Recall that in this case g≅gosp(2|4), and a∗Ω is the subspace of h∗ that is given in (39). Let σ:C3→a∗Ω be defined by σ(a,b,c):=μa,b,c, where μa,b,c is defined in (38). We define the map σ∗:P(a∗Ω)→P(C3)≅C[a,b,c] by σ∗(f):=f∘σF.

For a finite dimensional unital complex simple Jordan superalgebra $J$, the Tits-Kantor-Koecher construction yields a 3-graded Lie superalgebra $\mat…

As mentioned in the introduction, the equations f6 and f16 provide modules of equations for all other 5th secant varieties of Segre products, both when the dimensions of the factors increase (by “inheritance”) and when the number of factors increase…

We describe a computational proof that the fifth secant variety of the Segre product of five copies of the projective line is a codimension 2 complet…

Restrictions of the sums that occur in the Kronecker-Hurwitz relation to congruence classes, i.e. sums of the form

For any number $m \equiv 0,1 \, (4)$ we correct the generating function of Hurwitz class number sums $\sum_r H(4n - mr^2)$ to a modular form (or quas…

In this section, we present a generalization of Guţă’s q-product of noncommutative generalized Brownian motions.

We consider certain questions pertaining to noncommutative generalized Brownian motions with multiple processes. We establish a framework for general…

I would like to credit and thank Denis Auroux, Chris Douglas, Dan Freed, David Gay, Robert Lipshitz, Tim Perutz, Dietmar Salamon, Chris Schommer-Priess, Peter Teichner, and Chris Woodward for illuminations of various aspects of the ideas presented h…

Floer field theory is a construction principle for e.g. 3-manifold invariants via decomposition in a bordism category and a functor to the symplectic…

Let us conclude with some natural questions raised by our construction of generalized logarithmic derivations.

Let $Y$ be a complex algebraic variety, $G \curvearrowright Y$ an action of an algebraic group on $Y$, $U \subseteq Y({\mathbb C})$ a complex submani…

Coates was supported in part by a Royal Society University Research Fellowship, ERC Starting Investigator Grant number 240123, and the Leverhulme Trust. Givental was supported in part by NSF grants DMS-0604705 and DMS-1007164. Tseng was supported in…

We show that the Virasoro conjecture in Gromov--Witten theory holds for the the total space of a toric bundle $E \to B$ if and only if it holds for t…

In this section we start an explicit study of certain classes of structure sets, equipped with extra properties.

Continuing with the authors concept (and results) of defining independence for columns of a boolean and superboolean matrix, we apply this theory to …

We first give the proofs of the main results, Theorem 2.2, Lemma 3.1 and Corollary 3.2 and then turn to the other statements which form the basis of the proof of Theorem 2.2.

We continue our analysis of the thresholding scheme from the variational viewpoint and prove a conditional convergence result towards Brakke's notion…

We next approach Theorems B and C. These will use the quantitative version of our basic smoothing argument via the following two notions.

A version of group cohomology for locally compact groups and Polish modules has previously been developed using a bar resolution restricted to measur…

In this section we prove Proposition 3.4. We use an argument developed in [25] that is based on exterior energy estimates for the free wave equation in R1+5. This method is a refinement of the channels of energy method developed by Duyckaerts, Kenig…

In this paper we study the focusing cubic wave equation in 1+5 dimensions with radial initial data as well as the one-equivariant wave maps equation …

The movement of data (communication) between levels of a memory hierarchy, or between parallel processors on a network, can greatly dominate the cost…

For a large Hermitian matrix $A\in \mathbb{C}^{N\times N}$, it is often the case that the only affordable operation is matrix-vector multiplication. …

Graph expansion analysis of computational DAGs is useful for obtaining communication cost lower bounds where previous methods, such as geometric embe…

We describe a massively parallel implementation of the recently developed discontinuous Galerkin density functional theory (DGDFT) [J. Comput. Phys. …

A convex co-compact group Γ of isometries of hyperbolic space Hn+1 is a discrete group of hyperbolic transformations (their fixed points on ¯¯¯¯B={m∈Rn+1;|m|≤1} are 2 disjoint points on Sn=∂¯¯¯¯¯¯M) with a compact convex core. The limit set ΛΓ of th…

For a Riemannian manifold $(M,g)$ which is isometric to the Euclidean space outside of a compact set, and whose trapped set has Liouville measure zer…

Consider the set of reals that given any computable system (C,f) can compute an almost periodic point for this system. This is an upwards-closed subclass of the PA degrees. By Theorem 12, we know that this is a strict subclass of the PA degrees. The…

This paper uses the framework of reverse mathematics to investigate the strength of two recurrence theorems of topological dynamics. It establishes t…

Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. …

The Antimagic Graph Conjecture asserts that every connected graph $G = (V, E)$ except $K_2$ admits an edge labeling such that each label $1, 2, \dots…

For both theorems, we argue by contradiction. Suppose that the conclusion of the Dichotomy Theorem 1.11 is false, i.e., there exists a solution A for which both alternatives a) and b) are false. Then we are in one of the following two scenarios:

This article represents the fourth and final part of a four-paper sequence whose aim is to prove the Threshold Conjecture as well as the more general…

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