**Title: Topics in Algebraic Geometry**

Duration:

March to June, 4 months, meeting twice a week, 90 minutes each class. Classes will be held Tuesdays and Thursdays from 15:30 to 17:00 at IMPA, Room 347, unless communicated otherwise.

Syllabus (Partial):

09.03 - 20.03: Intersection Theory (E. Esteves):

Chow groups, Chern classes, Chow rings, Schubert Calculus, Porteous Formula, Grothendieck-Riemann-Roch Theorem, Applications.

Amoebas, Tropical varieties, Non-Archimedean valuations, Tropicalization, Berkovich spaces, Toric varieties, F1-geometry.

06.04 - 10.04: Moduli Theory (E. Esteves):

Functors, Representation by schemes, Algebraic spaces, Stacks, GIT quotients.

13.04 - 24.04: Higher Dimension Geometry (C. Araujo and S. Kovács):

Kodaira dimension, Fano varieties, Rational curves, Mori’s Bend and Break, Minimal Model Program, Moduli of varieties of general type.

Rational points on algebraic curves, Rational points on algebraic surfaces, Rational surfaces, del Pezzo surfaces, K3 surfaces, Surfaces of general type, Potential density, Local-global principle.

11.05 - 15.05: Mini-courses at the Workshop “Tropical Geometry in the Tropics”.

18.05 - 22.05: Introductory talks at the Workshop “Higher Dimension Algebraic Geometry”.

25.05 - 29.05: Mini-courses at the Workshop “Rational Points/Pontos Racionais”.

01.06 - 05.06: Mini-courses at II ELGA.

08.06 - 12.06: II ELGA.

15.06 - 26.06: Applications of Algebraic Geometry (A. Dickenstein and K. Ranestad):Higher secant varieties with applications to rank and power sum varieties for homogeneous polynomials. Tools from computational algebraic geometry with applications to biochemical reaction networks.

Details on the remaining weeks will appear soon.

Observation: This is a regular course of the Doctor Program at IMPA, so it can be taken for credit.