Berlin Mathematical School
Sotiris Karanikolopoulos earned his PhD at the University of the Aegean, Greece in 2010. After his (mandatory) military service, his research project Automorphisms Of Algebraic Curves (AoC) was co-financed by the E.U. and Freie Universitat Berlin. He held a Dahlem Research School fellowship for Berlin Mathematical School for fifteen months. During that time he also expanded his networking activities as he gained a membership for the German national research project SFB 647: Space-Time-Matter. There, he was a research associate for the following four months after his fellowship ended. His last appointment in Germany was a three month stay at Max-Planck-Institute at Bonn that lasted until early in 2014.
Focus of research
His research focuses on the study of algebraic function/number/congruence fields. He is interested in the arithmetic of algebraic curves, study their automorphisms and use representation theory for their groups. Part of his work finds applications over finite fields, in coding theory and cryptography.
Keywords that can be found widely through his work:
Automorphisms, curves, positive characteristic, holomorphic (poly-) differentials, modular representations, (relative) Galois module structure, Hasse Witt invariant, Boseck Invariant, Weierstrass Points, Numerical Semigroups, curves with many automorphisms.
Postdoctoral Research Project during the time as a COFUND fellow
Automorphisms of Algebraic Curves
1. “Integral representations of cyclic groups acting on relative holomorphic differentials of deformations of curves with automorphisms”, joint work with Kontogeorgis Aristides, Proc. Amer. Math. Soc.142 (2014), 2369-2383.
2.”Representation of cyclic groups in positive characteristic and Weierstrass semigroups”, joint work with Kontogeorgis Aristides, J. Number Theory, 133 no.1, (2013), 158-175, ISSN 0022-314X.
3. "On holomorphic polydiferentials in positive characteristic", 2012, Mathematische Nachrichten, DOI: 10.1002/mana.201000114.
1. “Automorphisms of curves and Weierstrass semigroups for Harbater-Katz-Gabber covers”, (2013), joint work with Aristides Kontogeorgis, arXiv:1302.2528.
2. "Representations of cyclic groups in positive characteristic and Weierstrass semigroups", 2011, joint work with Kontogeorgis Aristides (arXiv:1107.4849v1).
3. ”Automorphisms of Curves and Weierstrass semigroups ”,(2010) joint work with Kontogeorgis Aristides, arXiv:1005.2871.
Work In progress
1. "Deforming Automorphisms Acting on Curves", joint work with Kontogeorgis Aristides.
Theses (in Greek)
1. "On automorphisms of Algebraic curves", (2010), PhD thesis.(http://www.didaktorika.gr/eadd/handle/10442/18642)
2. "Uniformization for Algebraic curves", (2005), Master thesis. (http://users.uoa.gr/~kontogar/students/karanikolopoulos/ptyxiakn.pdf)
3. "An introduction to Algebraic Topology", (2003), Senior thesis.