New Directions in Rational Points

The Chennai Mathematical Institute will host the "New Directions in Rational Points" workshop in Chennai, India from January 7 to January 12, 2024. Rational points are rational solutions of polynomial equations with integer or rational coefficients. Solubility of such equations is one of the major questions that drive the development of mathematics since Diophantus of Alexandria (circa 200-280 AD). Modern number theory to a large extend grew out of the attempts to prove Fermat's Last Theorem that describes all rational solutions of a particular kind of equations. Presently, polynomial equations of degree 2 are well understood, and a good deal is known about equations of degree 3. Modern methods aim to deal with large families of more complicated equations statistically, establishing the proportion of soluble equations in a given family. This relies on the development of new techniques in analysis, geometry and algebra.