Speaker: 朱家林(msrc)
Time: 14:00-15:00, Sep. 26, 2024
Venue: 数学中心研讨室（至善楼602）
Title: Spectral convergence under Gromov-Hausdorff convergence
Abstract:
In this talk, we will talk about the spectral convergence under the Gromov-Hausdorff convergence. We focus on the behavior of the spectrum of Hodge-Laplacian for a non-collapsed Gromov-Hausdorff convergent sequence of Riemannian manifolds with a uniform bound of Ricci curvature.
Speaker: 朱家林(msrc)
Time: 10:00-11:00, Sep. 6, 2024
Venue: 数学中心研讨室（至善楼602）
Title: On a theorem of Beilinson-Schechtman and its generalization to parabolic case
Abstract:
In this talk, we first talk about a theorem of Beilinson-Schechtman on the Atiyah algebra of the determinant cohomology line bundle, associated to a smooth family of algebraic curves.
Secondly, we will give an introduction to the recent work of Biswas-Mukhopadhyay-Wentworth (arXiv:2103.03792 ; 2307.09196) on the generalization of BS-theorem to the parabolic case.
Speaker: 朱家林(msrc)
Time: 10:00-11:00, July. 31, 2024
Online: Zoom: 811 5638 1768 （Password：msrc）
Title: Integral invariants for framed 3-manifolds associated to trivalent graphs（线上）
Abstract:
In this talk, we will give an introduction on the recent work of H. Kodani and X. Liu (arXiv:2311.02682v2) on constructing integral invariants for framed 3-manifolds associated to trivalent graphs.
In Chern-Simons perturbation gauge theory, Bott and Cattaneo defined some integral invariants for framed rational homology 3-sphere in terms of graph cocycles without self-loops. In the work of Kodani-Liu, they construct a theory of graph complexes and cocycles to define integral invariants for graphs with higher self loops.
Speaker: 朱家林(msrc)
Time: 10:00-11:00, July. 11, 2024
Venue: 数学中心研讨室（至善楼602）
Title: On the linear Singer-Hopf conjecture
Abstract:
In this talk, we will give an introduction on the recent work of Deng and Wang (arXiv:2405.12012) on the linear Singer-Hopf conjecture. If X is a closed 2n-dimensional aspherical manifold, the Singer-Hopf conjecture says that (-1)^n\chi(X)\geq 0. In the work of Deng-Wang, they solved this conjecture for complex projective manifolds equipped with an almost faithful linear representation of its fundamental group.
