The Department of Mathematics is hosting a series of colloquia, open for all to attend. On 14 March 2025, Minhyong Kim from the University of Edinburgh will give a talk on 'Diophantine Equations in Two Variables.'

Registration

This talk will take place in person at King's College London  in Room S-1.27 in the Strand Building. It will be streamed online via Microsoft Teams. Please click 'Register for this event' to sign up for either an In-Person Ticket or an Online Ticket. If you wish to attend the in-person event, you must select the correct ticket type.

A reception will follow from 17:00 in Room K4.31 in the King's Building.

Abstract: 

The equation

y^3 = x^6 + 23x^5 + 37x^4 + 691x^3 − 631204x^2 + 5169373941

obviously has the solution (1, 1729). Are there any other solutions in rational numbers? The study of integral or rational solutions to polynomial equations, sometimes known as the theory of Diophantine equations, is among the oldest pursuits in mathematics. This lecture will give an idiosyncratic survey of the remarkable advances made in the 20th and 21st century for the special case of equations of two variables. The emphasis will be on the techniques of arithmetic geometry, the study of spaces built up of finitely-generated systems of numbers.

About the Speaker: 

Minhyong Kim grew up in Korea and earned his PhD from Yale University. He has held positions at prestigious institutions such as MIT, Columbia, and the University of Oxford, where he led the Number Theory group. Currently, he is a professor at the University of Edinburgh. His research focuses on arithmetic geometry, exploring spaces built from finitely-generated number systems, and he is best known for developing the non-abelian method of Chabauty. He also has a strong interest in mathematical physics, including topological quantum field theory.

Beyond his remarkable contributions to mathematics, he is passionate about public engagement and has extensive experience in making complex ideas accessible to a general audience.

Future colloquia

Please check our event series for details of upcoming speakers.