Seminar by Prof. Ho Hai Phung on Thursday, April 24th, at 2:30 pm

[PERRONI FABIO]

UNIVERSITA’ DEGLI STUDI DI TRIESTE
DIPARTIMENTO DI MATEMATICA, INFORMATICA E GEOSCIENZE

SEMINAR ANNOUNCEMENT

Thursday, April 24th, 2025, at 14:30.

Prof. Ho Hai Phung (Institute of Mathematics, Vietnam Academy of Science and Technology;
Mathematics Associate at ICTP) will give a seminar.

Title: On comparison theorem for cohomologies of curves
Abstract: For a Riemann surface X, the Riemann-Hilbert correspondence establishes a one-one correspondence between complex representations of the topological fundamental group of X and linear systems of differential equations on X. For a (smooth, projective) curve over a field of characteristic zero, there is a similar correspondence, where the topological fundamental group is replaced by an affine group scheme, called the differential fundamental group. The knowledge of this group is very limited as it does not base change. We propose to study the cohomology of this group to shed some light on its structure. It turns out that the group cohomology agrees with the de Rham cohomology. A similar consideration can also be carried out for curves in positive characteristic, where the de Rham cohomology is replaced by the infinitesimal cohomology.

Venue: Seminar Room of the Department (Sezione di Matematica, H2 building, Via Valerio 12/1, 3rd floor, room 334).
Everyone interested is welcome to attend.
Kind regards,
Fabio Perroni

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Fabio Perroni
Professore | Professor
Università degli Studi di Trieste | University of Trieste
Dipartimento di Matematica, Informatica e Geoscienze
Via Valerio, 12/1 - 34127 Trieste (Italy)
fperroni at units.it<mailto:fperroni at units.it>
Tel.| Ph. +39 040 558 2639<tel:+390405582639>