Related papers: On NSOP$_2$ Theories

We prove the following conjecture of Leighton and Moitra. Let $T$ be a tournament on $[n]$ and $S_n$ the set of permutations of $[n]$. For an arc $uv$ of $T$, let $A_{uv}=\{\sigma \in S_n \, : \, \sigma(u)<\sigma(v) \}$. $\textbf{Theorem.}$…

Any non-critical N=2 string is shown to have an affine sl(2|1) worldsheet symmetry in the conformal gauge.

A type analysable in one-based types in a simple theory is itself one-based.

We classify all possible four-dimensional N=2 supersymmetric UV-complete gauge theories composed of semi-simple gauge groups and hypermultiplets. We also give appropriate references for all theories with known Seiberg-Witten solutions.

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

We investigate the decidability of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N};<,P_1, \ldots,P_d \rangle$, for various unary predicates $P_1,\ldots,P_d \subseteq \mathbb{N}$. We focus in particular on…

In this paper, we build a dimension theory related to Shelah's 2-rank, dp-rank, and o-minimal dimension. We call this dimension op-dimension. We exhibit the notion of the n-multi-order property, generalizing the order property, and use this…

We prove that the NTP$_1$ property of a geometric theory $T$ is inherited by theories of lovely pairs and $H$-structures associated to $T$. We also provide a class of examples of nonsimple geometric NTP$_1$ theories.

We calculate the effective prepotentials for N=2 supersymmetric SO(N_c) and Sp(N_c) gauge theories, with an arbitrary number of hypermultiplets in the defining representation, from restrictions of the prepotentials for suitable N=2…

We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: for every $\theta$ there is a dependent theory $T$ of size $\theta$ such that for all $\kappa$ and $\delta$,…

Let n be any integer greater than two. We prove that there exists a projection P having the following properties. (1) P is not the projection of any unknotted knot. (2) The singular point set of P consists of double points. (3) P is the…

We indicate that an argument of da Costa and Doria in fact proves P=NP. This observation makes their argument appear dubious. We isolate a weak version of one of their lemmas which would already prove P=NP. We point out that even this weak…

We prove a version of the Loebl-Komlos-Sos Conjecture for dense graphs. For each q>0 there exists a number $n_0\in \mathbb{N}$ such that for any n>n_0 and k>qn the following holds: if G be a graph of order n with at least n/2 vertices of…

An important dividing line in the class of unstable theories is being NSOP$_1$, which is more general than being simple. In NSOP$_1$ theories forking independence may not be as well-behaved as in stable or simple theories, so it is replaced…

We construct the N=1 supersymmetric extension of double field theory for D=10, including the coupling to an arbitrary number n of abelian vector multiplets. This theory features a local O(1,9+n) x O(1,9) tangent space symmetry under which…

We establish an expansion theory for $\text{SL}_2(\mathbb Z/q\mathbb Z)$. Incorporating this into a framework recently developed by Shkredov, we confirm Zaremba's conjecture.

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with a^2 in A for all a in A. In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory…

I present a criterion for all-order finiteness in N=1 SYM theories. Three applications are given; they yield all-order finite N=1 SYM models with global symmetries of the superpotential.

A method for quantizing the bidimensional N=2 supersymmetric non-linear sigma model is developed. This method is both covariant under coordinate transformations (concerning the order relevant for calculations) and explicitly N=2…

We prove that, with high probability, in every $2$-edge-colouring of the random tournament on $n$ vertices there is a monochromatic copy of every oriented tree of order $O (n / \sqrt{\log n})$. This generalises a result of the first, third…