Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
|
Speaker |
: |
Dr. Ritabrata Munshi |
| Affiliation | : | Rutgers University, USA |
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Subject Area |
: |
Mathematics
|
|
Venue |
: |
Lecture Hall - I, Dept of Mathematics
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|
Time |
: |
2.00 pm
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|
Date |
: |
August 1,2007 (wednesday) |
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Title |
: |
The arithmetic of elliptic surfaces |
| Abstract | : |
A family of elliptic curves (or an elliptic
surface) is given by a Weierstrass equation
E_t : y^2= x^3+ A(t)x + B(t), where A(t) and B(t) are polynomials. Little is known about the rational points on such families. However there are interesting predictions. For example, a conjecture of Mazur states that if one fiber E_t has infinite number of rational points, then there is a dense set of fibers with infinite number of rational points. In the special case when deg A<= 4 and deg B<= 6, there is a more precise conjecture of Manin about the number of rational points of a fixed height. In this talk I will describe recent results towards these conjectures. I will also discuss other open problems regarding distribution of Mordell-Weil ranks. |