This Wednesday 10/5 from 5:30-6:30 in LGRT 1634 LGRT 1528 (the actuarial fair will be in 1634 from 4-7 PM – be sure to check that out as well) Holley Friedlander will present “An introduction to Diophantine equations and elliptic curves.” Come listen and enjoy free pizza and soda!
Abstract:
We will consider rational solutions to polynomial equations of the form F(x,y)=0 with integer coefficients. These types of equations were first studied by Greek mathematician Diophantus of Alexandria in the 3rd century. Since then, many interesting applications of Diophantine equations have been discovered. Two natural questions one can ask about these types of equations are: is there a rational solution? and if so, are there infinitely many rational solutions? We will completely answer these questions when the degree of F is 1 or 2. The case degree of F equal to 3 is more delicate and will lead us to the definition of an elliptic curve. The talk will focus on specific examples that emphasize how algebra, number theory, and geometry all play a role in the study of Diophantine equations.