Menelaos Zikidis- PhD Student in Mathematics
Algebraic Geometry and Mathematical Physics
University of Sheffield, UK
Email: mzikidis1@sheffield.ac.uk
Office: Room J14B ; Hicks Building, School of Mathematics and Statistics
I am a PhD Student at the University of Sheffield, working under the supervision of Prof. Tom Bridgeland, within the AGMP research group.
Research Interests : (i.e. things I know almost nothing about, but really wish I did..)
Geometric Structures and Geometry of Moduli Spaces (Geometric Structures on Moduli of Geometric Structures)
Integrable Systems , Riemann-Hilbert Problems, Irregular Higgs Bundles, Flat Connections and Quadratic Differentials
Bridgeland Stability Structures, Geometry arising from Homological Algebra and Derived MacGuffin, Donaldson-Thomas Theory, Mirror Symmetry.
Geometric Langlands, Non-Abelian Hodge Theory
Mathematical Physics, String Theory ( nodding acquaintance )
Arithmetic incarnations of all of the above (hobby level:)
My current focus is the study of Joyce Structures on Spaces of Stability Conditions of derived Calabi-Yau-3 categories associated to supersymmetric field theories of Class-S, aiming to encode Donaldson-Thomas invariants of the associated category. The Geometric structure at hand admits an explicit moduli theoretic description in terms of Flows of Isomonodromic Deformations of Meromorphic Stokes-Riemann-Hilbert data over the moduli of wild algebraic curves, and giving rise to a Complex Hyperkähler Structure on the moduli of stability conditions.
In Preparation: "Joyce Structures on Spaces of Meromorphic Quadratic Differentials"
Current:
Yiwei Wang -MSc- " Galois Representations and Arithmetic Equivalence of Number Fields "[Graduated October 2022].
Past:
In Autumn 2021, I organized a Seminar on the Theory of Algebraic Stacks .
Since Autumn 2021: Towards Arithmetic Geometry.
Conferences and Travel: 2023-24
Upcoming:
Moduli and Enumerative Geometry- VBAC at INI- Cambridge (Presenting) 17.06-21.06.24
Ramification in Geometric Langlands and Non-Abelian Hodge Theory - University of Heidelberg (Presenting) 09.09-13.09.24
Geometry and Physics of Mirror Symmetry -University of Sheffield 02.09-06.09.24
Past:
Simons Center for Geometry and Physics, Stony Brook : 20.05-03.06.23
University of Oxford: 04-10.06.23
Imperial College London: 03-08.07.23
Banff International Research Station: 10-20.10.23
CIRM, Marseille: 10.23
Simons Center for Geometry and Physics, Stony Brook : 13.05-21.06.24
Short Bio:
I completed my Masters and undergraduate studies in Mathematics and Physics at the University of Heidelberg, under the supervision of Prof. Anna Wienhard and Prof. Johannes Walcher, resulting in:
- a MSc Thesis with title '' G-Opers as Conformal Limits of Deligne Connections in Non-Abelian Hodge Theory''
- a BSc Thesis with title '' Arithmetic of Holography, p-adic AdS/CFT and Discrete Black Holes''
During my Masters in Heidelberg, I was a student research assistant at the Heidelberg Institute for Theoretical Studies (HITS), co-organiser of the Heidelberg Experimental Geometry Lab , and student representative of the YRC within the Structures Cluster.
