KNOWLEDGE AND UNDERSTANDING: becoming familiar with the foundational results of Kähler geometry and of the theory of special Lagrangians. 
 APPLYING KNOWLEDGE AND UNDERSTANDING: developing the ability to solve independently exercises in Kähler geometry and in the theory of special Lagrangians, as well as that of drawing simple corollaries from theoretical results proved in lectures. MAKING JUDGEMENTS: recognising and applying the basic techniques of Kähler geometry and of the theory of special Lagrangians to relevant problems and situations. COMMUNICATION SKILLS: achieving proficiency in the languages of Kähler geometry and of special Lagrangians. LEARNING SKILLS: developing the ability to use with profit the main textbooks in Kähler geometry and in the theory of special Lagrangians.

Basic notions in differential topology and tensor calculus. Basic notions in real and complex analysis.

Complex manifolds. Hermitian and Kähler metrics. Aubin-Calabi-Yau Theorem. Deformed Hermitian Yang-Mills connections. Special Lagrangian submanifolds and the Thomas-Yau Conjecture.

G. Tian, Canonical metrics in Kähler geometry. Notes taken by Meike Akveld. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 2000. vi+101 pp. ISBN: 3-7643-6194-8 D. Joyce, Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow. EMS Surv. Math. Sci. 2 (2015), no. 1, 1–62.

Complex manifolds: basic theory, examples (projective spaces, complex tori, Grassmannians, toric manifolds). Hermitian and Kähler metrics, including Kodaira embedding, with examples (Fubini-Study, abelian varieties). Aubin-Calabi-Yau Theorem: continuity method, a priori estimates. Deformed Hermitian Yang-Mills connections: outline of existence theory. Special Lagrangian submanifolds and the Thomas-Yau Conjecture: the current viewpoint following D. Joyce and Y. Li.

Traditional lectures will be complemented by example classes focusing on the application of theoretical results. The active participation of students will always be encouraged.

Oral exam. Initially students will be required to show their understanding of the context, structure and proof of one or more of the main theoretical results proved in lectures. Subsequently they will be tested with respect to their ability to solve simple problems and to produce relevant examples or counterexamples. The final mark will reflect the outcome of these two steps.