Counting things: enumerative algebraic geometry from physics (Richard Thomas, Imperial College, Londres)

28.02.2019 16:15

For centuries mathematicians have generalised statements like ³there is a unique line through any 2 points², but with increasing technical difficulties. It was not until the late 1990s that new ideas from mathematics and string theory allowed rigorous definitions to be made of these ³curve counting problems².
I will outline two different ways to count curves, assuming only a bit of undergraduate complex analysis. The famous ³MNOP conjecture² is that the two definitions give equivalent information. Its recent proof by Pandharipande and Pixton has enabled the solution of various counting problems, such as the ³KKV conjecture² from string theory, expressing all curve counting problems on ³K3 surfaces² in terms of modular forms.
If time allows I will also outline some other enumerative theories suggested by physics and implemented in algebraic geometry, such as
Vafa-Witten theory.

PS. The Colloquium will be followed by an aperitif

Lieu

Room 17

Organisé par

Section de mathématiques

Intervenant-e-s

Richard Thomas, Imperial College, Londres

entrée libre

Classement

Catégorie: Colloque