|Colloquium, 清華大學數學系 卓士堯教授|
Thursday, October 5, 16:10—17:00 數學系3174
Title: Iitaka Dimensions of Vector Bundles
Abstract: To understand an abstract space X, one often tries to embed it into more familiar spaces such as the Euclidean space or the projective space. It has long been understood that giving a map from X to a projective space is equivalent to giving a line bundle L on X with nonzero global sections. A well-known result of Iitaka in algebraic geometry says that the maps from X to projective spaces given by higher and higher tensor powers of L eventually stabilize to a fibration. In a recent preprint, Mistretta and Urbinati generalize this when L is replaced by a vector bundle, which gives a map from X to a Grassmannian. I will explain their result and answer one of their questions.
|Algebraic Geometry Seminar (具備線性代數基礎即可), 國家理論中心主任 陳榮凱教授|
Friday, October 13, 10:30—11:30 數學系4F電腦教室
Title: Taiwan Math School - Derived and Homological Algebraic Geometry
Abstract: We plan to run a program consisting of joint courses on Derived and Homological Algebraic Geometry during the coming academic year. The purpose is to introduce the exciting area and technique involving derived category. We will start from scratch, that is, basic homological algebra, construction of derived categories. We hope that the participants will be able to understand and appreciate the new research work involving derived categories, such as Fourier-Mukai transform, derived category in birational geometry and minimal model program, and Bridgeland stability. A brief outline of courses consists of: 2017/10-2017/12: homological and commutative algebra, and construction of derived categories. 2018/01-2018/02: Winter School on Homological Algebraic Geometry (sheaf theory, base change and cohomology theorem, etc) 2018/02-2018/05: derived category in algebraic geometry, semiorthogonal decomposition, Fourier-Mukai transform, and t-structure 2018/06 : advanced topics 2018/06-2018/07: Mini-courses by Y. Kawamata and P. Cascini.
|Colloquium, 中央大學數學系 陳正傑教授|
Friday, October 13, 14:10—15:00 數學系3174
Title: A generalization of Kawamata Blowup in Higher Dimension
Abstract: In this talk, we would introduce some basic facts about cyclic quotient singularities and discuss about some divisorial contractions in dimension . Then, we show that the divisorial contraction to a terminal cyclic quotient singularity of index r with minimal discrepancy 1/r is unique. This generalizes a result of Kawamata to higher dimension. However, there exist some terminal cyclic quotient singularities (X,P) with minimal discrepancy >1/r which allows infinitely many divisorial contractions to (X,P).
|Colloquium, 高雄師範大學數學系 何忠益教授|
Thursday, October 19, 16:10—17:00 數學系3174
Title: Non-orientable Lagrangian surfaces on Symplectic Rational 4-Manifolds
Abstract: The existence of Lagrangian submanifolds is an important problem in symplectic geometry. In this talk, I will talk about this problem for non-orientable surfaces on symplectic rational 4-manifolds. More precisely, I will show how to construct Lagrangian surfaces concretely and discuss their topological properties.
|Colloquium, 香港中文大學數學系 Ryosuke Takahashi博士|
Thursday, October 26, 16:10—17:00 數學系3174
Title: Index Theorem for the Z/2-Harmonic Spinors