Graduate Student Singularity Theory
If you would like to present a topic, please contact Tommy Wong. Please check below for time and location.
We continue with Professor Alex Suciu's work.
We follow Professor Alex Suciu's work this semester.
But we will not meet at a regular basis.
We meet on Tuesdays 3:30-4:25pm in room B211.
|Feb. 25 (Tue)||Yongqiang Liu||Monodromy Decomposition I|
|Mar. 4 (Tue)||Yongqiang Liu||Monodromy Decomposition II|
|Mar. 25 (Tue)||KaiHo Wong||Conjecture of lower bounds of Alexander polynomial|
|Apr. 8 (Tue)||Yongqiang Liu||Nearby Cycles and Alexander Modules|
We are learning Hodge Theory this semester and will be following three books:
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II
2. Peters, Steenbrink, Mixed Hodge Structures
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.
|Sep. 18 (Wed)||KaiHo Wong||Discussions on book material|
|Sep. 25 (Wed)||Yongqiang Liu||Milnor Fibration at infinity of polynomial map|
|Oct. 9 (Wed)||KaiHo Wong||Discussions on book material|
|Oct. 16 (Wed)||Yongqiang Liu||Polynomial singularities|
|Nov. 13 (Wed)||KaiHo Wong||Discussions on book material|
|Feb. 6 (Wed)||Jeff Poskin||Toric Varieties III|
|Feb.13 (Wed)||Yongqiang Liu||Intersection Alexander Module|
|Feb.20 (Wed)||Yun Su (Suky)||How do singularities change shape and view of objects?|
|Feb.27 (Wed)||KaiHo Wong||Fundamental groups of plane curves complements|
|Mar.20 (Wed)||Jörg Schürmann (University of Münster, Germany)||Characteristic classes of singular toric varieties|
|Apr. 3 (Wed)||KaiHo Wong||Fundamental groups of plane curves complements II|
|Apr.10 (Wed)||Yongqiang Liu||Milnor fiber of local function germ|
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)||KaiHo Wong||Formula of Alexander polynomials of plane curves|
Wed, 2/27: Tommy
Fundamental groups of plane curves complements
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed.
|Sept. 18 (Tue)||KaiHo Wong||Organization and Milnor fibration and Milnor Fiber|
|Sept. 25 (Tue)||KaiHo Wong||Algebraic links and exotic spheres|
|Oct. 4 (Thu)||Yun Su (Suky)||Alexander polynomial of complex algebraic curve (Note the different day but same time and location)|
|Oct. 11 (Thu)||Yongqiang Liu||Sheaves and Hypercohomology|
|Oct. 18 (Thu)||Jeff Poskin||Toric Varieties II|
|Nov. 1 (Thu)||Yongqiang Liu||Mixed Hodge Structure|
|Nov. 15 (Thu)||KaiHo Wong||Euler characteristics of hypersurfaces with isolated singularities|
|Nov. 29 (Thu)||Markus Banagl, University of Heidelberg||High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres|
Thu, 10/4: Suky
Alexander polynomial of complex algebraic curve
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. From the definition, it is clear that Alexander polynomial is an topological invariant for curves. I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. Calculations of some examples will be provided.