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 1¤ëºtÁ¿ Algebraic Geometry Seminar, California State University, Northridge (CSUN), Prof. Jason Lo Thursday, January 4, 14:10¡X15:00 ¼Æ¾Ç¨t3F·|Ä³«Ç 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, ­»´ä¤¤¤å¤j¾Ç¼Æ¾Ç¨t ¬xÙy­õ±Ð±Â Thursday, January 4, 15:10¡X16:00 ¼Æ¾Ç¨t3174 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, »OÆW®v½d¤j¾Ç¼Æ¾Ç¨t ³¢®xº_±Ð±Â Thursday, January 4, 16:10¡X17:00 ¼Æ¾Ç¨t3174 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, ²MµØ¤j¾Ç¼Æ¾Ç¨t ¦ó«n°ê±Ð±Â Friday, January 5, 14:10¡X15:00 ¼Æ¾Ç¨t3174 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, °ê®a²z½×¬ì¾Ç¤¤¤ß¼Æ¾Ç²Õ ³¯§Ó°¶³Õ¤h Thursday, January 11, 16:10¡X17:00 ¼Æ¾Ç¨t3174 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. PDE Seminar, ¦¨¥\¤j¾Ç¼Æ¾Ç¨t §d®¥»ü±Ð±Â Friday, January 26, 11:00¡X15:00 ¼Æ¾Ç¨t3175 Title: Linearized Boltzmann Equation for Hard Potentials Abstract: Reading Seminar on Kinetic Theory.

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 °ê¥ß¦¨¥\¤j¾Ç¼Æ¾Ç¨t 70101 ¥x«n¥«¤j¾Ç¸ô¤@¸¹ ¹q¸Ü¡J(06) 2757575 Âà 65100   ¶Ç¯u¡J(06) 2743191 em65100[at]email.ncku.edu.tw