinatorics, asserts the maximum…

Superquantum ("PR-box") correlations, though designed to respect relativistic causality, violate relativistic causality in the classical limit. Generalizing to all stronger-than-quantum bipartite correlations, I derive Tsirelson's bound…

Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the…

Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms…

A super-modular category is a unitary pre-modular category with M\"uger center equivalent to the symmetric unitary category of super-vector spaces. Super-modular categories are important alternatives to modular categories as any unitary…

We prove the conjecture that exotic and block-exotic fusion systems coincide holds for all fusion systems on exceptional $p$-groups of maximal nilpotency class, where $p \geq 5$. This is done by considering a family of exotic fusion systems…