Columbia Undergraduate Math Society

Spring 2022 <<  Summer 2022 Learning Seminar >> Fall 2022

Day and Time: Sundays, 2pm ; on Zoom
Topic: Graph Theory and Combinatorics
Reference: Harris, Hirst, and Mossinghoff, Combinatorics and Graph Theory

Contact UMS (Email Zachary Lihn)
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Date Speaker Title Abstract
June 5
Zachary Lihn
Introduction
We will first introduce Summer UMS and then decide on the logistics for the next weeks. We will go over some potential textbooks we could cover and then pick one by vote. Every member will then have the opportunity to sign up to give a talk.
June 12
Zachary Lihn
The Ubiquity of Graphs
This summer, we will be studying graph theory and combinatorics: the study of discrete structures and counting. We will begin with an overview of graph theory, combinatorics, and the infinite analogues of these. We will then begin the study of graphs with basic definitions and examples, including the notions of a path, degree of a vertex, connectivity, complex and bipartite graphs, and more. Throughout the talk, I will also mention interesting applications to mathematics such as graph-theoretic proofs of the Cantor-Schroder-Bernstein theorem and Fermat's Little Theorem.
June 19
Ekene Ezeunala
Distance and Related Notions in Graphs
In this talk, we will begin by recalling the introductory notions of graph theory, briefly discussing connected graphs, graph isomorphisms, and metrics (as related to graph theory). We will then continue by defining the relevant terminology in the study of distances in graphs, invoking relevant intuition along the way. We will then delve into a relatively detailed discussion of adjacency matrices, and conclude with a recent (and interesting!) application of graph models using real-world data.
June 26
Iris Liu
Ramsey Numbers and Related Notions and Proofs
In tomorrow’s talk, we will begin by recalling the notions of complete graphs and subgraphs and introducing cliques and edge coloring. We will then use these notions to solve two problems, one of which once appeared in the Putnam Competition and the other is an algebra problem. After that, I will introduce Ramsey numbers and Ramsey’s Theorem. They will then help us prove Schur’s Theorem.
July 3
Jeffrey Xiong
 
 
July 10
Mark Kirichev
 
 
July 17
Noah Bergam
 
 
July 24
Tsigemariam Assegid
 
 
July 31
Boris Ter-Avanesov
 
 
August 7
Aiden Sagerman
 
 
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