A recurring theme in mathematics is the problem of classifying certain objects modulo a suitable notion of isomorphism. In some cases the resulting set of equivalence classes can be naturally endowed with some geometric structure (a topological space, etc.). When this happens, the resulting geometric object is called a moduli space. In this talk we present some examples of this phenomenon starting from familiar objects such as spheres, triangles (modulo isometry) and linear subspaces of a given vector space (modulo automorphisms of the ambient vector space). We will then explore applications of this approach to problems in enumerative geometry and then try to give a hint of how and why moduli spaces are used in physics.
Nicola Pagani is Senior Lecturer in Pure Mathematics at the University of Liverpool. He received his Ph.D. in Mathematics from SISSA/ISAS in 2009, under the supervision of Barbara Fantechi. Before being appointed in Liverpool in 2013, he held postdoc positions in Hannover and Stockholm.
Nicola's research area is Algebraic Geometry, focussing on the study of moduli spaces of curves, a highly interdisciplinary research topic inside Mathematics with connections to other areas of Geometry as well as to Number Theory and Mathematical Physics. He is very active both as a researcher, publishing regularly in influential mathematical journals, and an organizer of scientific events. He is the recipient of an EPSRC First Grant, in 2016.
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