Publication

Motivic Donaldson-Thomas invariants for the one-loop quiver with potential

2015
Journal Articles

Abstract

We compute the motivic Donaldson-Thomas invariants of the one-loop quiver, with an arbitrary potential. This is the first computation of motivic Donaldson-Thomas invariants to use in an essential way the full machinery of (mu) over cap -equivariant motives, for which we prove a dimensional reduction result similar to that of Behrend, Bryan and Szendroi in their study of degree- zero motivic Donaldson-Thomas invariants. Our result differs from theirs in that it involves nontrivial monodromy.

Official source

https://infoscience.epfl.ch/entities/publication/967db754-0fc1-45cb-bc38-46ad5e7f5dd7

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2015
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/967db754-0fc1-45cb-bc38-46ad5e7f5dd7

About this result

Related concepts (11)

Dimensionality reduction

Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with).

Quiver (mathematics)

In graph theory, a quiver is a directed graph where loops and multiple arrows between two vertices are allowed, in other words a multidigraph. They are commonly used in representation theory: a representation V of a quiver assigns a vector space V(x) to each vertex x of the quiver and a linear map V(a) to each arrow a. In , a quiver can be understood to be the underlying structure of a , but without composition or a designation of identity morphisms. That is, there is a forgetful functor from Cat to Quiv.

Nonlinear dimensionality reduction

Nonlinear dimensionality reduction, also known as manifold learning, refers to various related techniques that aim to project high-dimensional data onto lower-dimensional latent manifolds, with the goal of either visualizing the data in the low-dimensional space, or learning the mapping (either from the high-dimensional space to the low-dimensional embedding or vice versa) itself. The techniques described below can be understood as generalizations of linear decomposition methods used for dimensionality reduction, such as singular value decomposition and principal component analysis.

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