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Papers by Salomon Dominguez

arXiv (Cornell University), Sep 10, 2012

arXiv (Cornell University), Sep 25, 2017

This paper was inspired by four articles: surface cluster algebras studied by Fomin-Shapiro-Thurs... more This paper was inspired by four articles: surface cluster algebras studied by Fomin-Shapiro-Thurston [6], the mutation theory of quivers with potentials initiated by Derksen-Weyman-Zelevinsky [3], string modules associated to arcs on unpunctured surfaces by Assem-Brüstle-Charbonneau-Plamondon [1] and Quivers with potentials associated to triangulated surfaces, part II: Arc representations by Labardini-Fragoso. [10]. For a surface with marked points (Σ, M) Labardini-Fragoso associated a quiver with potential (Q(τ), S(τ)) then for an ideal triangulation of (Σ, M) and an ideal arc Labardini-Fragoso defined an arc representation of (Q(τ), S(τ)). This paper focuses on extent the definition of arc representation to a more general context by considering a tagged triangulation and a tagged arc. We associate in an explicit way a representation of the quiver with potential constructed Labardini-Fragoso and prove that the Jacobian relations are met.

Revista Finanzas y Política Económica

This paper provides economic theory with a dynamic structural model that mathematically proves bo... more This paper provides economic theory with a dynamic structural model that mathematically proves both a positive effect of wages on the workers’ human capital intertemporal investment decisions and the existence of a virtuous dynamic cycle between wages and human capital.Among the desired characteristics of the proposed model is that it has an analytical solution, permitting the achievement of an optimal decision rule for each choice variable and the calibration of its parameters using observed data; this favors an easy implementation by policymakers and researchers. The constructed statistics and the results of the empirical application of the model, to the Mexican developing economy, support the mathematical conclusions. The model predicts two benchmark human capital gross returns and their corresponding wages, by levels of education. Below the second one, human capital coming from formal education vanishes over time, due to investment not being enough to offset its depreciat...

arXiv (Cornell University), Aug 17, 2021

Given a Jacobian algebra arising from the punctured disk, we show that all non-split extensions c... more Given a Jacobian algebra arising from the punctured disk, we show that all non-split extensions can be found using the tagged arcs and skein relations previously developed in cluster algebras theory. Our geometric interpretation can be used to find non-split extensions over other Jacobian algebras arising form surfaces with punctures. We show examples in type D and in a punctured surface.

arXiv (Cornell University), Aug 17, 2021

Given a Jacobian algebra arising from the punctured disk, we show that all non-split extensions c... more Given a Jacobian algebra arising from the punctured disk, we show that all non-split extensions can be found using the tagged arcs and skein relations previously developed in cluster algebras theory. Our geometric interpretation can be used to find non-split extensions over other Jacobian algebras arising form surfaces with punctures. We show examples in type D and in a punctured surface.

This paper was inspired by four articles: surface cluster algebras studied by Fomin-ShapiroThurst... more This paper was inspired by four articles: surface cluster algebras studied by Fomin-ShapiroThurston [6], the mutation theory of quivers with potentials initiated by Derksen-WeymanZelevinsky [3], string modules associated to arcs on unpunctured surfaces by Assem-BrüstleCharbonneau-Plamondon [1] and Quivers with potentials associated to triangulated surfaces, part II: Arc representations by Labardini-Fragoso. [10]. For a surface with marked points (Σ,M) Labardini-Fragoso associated a quiver with potential (Q(τ ), S(τ )) then for an ideal triangulation of (Σ,M) and an ideal arc Labardini-Fragoso defined an arc representation of (Q(τ ), S(τ )). This paper focuses on extent the definition of arc representation to a more general context by considering a tagged triangulation and a tagged arc. We associate in an explicit way a representation of the quiver with potential constructed Labardini-Fragoso and prove that the Jacobian relations are met.

arXiv (Cornell University), Sep 10, 2012

arXiv (Cornell University), Sep 25, 2017

This paper was inspired by four articles: surface cluster algebras studied by Fomin-Shapiro-Thurs... more This paper was inspired by four articles: surface cluster algebras studied by Fomin-Shapiro-Thurston [6], the mutation theory of quivers with potentials initiated by Derksen-Weyman-Zelevinsky [3], string modules associated to arcs on unpunctured surfaces by Assem-Brüstle-Charbonneau-Plamondon [1] and Quivers with potentials associated to triangulated surfaces, part II: Arc representations by Labardini-Fragoso. [10]. For a surface with marked points (Σ, M) Labardini-Fragoso associated a quiver with potential (Q(τ), S(τ)) then for an ideal triangulation of (Σ, M) and an ideal arc Labardini-Fragoso defined an arc representation of (Q(τ), S(τ)). This paper focuses on extent the definition of arc representation to a more general context by considering a tagged triangulation and a tagged arc. We associate in an explicit way a representation of the quiver with potential constructed Labardini-Fragoso and prove that the Jacobian relations are met.

Revista Finanzas y Política Económica

This paper provides economic theory with a dynamic structural model that mathematically proves bo... more This paper provides economic theory with a dynamic structural model that mathematically proves both a positive effect of wages on the workers’ human capital intertemporal investment decisions and the existence of a virtuous dynamic cycle between wages and human capital.Among the desired characteristics of the proposed model is that it has an analytical solution, permitting the achievement of an optimal decision rule for each choice variable and the calibration of its parameters using observed data; this favors an easy implementation by policymakers and researchers. The constructed statistics and the results of the empirical application of the model, to the Mexican developing economy, support the mathematical conclusions. The model predicts two benchmark human capital gross returns and their corresponding wages, by levels of education. Below the second one, human capital coming from formal education vanishes over time, due to investment not being enough to offset its depreciat...

arXiv (Cornell University), Aug 17, 2021

Given a Jacobian algebra arising from the punctured disk, we show that all non-split extensions c... more Given a Jacobian algebra arising from the punctured disk, we show that all non-split extensions can be found using the tagged arcs and skein relations previously developed in cluster algebras theory. Our geometric interpretation can be used to find non-split extensions over other Jacobian algebras arising form surfaces with punctures. We show examples in type D and in a punctured surface.

arXiv (Cornell University), Aug 17, 2021

Given a Jacobian algebra arising from the punctured disk, we show that all non-split extensions c... more Given a Jacobian algebra arising from the punctured disk, we show that all non-split extensions can be found using the tagged arcs and skein relations previously developed in cluster algebras theory. Our geometric interpretation can be used to find non-split extensions over other Jacobian algebras arising form surfaces with punctures. We show examples in type D and in a punctured surface.

This paper was inspired by four articles: surface cluster algebras studied by Fomin-ShapiroThurst... more This paper was inspired by four articles: surface cluster algebras studied by Fomin-ShapiroThurston [6], the mutation theory of quivers with potentials initiated by Derksen-WeymanZelevinsky [3], string modules associated to arcs on unpunctured surfaces by Assem-BrüstleCharbonneau-Plamondon [1] and Quivers with potentials associated to triangulated surfaces, part II: Arc representations by Labardini-Fragoso. [10]. For a surface with marked points (Σ,M) Labardini-Fragoso associated a quiver with potential (Q(τ ), S(τ )) then for an ideal triangulation of (Σ,M) and an ideal arc Labardini-Fragoso defined an arc representation of (Q(τ ), S(τ )). This paper focuses on extent the definition of arc representation to a more general context by considering a tagged triangulation and a tagged arc. We associate in an explicit way a representation of the quiver with potential constructed Labardini-Fragoso and prove that the Jacobian relations are met.