# Browse Dissertations and Theses - Mathematics by Contributor "Bergvelt, Maarten"

• (2017-04-13)
This dissertation presents connections between cluster algebras and discrete integrable systems, especially T-systems and their specializations/generalizations. We give connections between the T-system or the octahedron ...

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• (2017-05-03)
Nakajima introduced a t-deformation of q-characters, (q,t)-characters for short, and their twisted multiplication through the geometry of quiver varieties. The Nakajima (q, t)-characters of Kirillov-Reshetikhin modules ...

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• (2017-07-10)
We study tau-functions given as matrix elements for the action of loop groups, $\widehat{GL_n}$ on $n$-component fermionic Fock space. In the simplest case, $n=2$, the tau-functions are equal to Hankel determinants and ...

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• (2017-07-05)
Suppose $f(x,y)$ is a binary form of degree $d$ with coefficients in a field $K \subseteq \cc$. The {\it $K$-rank of $f$} is the smallest number of $d$-th powers of linear forms over $K$ of which $f$ is a $K$-linear ...

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• (2018-04-18)
This thesis is motivated by the W-operators introduced by Mironov et al. We prove that the W-operators are generalizations of the cut-and-join operator studied by Goulden and Jackson. We give a new description of the ...

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