Moduli spaces of bundles and Kloosterman sheaves
Event details
| Date | 20.02.2013 |
| Hour | 13:15 › 15:00 |
| Speaker | Jochen Heinloth, Universität Duisburg-Essen |
| Location | |
| Category | Conferences - Seminars |
The relation between analytic properties of modular forms and arithmetic results has led to many famous results and conjectures. In the geometric analogue of this conjectural relation - called geometric Langlands correspondence quotients of the upper half plane are replaced by moduli spaces of bundles on a curve (or a Riemann surface). In the first part of the talk I will try to motivate this analogy.
Since the geometry of these moduli spaces is complicated in general, very few explicit examples of such modular forms are known. In joint work with
B.C. Ngô and Z. Yun, which was motivated by work of Gross and Frenkel, we found an explicit series of such forms which turn out to be closely related to classical Kloosterman sums.
This gives a rather explicit example of the (wild) geometric Langlands correspondence. Recently X. Zhu managed to relate this example back to the original work of Gross and Frenkel. In particular this allows to remove the word "rather" from the above. If time permits we will end by giving some indication on his argument.
Since the geometry of these moduli spaces is complicated in general, very few explicit examples of such modular forms are known. In joint work with
B.C. Ngô and Z. Yun, which was motivated by work of Gross and Frenkel, we found an explicit series of such forms which turn out to be closely related to classical Kloosterman sums.
This gives a rather explicit example of the (wild) geometric Langlands correspondence. Recently X. Zhu managed to relate this example back to the original work of Gross and Frenkel. In particular this allows to remove the word "rather" from the above. If time permits we will end by giving some indication on his argument.
Practical information
- General public
- Free