# Browse Dissertations and Theses - Mathematics by Contributor "Di Francesco, Philippe"

• (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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• (2016-07-06)
A central result in algebraic combinatorics is the Littlewood-Richardson rule that governs products in the cohomology of Grassmannians. A major theme of the modern Schubert calculus is to extend this rule and its associated ...

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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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• (2018-07-03)
A. Lascoux and M.-P. Schutzenberger introduced Schubert polynomials to study the cohomology ring of the complete flag variety Fl(C^n). Each Schubert polynomial corresponds to the class defined by a Schubert variety X_w ...

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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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• (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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