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Persistent homology in action: bridging topology and machine learning – Davide Moroni (CNR, Pisa)

Based on recent advances in representations based on topological descriptors, the talk will discuss how to leverage persistent homology for dealing with classification tasks of digital data. Applications to biomedical signal processing will be given…

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Vertex labeling properties on simplicial complexes – Bruno Benedetti (University of Miami)

Hamiltonian graphs are graphs where one can find a closed walk that touches all vertices exactly once. Equivalently, they are the graphs whose vertices can be labeled from 1 to n so that all of  12, 23, 34, …, n1  feature among the edges. This…

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Charge, Atoms and Crystals in Representation Theory – Leonardo Patimo (Albert-Ludwigs-Universität Freiburg)

The dimensions of the weight spaces of irreducible representations of reductive groups can be q-deformed, obtaining the Kostka-Foulkes polynomials, which measure the dimensions of the Brylinski-Kostant filtration and therefore have positive…

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The mod $p$ cohomology of complete unordered flag manifolds in $\mathbb{C}^n$ and $\mathbb{R}^n$ – Lorenzo Guerra (Università di Roma ‘Tor Vergata’)

Flag manifolds are topological spaces parametrizing nested subspaces in a fixed vector space. On the complete flag manifold of $\mathbb{C}^n$ and $\mathbb{R}^n$ there is a natural action of the symmetric group on $n$ letters. In this talk I will…

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Baxter Q-operators, QQ-systems and the shifted Yangian – Rouven Frassek (Università di Modena e Reggio Emilia)

I plan to discuss the construction of Baxter Q-operators within the framework of the Quantum Inverse Scattering Method. The method follows the standard procedure for the transfer matrix construction of spin chains that was developed by Faddeev and…

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Hyperplane arrangements, monodromy via deformation theory, and stability conditions – Michael Wemyss (University of Glasgow)

The infinite hyperplane arrangements associated to affine Dynkin diagrams (and their associated braid groups) are fundamental throughout mathematics. I will explain a variation on this, which allows us to produce many more arrangements. Whilst these…

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