Andreas Bernig

Prof. Andreas Bernig is a faculty member at Goethe University Frankfurt am Main, affiliated with the Department of Computer Science and Mathematics. He has held a W3 professorship in Differential Geometry since October 2009 and served as Dean of the Faculty (2017-2019) and Director of the Institute for Mathematics (2022-2024). His research spans Integral Geometry, Finsler Geometry, Riemannian Geometry, Geometric Inequalities, and Geometric Measure Theory, with a focus on valuations, kinematic formulas, and curvature measures in singular and pseudo-Riemannian settings.

His recent publications explore topics such as the

• Hard Lefschetz theorem in convex valuation theory
• Weyl principle for Kähler manifolds
• Kinematic formulas in pseudo-Riemannian space forms
• Dual area measures in Hermitian integral geometry
• Invariant valuations on complex and quaternionic spaces

These works often involve collaborations with leading mathematicians like J.H.G. Fu, Gil Solanes, and Thomas Wannerer.

Prof. Bernig has received notable scientific recognition, including

• First prize at the German Mathematical Olympiad (1991, 1992)
• DFG and SNFS funding for projects like "Invariants of Singular Spaces" and "Tensor Valuations"

He has supervised doctoral and Master’s students such as Luca Iffland, Frederik Herget, and Frank Steinke, and actively participates in international conferences and workshops in integral geometry, convex geometry, and geometric analysis.