Humboldt Research Fellowship for Dr Amedeo Sgueglia

Graph theory has been experiencing a significant growth in the last century with the development of more sophisticated tools and enlightening connections to other fields, and has nowadays applications in computer science, engineering, social sciences, and more. Dr Amedeo Sgueglia has been awarded a Humboldt Research Fellowship to shed light on unsolved questions in the field. Among other problems, he will work on discrepancy theory for graphs. This is a classical topic initiated by the famous Hungarian mathematician Paul Erdős and his collaborators. Discrepancy means a deviation from the expectation and is a measure of how far we are from the expected ideal situation. “Suppose you have a fair coin with one red and one blue face. If you flip it 100 times, you expect to see 50 red and 50 blue faces; if you get 72 red, then there is a discrepancy”, explains Dr Sgueglia informally. In mathematical terms, the problem is modeled as follows. Given a family of subsets of objects, can we colour each object in red or blue such that every subset in the family contains (roughly) the same number of red and blue objects?

If any two subsets of the family do not share any object, this is easy: for each subset, we arbitrarily colour half of the objects red and the other half blue (if the number of objects is odd, then the number of red and blue ones will differ by one only).  “The same is true if the family is sparse enough” continues Amedeo Sgueglia, “However, when the family is too dense, this may be no longer possible: in whichever way we try to colour the objects, we will always create some discrepancy, that is, there will always be a subset of the family with significantly more red objects than blue ones, or vice versa”. One of the objectives of the project is to capture and describe this phenomenon quantitatively.

Sgueglia’s research project will be hosted by Professor Stefan Glock who is leading the Discrete Mathematics group at the University of Passau. “I am very thrilled that Amedeo Sgueglia decided to join our group. He is an expert on various research directions in extremal and probabilistic combinatorics, and a great asset to our team both personally and professionally”, says Professor Glock.

Principal Investigator(s) at the University	Prof. Dr. Stefan Glock (Professur für Diskrete Mathematik)
Source of funding	Alexander von Humboldt-Stiftung