Title of Seminar: Algebraic Geometry Preprint Seminar
Title of Talk: The Singer-Hopf conjecture for Algebraic Varieties
Speaker: Ashutosh Roy Choudhury, TIFR, Mumbai
Date: April 16, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: In the 1930s, Hopf conjectured that a closed 2d-dimensional compact Riemannian manifold X with non-positive sectional curvature satisfies $(-1)^d \xi(X) \ge 0$, later strengthened by Singer for aspherical manifolds (i.e., those with contractible universal cover). In the context of algebraic varieties, one can ask much more general questions about the euler characteristic of perverse sheaves even over positive characteristic. In this talk I would like to start with a survey of the known results and methods for Abelian Varieties and Tori(here an interesting perspective is offered by the Fourier-Mellin transform on Constructible Sheaves) following which, I'd like to present some results in the paper: Perverse Sheaves on Varieties with large fundamental group (https://arxiv.org/pdf/2109.07887.pdf) by D.Arapura and B.Wang.
Title of Talk: The Singer-Hopf conjecture for Algebraic Varieties
Speaker: Ashutosh Roy Choudhury, TIFR, Mumbai
Date: April 16, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: In the 1930s, Hopf conjectured that a closed 2d-dimensional compact Riemannian manifold X with non-positive sectional curvature satisfies $(-1)^d \xi(X) \ge 0$, later strengthened by Singer for aspherical manifolds (i.e., those with contractible universal cover). In the context of algebraic varieties, one can ask much more general questions about the euler characteristic of perverse sheaves even over positive characteristic. In this talk I would like to start with a survey of the known results and methods for Abelian Varieties and Tori(here an interesting perspective is offered by the Fourier-Mellin transform on Constructible Sheaves) following which, I'd like to present some results in the paper: Perverse Sheaves on Varieties with large fundamental group (https://arxiv.org/pdf/2109.07887.pdf) by D.Arapura and B.Wang.