SISSA MATH PHYS & GEOMETRY SEMINARS

[Ugo Bruzzo]

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SISSA MATH PHYS & GEOMETRY SEMINARS

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Kurusch Ebrahimi-Fard 
Instituto de Ciencias Matemáticas (ICMAT-CSIC)
Madrid, Spain

Monday, January 14th, 4 pm room 136

Title: Exponential renormalization

Abstract: In this talk we introduce the so-called exponential renormalization method, developed in the context of the Connes-Kreimer Hopf algebra of Feynman graphs. Using Dyson's identity for Green's functions as well as the link between the Faà di Bruno Hopf algebra and Hopf algebras of Feynman graphs, its relation to the composition of formal power series is analyzed. This leads to the introduction of the notion of counterfactors and order n bare coupling constants. Eventually we analyze the role of the Rota-Baxter property for renormalization scheme maps. 

KEF, F. Patras: "Exponential renormalization", Ann. Henri Poincaré 11 (2010), 943-971; "Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes", J. Math. Phys. 53, 083505 (2012).

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Elisa Tenni (SISSA)

Wednesday, January 16th, 4:30 pm room 136

Title: Clifford theorem for singular curves and some applications

Abstract: I will discuss a generalization of the classical Clifford's theorem to singular curves, reducible or non reduced.
I will prove that for 2-connected curves a Clifford-type inequality holds for a vast set of torsion free rank one sheaves. I intend to show that our assumptions on the sheaves are the most natural when working with this kind of results. 
I will moreover show that this result has many applications to the study of the canonical morphism of a singular curve, in particular that it implies a generalization of the classical Noether's theorem to 3-connected curves. 
This is a joint work with M. Franciosi.

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U. Bruzzo