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Elliptic Curves and Elliptic Functions
INSTRUCTOR: YURI ZARHIN
MAIN TOPICS include:
- Plane algebraic curves
- A rational parametrization of quadrics and singular cubics
- Elliptic functions; Divisors and principal divisors; The Weierstrass P-function; The field of elliptic functions
- Elliptic curves; A parametrization of elliptic curves by elliptic functions; Addition theorems for the Weierstrass P-function and its derivative
- A characterization of the divisors of elliptic functions
- The projective line, projective plane and infinite points; The group law on elliptic curves
Introducation to Complex Dynamics
INSTRUCTOR: BRYNA KRA
MAIN TOPICS include:
- Iteration of functions, fixed points, periodic points, attracting and repelling fixed points
- Dynamics of the quadratic family
- Transitivity, sensitive dependence to initial conditions
- Chaos, Julia and Fatou Sets
- Mandelbrot Set