Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Surjectivity of the Cannon-Thurston map in metric bundle.
Speaker: Rakesh Halder, TIFR, Mumbai
Date: November 18, 2024
Time: 15:15:00 Hours
Venue: A-369
Abstract: Consider a hyperbolic metric bundle X over (a hyperbolic base) B such that fibers are uniformly hyperbolic and possess uniformly coarsely surjective barycenter maps. Mj and Sardar showed that the inclusion of a(ny) fiber into X extends continuously to their (Gromov) boundaries. (Such maps known as Cannon-Thurston (CT) maps.) Later, Bowditch proved that if fibers are isometric to hyperbolic plane and base is a geodesic ray then this CT map is surjective. (It is a result of Krishna and Sardar that it suffices to prove the surjectivity of the CT map when base is a geodesic ray to get surjectivity when base is arbitrary hyperbolic space.) Motivated by this result, in a paper by Lazarovich, Margolis and Mj posed the question whether surjectivity holds when fibers are one-ended, uniformly hyperbolic and barycenter maps are uniformly coarsely surjective. In this talk, we provide a positive answer to this question. If time permits, we will discuss a discretized version of the result, where one-ended condition on the fiber can be removed. This is ongoing work.
Title of Seminar: Algebraic Geometry Preprint Seminar
Title of Talk: Existence of global Néron models beyond semi-abelian varieties
Speaker: Subhadip Majumder, TIFR, Mumbai
Date: November 18, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Let $S$ be an excellent Dedekind scheme with function field $K$. For a smooth connected commutative group scheme $G_K$ over $K$, it was conjectured in the book ``Néron Models" by Bosch, Lütkebohmert and Raynaud that a Néron-lift model for $G_K$ over $S$ exists if it doesn't contain $\mathbb{G}_a$. This conjecture is known to be true if $S$ is local or $char S=0$. However, if $char S=p>0$, then this is an open question. In the preprint {\tt arxiv.org/abs/2310.14567v2}, the authors showed that the conjecture holds when the residue fields of $S$ at closed points are perfect, but is false in general. In this talk, I will discuss the proof of this result.
Title of Talk: Surjectivity of the Cannon-Thurston map in metric bundle.
Speaker: Rakesh Halder, TIFR, Mumbai
Date: November 18, 2024
Time: 15:15:00 Hours
Venue: A-369
Abstract: Consider a hyperbolic metric bundle X over (a hyperbolic base) B such that fibers are uniformly hyperbolic and possess uniformly coarsely surjective barycenter maps. Mj and Sardar showed that the inclusion of a(ny) fiber into X extends continuously to their (Gromov) boundaries. (Such maps known as Cannon-Thurston (CT) maps.) Later, Bowditch proved that if fibers are isometric to hyperbolic plane and base is a geodesic ray then this CT map is surjective. (It is a result of Krishna and Sardar that it suffices to prove the surjectivity of the CT map when base is a geodesic ray to get surjectivity when base is arbitrary hyperbolic space.) Motivated by this result, in a paper by Lazarovich, Margolis and Mj posed the question whether surjectivity holds when fibers are one-ended, uniformly hyperbolic and barycenter maps are uniformly coarsely surjective. In this talk, we provide a positive answer to this question. If time permits, we will discuss a discretized version of the result, where one-ended condition on the fiber can be removed. This is ongoing work.
Title of Seminar: Algebraic Geometry Preprint Seminar
Title of Talk: Existence of global Néron models beyond semi-abelian varieties
Speaker: Subhadip Majumder, TIFR, Mumbai
Date: November 18, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Let $S$ be an excellent Dedekind scheme with function field $K$. For a smooth connected commutative group scheme $G_K$ over $K$, it was conjectured in the book ``Néron Models" by Bosch, Lütkebohmert and Raynaud that a Néron-lift model for $G_K$ over $S$ exists if it doesn't contain $\mathbb{G}_a$. This conjecture is known to be true if $S$ is local or $char S=0$. However, if $char S=p>0$, then this is an open question. In the preprint {\tt arxiv.org/abs/2310.14567v2}, the authors showed that the conjecture holds when the residue fields of $S$ at closed points are perfect, but is false in general. In this talk, I will discuss the proof of this result.