--- date: 2022-03-24 23:50 modification date: Thursday 24th March 2022 23:50:53 title: Contact project aliases: [Contact project] --- Last modified date: <%+ tp.file.last_modified_date() %> --- - Tags - #projects/my-talks - Refs: - - - - Links: - [Reading notes - Singular Points on Complex Hypersurfaces](Reading%20notes%20-%20Singular%20Points%20on%20Complex%20Hypersurfaces.md) - [Milnor fiber](Milnor%20fiber) - [nearby cycles](nearby%20cycles) - [vanishing cycles](vanishing%20cycles.md) - [Contact Project Draft 2](Contact%20Project%20Draft%202.md) --- # Contact project Topic: the Milnor fibration. See *Singular Points on Complex Hypersurfaces*. Sasha: covering 6 and 7: isolated singularities, Milnor numbers. Skip 1 and 2. State curve selection lemma. Focus on setting up topologically locally trivial fibration. Vanishing cycles: ![](attachments/Pasted%20image%2020220324235106.png) ![](attachments/Pasted%20image%2020220324235131.png) # In formal geometry ![](attachments/Pasted%20image%2020220325101019.png) # Motivations ![](attachments/Pasted%20image%2020220410190108.png) ![](attachments/Pasted%20image%2020220410190135.png) ![](attachments/Pasted%20image%2020220410190502.png) ![](attachments/Pasted%20image%2020220410205453.png) # Summary ![](attachments/Pasted%20image%2020220410200559.png) ![](attachments/Pasted%20image%2020220410200617.png) ![](attachments/Pasted%20image%2020220410190221.png) ![](attachments/Pasted%20image%2020220410190232.png) ![](attachments/Pasted%20image%2020220410190314.png) ![](attachments/Pasted%20image%2020220410190337.png) ![](attachments/Pasted%20image%2020220410190351.png) ![](attachments/Pasted%20image%2020220410190430.png) ![](attachments/Pasted%20image%2020220410190520.png) ![](attachments/Pasted%20image%2020220410190854.png) See [plumbing](plumbing.md). Fillings: ![](attachments/Pasted%20image%2020220410191352.png) ![](attachments/Pasted%20image%2020220410191814.png) ![](attachments/Pasted%20image%2020220410191827.png) ![](attachments/Pasted%20image%2020220410200709.png) ![](attachments/Pasted%20image%2020220410200835.png) # Intro info ![](attachments/Pasted%20image%2020220410210251.png) ![](attachments/Pasted%20image%2020220410210325.png) ![](attachments/Pasted%20image%2020220410210357.png) ![](attachments/Pasted%20image%2020220410210456.png) ![](attachments/Pasted%20image%2020220410210538.png) ![](attachments/Pasted%20image%2020220410210643.png) ## Topological degree ![](attachments/Pasted%20image%2020220410210949.png) ![](attachments/Pasted%20image%2020220410211013.png) ![](attachments/Pasted%20image%2020220410211527.png) ![](attachments/Pasted%20image%2020220410211700.png) ![](attachments/Pasted%20image%2020220410211720.png) ![](attachments/Pasted%20image%2020220410212155.png) ![](attachments/Pasted%20image%2020220410220122.png) ![](attachments/Pasted%20image%2020220410220142.png) ![](attachments/Pasted%20image%2020220410220231.png) ![](attachments/Pasted%20image%2020220410220306.png) What are [ADE singularities](Unsorted/ADE%20singularities.md) and [du Val singularities](du%20Val%20singularities)? # Example using motivic homotopy Example using [motivic homotopy](Unsorted/motivic%20homotopy.md): ![](attachments/Pasted%20image%2020220410220922.png) ![](attachments/Pasted%20image%2020220410220854.png) ![](attachments/Pasted%20image%2020220410221210.png) # Paper notes ![](attachments/Pasted%20image%2020220410163241.png) ![](attachments/Pasted%20image%2020220410163258.png) ![](attachments/Pasted%20image%2020220410163538.png) ![](attachments/Pasted%20image%2020220410163509.png) ## Milnor class ![](attachments/Pasted%20image%2020220410165029.png) ![](attachments/Pasted%20image%2020220410165154.png) ![](attachments/Pasted%20image%2020220410165208.png) ![](attachments/Pasted%20image%2020220410165355.png) ![](attachments/Pasted%20image%2020220410165452.png) ![](attachments/Pasted%20image%2020220410165922.png) ![](attachments/Pasted%20image%2020220410165941.png) ![](attachments/Pasted%20image%2020220410170555.png) ![](attachments/Pasted%20image%2020220410170715.png) ![](attachments/Pasted%20image%2020220410170801.png) ![](attachments/Pasted%20image%2020220410170833.png) # Chern-Schwartz-MacPherson class Relation to Schubert calculus ![](attachments/Pasted%20image%2020220410181954.png) ![](attachments/Pasted%20image%2020220410181919.png) ![](attachments/Pasted%20image%2020220410181912.png) ![](attachments/Pasted%20image%2020220410171334.png) ![](attachments/Pasted%20image%2020220410171343.png) # Singularities Example singular subscheme ![](attachments/Pasted%20image%2020220410171731.png) ![](attachments/Pasted%20image%2020220410172211.png) ![](attachments/Pasted%20image%2020220410172708.png) # Main theorem ![](attachments/Pasted%20image%2020220410192724.png) ![](attachments/Pasted%20image%2020220410192733.png) ## Picard-Lefschetz theory ![](attachments/Pasted%20image%2020220410193004.png) ![](attachments/Pasted%20image%2020220410193436.png) ![](attachments/Pasted%20image%2020220410193606.png) ![](attachments/Pasted%20image%2020220410194703.png) # Orbifolds ![](attachments/Pasted%20image%2020220410193256.png) # Exotic spheres ![](attachments/Pasted%20image%2020220410200443.png) ![](attachments/Pasted%20image%2020220410200622.png) ![](attachments/Pasted%20image%2020220410200646.png) ![](attachments/Pasted%20image%2020220410200950.png) ![](attachments/Pasted%20image%2020220410201003.png) ![](attachments/Pasted%20image%2020220410203707.png) ![](attachments/Pasted%20image%2020220410203731.png) ![](attachments/Pasted%20image%2020220410203911.png) ![](attachments/Pasted%20image%2020220410204013.png) ![](attachments/Pasted%20image%2020220410204034.png) ![](attachments/Pasted%20image%2020220410204115.png) # Link ![](attachments/Pasted%20image%2020220410204228.png) ![](attachments/Pasted%20image%2020220410204307.png) ![](attachments/Pasted%20image%2020220410204323.png) ![](attachments/Pasted%20image%2020220410204344.png) ![](attachments/Pasted%20image%2020220410204553.png) ![](attachments/Pasted%20image%2020220410204603.png) # Vanishing cycles ![](attachments/Pasted%20image%2020220410204748.png) ![](attachments/Pasted%20image%2020220410204803.png # ? ![](attachments/Pasted%20image%2020220410224653.png) ![](attachments/Pasted%20image%2020220410224732.png) ![](attachments/Pasted%20image%2020220410224816.png) ![](attachments/Pasted%20image%2020220410224842.png) ![](attachments/Pasted%20image%2020220410225423.png) ![](attachments/Pasted%20image%2020220410225439.png) # Hodge structures ![](attachments/Pasted%20image%2020220410230349.png) ![](attachments/Pasted%20image%2020220410230358.png) ![](attachments/Pasted%20image%2020220410230418.png) ![](attachments/Pasted%20image%2020220410230438.png) $\E_8$ as a Milnor lattice: ![](attachments/Pasted%20image%2020220411140636.png) Resulting [open book decomposition](Unsorted/open%20book%20decomposition.md): ![](attachments/Pasted%20image%2020220411141512.png) ![](attachments/Pasted%20image%2020220411141631.png) ![](attachments/Pasted%20image%2020220411141846.png) ![](attachments/Pasted%20image%2020220411141901.png) # Fillability ![](attachments/Pasted%20image%2020220411141942.png) ![](attachments/Pasted%20image%2020220411142002.png) ![](attachments/Pasted%20image%2020220411142023.png) ![](attachments/Pasted%20image%2020220411142101.png)