On the crossroads of topology, geometry and algebra

About

The most important exciting results of mathematics connect different areas and build unexpected bridges between different aspects of the theory. During this Summer School we wish to emphasize such connections, bridges between (algebraic) topology, (metric) geometry and algebraic geometry. We focus on key starting examples/problems and ideas, which determined crucial interplays between these areas. E.g., how the local curvature determines the global topology of a space, how the degree of a polynomial determines the topology of its zero set? By such results we wish to picture the unity of mathematics, and to describe the cradles of several modern mathematical theories.

There will be five miniseries during the summer school, consisting of two or three 90 minutes lectures, some of them completed with practical/problem solving sessions. There will be some individual talks as well.

The title of the five minicourses:

• Balázs Csikós: Curvature and topology
• László Fehér: Enumerative geometry: classical and new problems
• András Némethi: Projective algebraic plane curves
• András Stipsicz: Invariants of knots: polynomials and homologies
• András Szűcs: Three Field medalists of Topology: Smale (immersions), Thom (cobordisms) , Milnor (exotic spheres)

Inidividual lecture:

• Gábor Moussong: From Poincaré to Thurston and Perelman: one hundred years of a conjecture

Course leader

The lecturers are professors at Eötvös Loránd University and the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences. The lectures will take place at the Lágymányos Campus of Eötvös Loránd University (1117 Budapest, Pázmány Péter sé

Target group

We expect that participants will have already covered basic courses of a BSc mathematics program but we do not assume preliminary acquaintance with the special topics of the school. Depending on the background of the participants and the difficulty of the topics, some lectures may leave the details to the intuition of the audience. We encourage participation of advanced BSc students of mathematics as well as MSc and PhD students, interested in this dynamic and highly appreciated area of mathematics.

Fee info