|Algebraic Geometry Seminar, California State University, Northridge (CSUN), Prof. Jason Lo|
Thursday, January 4, 14:10—15:00 數學系3F會議室
Title: Stability, Counting Invariants and Symmetries
Abstract: In algebraic geometry, any time we have a notion of `stability for coherent sheaves or complexes of coherent sheaves on a smooth projective variety , we can consider moduli spaces of the stable objects. When the moduli spaces have good enough properties, we can define associated `counting invariants' on X, such as Donaldson-Thomas (DT) invariants and Pandharipande-Thomas (PT) invariants. When X possesses an internal symmetry, the symmetry can induce relations between different stable objects, and relations between different counting invariants. In this talk, I will talk about some recent developments in this area on threefolds and possible future directions.
|Colloquium, 香港中文大學數學系 洪斌哲教授|
Thursday, January 4, 15:10—16:00 數學系3174
Title: On the Anticyclotomic Exceptional Zero Conjecture for Elliptic Curves
Abstract: We will first recall some history and background about the exceptional zero conjecture for elliptic curves. Our result extends the result of Bertolini-Darmon-Iovita-Spiess.
|Colloquium, 臺灣師範大學數學系 郭庭榕教授 |
Thursday, January 4, 16:10—17:00 數學系3174
Title: A Connection of Generalized Lame Equation and the Mean Field Equation
Abstract: In this talk, I will first introduce a second order linear complex ODE so called the generalized Lame equation (GLE) and discuss its monodromy representation. Secondly, I will focus on a class of mean field equation (MFE) which can induce a generalized Lame equation. By applying the theory we develop in GLE, we could give a criterion of the existence of solutions to the MFE.
|Colloquium, 清華大學數學系 何南國教授|
Friday, January 5, 14:10—15:00 數學系3174
Title: Hitchin's Equations on a Nonorientable Manifold
Abstract: We define and study Hitchin's moduli space over a compact non-orientable Riemannian manifold. We proved that this moduli space has a natural Kahler structure and we give a condition for points being smooth in the moduli space. In particular, when the nonorientable manifold is two dimensional, we show that irreducibility is not enough to promise smoothness. This is a joint work with Graeme Wilkin and Siye Wu.
|Colloquium, 國家理論科學中心數學組 陳志偉博士|
Thursday, January 11, 16:10—17:00 數學系3174
Title: Geometric Analysis and Data Representation
Abstract: One of the main issue in manifold learning theory is to represent the data set by appropriate embedding maps. Such process is expected to reduce the dimension of the data set and maintain as much geometric structures as possible. One method is to employ eigenfunctions of the Laplacian as embedding functions. Surprisingly, this technique could be applied to tackle problems occurring in an active area in modern geometric analysis - the Ricci flow. In this talk, I will show you the confluence of the Ricci flow and the manifold learning theory.