Uploaded May 2026 | Updated September 2026, 3 weeks ago
Prof. Dr. Jürg Kramer
Work Group Arithmetic Geometry
Humboldt-Universität zu Berlin
Math+ Special Talk given at the XXIX. Berlin Day of Mathematics
Diophantine equations are a classical topic in number theory: they are algebraic equations in which one seeks integer solutions. Despite their often simple appearance, they give rise to deep and structurally rich problems.
A modern approach is to consider rational solutions and to interpret the set of solutions as a geometric object. This leads to arithmetic geometry, a field that connects number theory with algebraic geometry.
At the center of this talk stands the work of Gerd Faltings. In the 1980s, he achieved a major breakthrough by proving a long-standing conjecture, now known as Faltings’s theorem. It states that certain algebraic curves have only finitely many rational points. The hyperelliptic curve shown in the poster is an example of such a curve: it has only finitely many rational solutions.
For his fundamental contributions to arithmetic geometry, Faltings was awarded the Abel Prize in 2026.
The talk provides an accessible introduction to these ideas and highlights the deep connections between number theory and geometry.
This is a Math+ Special Talk cohosted by the Berlin Mathematical School. It is supported by the Berlin Mathematics Center of Excellence Math+.
Jürg Kramer is the president of the German Mathematical Society, founder and long time director of the German Center for Mathematics Teacher Education, and Coeditor of the journal Elemente der Mathematik.
Prof. Dr. Jürg Kramer
Work Group Arithmetic Geometry
Humboldt-Universität zu Berlin
Math+ Special Talk given at the XXIX. Berlin Day of Mathematics
Diophantine equations are a classical topic in number theory: they are algebraic equations in which one seeks integer solutions. Despite their often simple appearance, they give rise to deep and structurally rich problems.
A modern approach is to consider rational solutions and to interpret the set of solutions as a geometric object. This leads to arithmetic geometry, a field that connects number theory with algebraic geometry.
At the center of this talk stands the work of Gerd Faltings. In the 1980s, he achieved a major breakthrough by proving a long-standing conjecture, now known as Faltings’s theorem. It states that certain algebraic curves have only finitely many rational points. The hyperelliptic curve shown in the poster is an example of such a curve: it has only finitely many rational solutions.
For his fundamental contributions to arithmetic geometry, Faltings was awarded the Abel Prize in 2026.
The talk provides an accessible introduction to these ideas and highlights the deep connections between number theory and geometry.
This is a Math+ Special Talk cohosted by the Berlin Mathematical School. It is supported by the Berlin Mathematics Center of Excellence Math+.
Jürg Kramer is the president of the German Mathematical Society, founder and long time director of the German Center for Mathematics Teacher Education, and Coeditor of the journal Elemente der Mathematik.
