Speakers and abstracts
Abstract of the mini-courses/contributed lectures
Jared Ongaro (University of Nairobi)
Title: “Algebraic curves”
Abstract: Abstract: In this mini-course we will introduce what are algebraic curves, focusing mainly on the basic example of curves in the complex affine plane. We will describe some famous example and discuss their main properties.
Sarah Nakato (Kabale University)
Title: "Commutative Algebra”
Abstract: Commutative algebra is the branch of algebra that studies commutative rings and objects relating to them, for instance, ideals and modules. Since commutative algebra pro- vides the algebraic foundation for algebraic geometry, in the first lectures, we will discuss several concepts in commutative algebra, for instance, commutative rings, fields, ideals, quotient rings, homomorphisms, maximal ideals, polynomials rings, among others.
Anne-Sophie Kaloghiros (Brunel University London)
Title: "Introduction to Algebraic Geometry I”
Abstract: The course will be an introduction to the objects studied in algebraic geometry (geometric shapes defined by systems of polynomial equations) and some of the techniques used to study them. I will discuss in detail some curve and surfaces examples to illustrate more general concepts.
Soumya Sankar (Utrecht University)
Title: "Curves over finite fields”
Abstract: Algebraic varieties over finite fields come with a distinguished action by the ‘Frobenius’ map, which gives them a lot of interesting structure and allows for new perspectives on them via (semi-)linear algebra, combinatorics, and other such tools. This course is a short introduction to curves over finite fields and invariants associated with them.
Diletta Martinelli (University of Amsterdam)
Title: "Introduction to Algebraic Geometry II”
Abstract: In this mini-course we will continue to introduce basic objects in algebraic geometry. The lectures will be mainly dedicated to explain some key examples such as conics in the projective spaces, algebraic curves and surfaces and toric varieties.
Alex Samuel Bomunoba (Makerere University)
Title: "Topics in Number Theory: Congruences and their applications”
Abstract: A congruence is just a statement about divisibility. Its theory was introduced by C.F. Gauss, who contributed to the basic ideas and proved several theorems related to con- gruence. In this mini course, we shall start by introducing congruences and their properties, state and prove theorems about the residue system in connection with the Euler phi function. We then present solutions to linear congruences which will serve as an introduction to the Chinese remainder theorem as well as its applications. We present finally the important con- gruence theorems derived by Wilson, Fermat and Euler as well as their applications in both arithmetic (primality and divisibility tests), cryptology.
Amos Turchet (Rome 3 University)
Title: “Introduction to Diophantine Geometry”
Abstract: Given a polynomial equation with integral coefficients, can we describe the inte- gral solutions? The negative answer to Hilbert 10th problem shows that this question cannot be solved algorithmically. Diophantine Geometry provides tools for this type of questions coming from Geometry. In this course we will see some of these tools in actions for poly- nomial equations in two or three variables.
Marta Pieropan (Utrecht University)
Title: “Introduction to geometry of numbers”
Abstract: How many points with integer coordinates lie inside a circle? How does this number grow as the radius increases? Is the area of the circle a good approximation? What if the circle is replaced by other regions? This course formalises the notion of point with integer coordi- nates via the theory of lattices, and introduces the basics of Minkowski theory for lattice points in convex bodies. We will discuss the sup norm as Weil height in projective space, and the equivalence to the Euclidean norm. We will introduce Möebius inversion and count points of bounded height in linear subspaces of projective space.
Contributed lectures by Shumbusho Rene Michel (University of Rwanda) and Vincent Umutabazi (University of Rwanda).