Abdelouahab Khelifati

Motivated Ph.D student and passionate about Mathematics. Endowed with a great ability of adaptation. I know how to be stimulating, and I aim to conduct research in Complex Algebraic and Differential Geometry.

• Member of the Mathwin Group as of 2019 : Participation in in-depth courses (focusing on Problem-solving), organized by the Mathwin group (www.mathwin.org) on various topics of fundamental mathematics and started taking part in some specialized courses as of 2022 :
• Algebraic Topology (February 2022 to May 2022): We took preliminary courses from ICTP then studied in depth Homotopy theory and Homology theory.
• Complex Geometry (July 2022 to October 2022): We studied Complex manifolds, Connections, curvature and Hermitian metrics, as we introduced basic notions of Kähler Geometry and Hodge Theory based on lecture notes by ANDREAS HÖRING and books of Jean-Pierre Demailly (Complex Analytic and Differential Geometry) and Claire Voisin.
• Riemannian Geometry (July 2022 to October 2022): We studied rigorously the notions of Riemannian metrics, Connections, and Curvature and we tackled important theorems such as Hopf-Rinow and Hadamard’s Theorem.
• Algebraic Geometry (July 2022 to October 2022): We have introduced Affine and Projective algebraic sets and discussed main theorems as the Nullstellensatz, Bezout theorem and Riemann-Roch theorem.
• Presentation of talks about my Master thesis (April 16th to June 16th, 2023): I gave talks about my Master subject “Numerical Characterization of the Kähler cone of a Kähler compact manifold”.
• Lectures on K3 Surfaces (December 12th, 2023 to April 21st, 2024): We started a series of lectures on K3 Surfaces and I gave about four talks on the topological and differential properties of Complex K3 Surfaces and their deformations.
• Tutoring (March 1st - ongoing): Now I am also tutoring undergraduate students within the Mathwin community on different materials.
• Seminars and Conferences : I participated in several seminars and conferences during the last couple of years where I had the chance to assimilate new methods and technics in complex geometry and other related fields and meet a lot of people to talk about mathematics in general and share ideas related to our specific domains :
• Presentation of mini-projects in Master 2 (January 5th & February 9th, 2023): I presented two talks on geometric group theory: the first was about Free Groups and Foldings, and the second was about Mapping Class Groups of Surfaces.
• MasterClass of Non-Commutative Geometry and Analysis on Manifolds (13th to 15th of April, 2023): I participated in a Masterclass of Non-Commutative Geometry in the University of Metz and it was the opportunity to get more knowledge about Representation Theory, Differential Operators, Poisson and Symplectic Geometry.
• MINT Summer school on Facets of Complex Dynamics (26th to 30th of June, 2023): I attended to this summer school in the University of Toulouse III about complex dynamics and the theory of currents with applications in complex dynamics.
• Conference in the memory of Jean-Pierre Demailly (3rd to 7th of June, 2024): This conference took place in the Fourier institute of Grenoble and it was for me the opportunity to meet a lot of experts of the domain of complex geometry and have very good discussions that helped me to get more ideas about my research topic and related problems.
• Complex Analysis, Geometry, and Dynamics III (10th to 14th of June, 2024): This was the chance to visit the beautiful city of Portorož and meet specialists in complex dynamics and complex differential geometry and learn some techniques that can be used in my work on deformation theory.
• GdT Komplex (ongoing) : I am attending since the beginning of my PhD in september a series of seminars on different topics of complex geometry organized by the complex geometry team in the mathematical institute of Toulouse led by Pr. Vincent Guedj.