This course aims to enhance the academic communication skills of graduate students with the long term goal of facilitating research output. To this aim, the rhetorical genres characteristic of scientific/technical writing will be discussed: a review of literature, thesis, article…

Plane curves, affine and projective varieties, intersection of curves, Bezout’s theorem, analysis of singularities, Riemann Roch theorem.

Upcoming lectures Past lectures Thu 25 Apr 2019 Giorgos Kapetanakis: The line and the translate problems for r-primitive elements (FENS G035, 13:40) Thu 18 Apr 2019 Ezgi Kantarcı: A Queer Crystal Structure on Shifted Tableaux (FENS G035, 13:40) Thu 11…

This course is a follow-up to GR 501E and aims to provide further opportunities for graduate students to develop their skills in teaching and learning in higher education. This course will enable graduate students to reflect on their first semester…

1) Categories and functors 2) Modules 3) Tensor products of modules 4) Projective, Injective, Flat modules 5) Localization 6) Homology 7) Tor and Ext 8) Homology and rings

Modules. Fields, extension fields, Galois theory. Categories and functors.

Metric spaces and general topological spaces. Connectedness, compactness, completeness and consequences. Baire category theorem. Linear topological spaces. Open mapping, closed graph theorems. Hahn Banach theorem. Hilbert and Banach spaces.

Algebraic varieties, affine and projective varieties, dimensions of varieties, singular points, divisors, differentials, intersections. Schemes, cohomology, curves and surfaces, varieties over the complex numbers.