IAS Lecture: How Simple Geometric Shapes Lead to Deep Math Insights
Guest Lecturer: Professor Sergei Tabachnikov, Pennsylvania State University, USA
Cusps of Caustics by Reflection and Other 4-Point Theorems
Tel Aviv University's Institute of Advanced Studies is pleased to welcome Professor Sergei Tabachnikov, Professor of Mathematics at Pennsylvania State University. He is visiting Tel Aviv University as part of the IAS Distinguished Scholars series 2025–2026 and will speak at the Math Colloquium of the TAU School of Mathematical Sciences.
In his talk, 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.
When: January 12, 2026 | 12:00
Where: Schreiber Building, Room 006
Light refreshments will be served before the lecture.
The lecture will be conducted in English and is open to the public.
The Institute of Advanced Studies at Tel Aviv University promotes academic excellence by hosting leading scholars from diverse fields worldwide.
