Explore spectral inequalities for the Laplacian on manifolds with bounded sectional curvature in this mathematical seminar presented by Dr. Jean Lagacé from King's College London. Delve into advanced topics in geometric spectral theory as part of the Isaac Newton Institute's research programme on geometric spectral theory and applications. Examine the relationship between geometric properties of manifolds and spectral characteristics of the Laplacian operator, focusing specifically on how bounded sectional curvature constraints influence spectral behavior. Learn about cutting-edge research methods and theoretical frameworks used to establish and analyze these spectral inequalities. Gain insights into the mathematical techniques employed to study eigenvalue problems on curved spaces and understand the implications for broader applications in mathematical physics and differential geometry.