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November 14th, 2025
November 14th, 2025
Speaker: Luca Morstabilini (SISSA)
Title: Topology vs geometry vs algebra: the nonabelian Hodge correspondence
Abstract: The aim of this talk is to discuss a deep and elegant correspondence between objects of very different nature on a Riemann surface C: representations of the fundamental group (topological), flat connections (differential), and Higgs bundles (holomorphic/algebraic). We will also see that the correspondence can be made geometric, i.e. it upgrades to diffeomorphisms between the moduli spaces of the aforementioned objects. This provides a bridge between the topology of the Riemann surface and its complex structure. Time permitting, i will also mention some consequences of this dictionary.
During the talk I will introduce all the relevant notions and try to justify their importance. Despite the name, no knowledge of Hodge theory is required.
November 7th, 2025
November 7th, 2025
Speaker: Valerio Tripodi (SISSA)
Title: Why does string theory require extra dimensions?
Abstract: One of the many additional physical ingredients required by string theory in order to have a consistent framework is the presence of extra (spatial) dimensions. This concept is rather challenging for our human minds used to living in a 3+1 dimensional spacetime, but it opens up the possibility of exploring new interesting physics phenomena.
In this seminar, I will explain how the constraint on the number of spacetime dimensions arises in (bosonic) string theory. First, I will briefly review the general set up by analyzing the Polyakov action and sketching its BRST quantization procedure, which introduces the "ghost" fields in the theory. The corresponding dynamics of the degrees of freedom naturally yields to a 2d conformal field theory and so to a Virasoro algebra. Than I will argue why we require the total central charge of the theory to vanish and how this fixes the number of spacetime dimensions.
If time permits, I'll shortly illustrate what this phenomenon implies in superstring theory and how one can recover a 4-dimensional theory, perhaps sketching the easiest and earliest example: Kaluza-Klein theory.
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