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 mathématiquesIntervenant-e-s
Richard Thomas, Imperial College, Londresentrée libre
Classement
Catégorie: Colloque