Disputation: Giovanni Domenico Di Salvo

Doctoral candidate Giovanni Domenico Di Salvo at the Department of Mathematics, Faculty of Mathematics and Natural Sciences, is defending the thesis Proper Holomorphic Embeddings of open Riemann Surfaces into C2 and holomorphic mappings between complex manifolds with dense images for the degree of Philosophiae Doctor.

Picture of the candidate.

Doctoral candidate Giovanni Domenico Di Salvo

The PhD defence will be partially digital, in room 720, Niels Henrik Abels hus and streamed directly using Zoom. The host of the session will moderate the technicalities while the chair of the defence will moderate the disputation.

Ex auditorio questions: the chair of the defence will invite the audience to ask questions ex auditorio at the end of the defence. If you would like to ask a question, click 'Raise hand' and wait to be unmuted.

  • Join the disputation

    The webinar opens for participation just before the disputation starts, participants who join early will be put in a waiting room.
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    • Submit the request to get access to the thesis (available from 25th March 12:15 until 8th April 12:15)

Trial lecture

7th of April, time: 11.15 am, room 720 and Zoom

"Oka theory applied to minimal surfaces” 
  • Join the trial lecture
    The webinar opens for participation just before the trial lecture starts, participants who join
    early will be put in a waiting room.

Main research findings

One of the biggest open problems in Complex Geometry is whether every open Riemann Surface admits a proper holomorphic embedding into the 2-dimensional euclidean complex space, as this provides a good representation of it.

We constructed examples of this representation for certain Riemann Surfaces that were thought to be good candidates for a counterexample, namely complements of large Cantor sets inside the Riemann sphere. A previous paper provided the desired representation for the same object; here we pointed out that from that construction it turns out that the resulting Cantor set is actually very thin.
Another important result contained in the thesis is the simultaneous construction of the above representation for a whole family of domains inside the Riemann sphere.

Holomorphic embeddings (non-proper) are studied in terms of approximation as well: we give sufficient conditions on domains inside euclidean complex spaces to approximate such mappings on the given domains with similar mappings with dense images. We finally extend this result to more general settings, presenting three further theorems.

Adjudication committee

Professor Barbara Drinovec Drnovšek, University of Ljubljana
Associate Professor Per Erik Manne, NHH Norwegian School of Economics
Professor Emeritus Erik LøwUniversity of Oslo 


Associate Professor Trung Tuyen TruongUniversity of Oslo
Professor Erlend Fornæss WoldUniversity of Oslo

Chair of defence

Professor Nadia S. Larsen, University of Oslo

Host of the session

Professor Emeritus Erik LøwUniversity of Oslo  

Published Mar. 24, 2022 10:06 AM - Last modified Oct. 19, 2022 11:09 AM