As in the grand canonical treatment of Reissner-Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes. Black hole thermodynam...

As in the grand canonical treatment of Reissner-Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes. Black hole thermodynam...

In contrast to the extremal variants of coNP-complete problems, which are frequently DP-complete, many extremal variants of NP-complete problems are in P. We investigate the extremal variants of two NP-complete problems, the extremal colorability problem with restricted degree and the extremal unfrozen non-implicant problem, and show that both of them are DP-complete. As far as we know, no extr...

We study the correlation functions of Coulomb branch operators four-dimensional $\mathcal{N} = 2$ Superconformal Field Theories (SCFTs). focus on rank-one theories, such as SU(2) gauge theory with four fundamental hypermultiplets. "Extremal" functions, involving exactly one anti-chiral operator, are perhaps simplest nontrivial in Quantum Theory. show that large charge limit extremal correlators...

A symmetric subset of the reals is one that remains invariant under some reflection x 7→ c − x. We consider, for any 0 < ε ≤ 1, the largest real number ∆(ε) such that every subset of [0, 1] with measure greater than ε contains a symmetric subset with measure ∆(ε). In this paper we establish upper and lower bounds for ∆(ε) of the same order of magnitude: for example, we prove that ∆(ε) = 2ε − 1 ...

We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive combinatorics, have been collected together because in each case the relevant proofs are quite short.

All indecomposable unimodular hermitian lattices in dimensions 14 and 15 over the ring of integers in Q( √ −3) are determined. Precisely one lattice in dimension 14 and two lattices in dimension 15 have minimal norm 3. In 1978 W. Feit [10] classified the unimodular hermitian lattices of dimensions up to 12 over the ring Z[ω] of Eisenstein integers, where ω is a primitive third root of unity. Th...

A 0-1 matrix is a matrix in which every element is either 0 or 1. The weight extremal function ex(n, P ) counts the maximum number of 1’s in an n × n matrix which avoids a pattern matrix P . The column extremal function exk(m,P ) counts the maximum number of columns that a matrix with m rows and k 1’s per column can contain such that the matrix avoids P . Set weight and column extremal function...

In this paper we introduce the notion of s-extremal lattice for unimodular Type I lattices. We give a bound on the existence of certain such s-extremal lattices: an s-extremal lattice of dimension n and minimal even norm μ must satisfy n < 12μ. This result implies that such lattices are also extremal and that there are a finite number of them. We also give an equivalent bound for s-extremal sel...

A bstract We study some aspects of the de Sitter version Jackiw-Teitelboim gravity. Though we do not have propagating gravitons, a boundary mode when compute observables with fixed dilaton and metric at boundary. no-boundary wavefunctions probability measures to all orders in perturbation theory. also discuss contributions from different topologies, borrowing recent results by Saad, Shenker Sta...