## 4/25 – Andrew Havens: Games with Topological Secrets

To close our Math Club meeting this semester, Andrew will bring mathematical games simply played using just pencils and papers.

Be noticed that we will start at 5:30 pm, later than usual, to avoid interfering with the talk given by people from Newgrange, who are recruiting math majored BS students.

Here is the abstract of Andrew:

Games with Topological Secrets

We will learn to play a pair of pencil and paper 2 player games, originally devised in the 1960’s by John Horton Conway and Michael Stewart Paterson when they were graduate students at Cambridge. The games will be a proxy for learning a little combinatorial game theory and topology. Participation is encouraged, as we will first play the games to uncover some their secrets before discussing some of their interesting mathematical properties and the corresponding strategies. This meeting will be accessible to students of any level, and presumes no formal familiarity with either topology or game theory.

## 4/18 – Jennifer Li: Convex Reflexive Lattice Polygons and the Number 12

After the Annie’s talk last week (see below for the abstract!), we will enjoy some more combinatorics.

Jennifer will give a talk about “Convex Reflexive Lattice Polygons and the Number 12”, revealing how a simple equality can be connected to a deep result from another side of mathematics, which is called algebraic geometry. Here is her abstract:

A lattice polygon is a polygon with integral vertices in R^2. This means that its vertices are of the form (a, b), where a and b are integers. A reflexive lattice polygon has the property that the origin (0,0) is the unique integral interior point of the polygon. These polygons have duals, which are also reflexive lattice polygons. Today I will present a curious relation between convex reflexive lattice polygons, their duals, and the number 12. I will explain how this relation has deep connections with toric varieties, forming a bridge between two beautiful areas in mathematics: combinatorics and algebraic geometry.

## 4/11 – Annie Raymond: An introduction to sums of squares and Turán’s Problem

Abstract:

What is the maximum number of edges in a graph on n vertices without triangles? Mantel’s answer in 1907 that at most half of the edges can be present started a new field: extremal combinatorics. More generally, what is the maximum number of edges in a n-vertex graph that does not contain any subgraph isomorphic to H? What about if you consider hypergraphs instead of graphs? I will introduce the technique of sums of squares and discuss how it can be used to attack such problems.

## Change Ringing in Amherst

We had a very fun time last week to playing handbells and figuring out mathematical patterns in it. Here, answering some questions about change ringing activities, I share the informations from Leland Kusmer:

Handbells (at UMass):
Tuesdays, 4 – 6pm, ILC N417
Towerbells (at Smith):
Mondays, 7 – 9pm; Wednesdays, 5 – 7pm

## 4/04 – William Schober: Group Theory in Change Ringing

If you would like to enjoy some bells ringing and see mathematical backgrounds of it,  join us in the math club this week. William from the Physic Department will give a talk about “Group Theory in Change Ringing”. His abstract is below:

Group Theory in Change Ringing

Change Ringing is a musical/mathematical team sport which consists of ringing a set of tuned bells in a controlled manner to produce variations in the order of the bells. These sets of permutations, when seen through the lens of abstract algebra, form mathematical Groups. We will construct the basic ringing groups, examine their structure and properties, and demonstrate how they are rung using hand bells.