Math Colloquium: Cusps of Caustics by Reflection and Other 4-Point Theorems
Guest Lecturer: Professor Sergei Tabachnikov, Department of Mathematics, Pennsylvania State University, USA
Have you ever wondered how simple geometric shapes can lead to deep mathematical insights?
The Institute of Advanced Studies is honored to welcome Professor Sergei Tabachnikov, Professor of Mathematics at Pennsylvania State University, as part of the IAS Distinguished Scholars series.
In his talk, “Cusps of Caustics by Reflection and Other 4-Point Theorems,” Professor Sergei Tabachnikov will explore a striking geometric phenomenon rooted in classical mathematics. The “Last Geometric Statement of Jacobi” claims that the conjugate locus of a non-umbilic point on a triaxial ellipsoid has exactly four cusps—a theorem proved only in recent decades.
Extending this idea, Professor Tabachnikov will present a billiard version of the problem, where reflections inside a plane oval reveal similar four-cusp patterns. He will also connect these results to broader settings, including Finsler and magnetic billiards, showing how a refined four-point theorem extends the classical four-vertex theorem of Mukhopadhyaya.
Monday, 12 January 2026, 12:00
Where: Room 006, Schreiber Building
The lecture will be conducted in English and is open to the public.
Light refreshments will be served before the lecture.
