*Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam.*

Friday, March 16 , 2018

2:30 p.m.

Fields Institute – 210

PhD Candidate: Fulgencio Lopez

Supervisor: Stevo Todorcevic

Thesis title: Construction schemes and their applications

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We study *capturing construction schemes*, a new combinatorial tool introduced by Todorcevíc to build uncountable structures. It consists of a ranked family of finite sets that provides a framework to do recursive constructions of uncountable objects by working with finite amal-gamations of finite isomorphic substructures, the uncountable substructures of the final object can be further study using capturing.

*m*-Knaster Hierarchy. We also show how capturing construction schemes can be used in constructing Suslin trees and Haus-dorff gaps of a special kind in an intuitive manner. And give some applications to the theory of nonseparable Banach spaces.

A copy of the thesis: Thesis Fulgencio Lopez

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