## 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.

## 3/28 – Ben Orlin: Numbers We Cannot Name

Check out the abstract below.

NUMBERS WE CANNOT NAME

The number line seems simple. It ain’t. The riddles of the continuum have bugged Chinese philosophers, Argentine poets, Greek trolls, and 20+ centuries of mathematicians. We’ll explore the puzzles of the irrational, the transcendental, and the non-computable. Bad drawings copiously featured.

## 3/21- Shelby Cox: Counting Curves in the Plane

We are very happy to restart the math club with the talk given by Shelby Cox, our own undergraduate student, after the spring break. Please see the abstract below.

Counting Curves in the Plane

Curve counting goes all the way back to Euclid, who asked how many lines pass through 2 given points in the plane. More generally, we can ask how many curves of degree d pass through 3d-1 points. In this talk, I will present a beautiful and well-known proof for the case when d=3, which uses methods from Topology, Geometry, and Algebraic Geometry. The talk will focus on introducing concepts like the Euler characteristic, projective space, and blow-ups, which can help us answer long-standing questions, like: how many pentagons are on a soccer ball? In particular, the talk should be accessible to most math majors.

## 3/07- GaYee Park: Seven Bridges of Königsberg

Here is the rescheduled GaYee’s  math club talk tomorrow about “Seven Bridges of Königsberg”. See her abstract below.

Long ago in a little town on a river in Prussia, the people wondered: can you visit every part of the city, crossing all seven bridges only once? This is called the Seven Bridges of Königsberg problem which was popular in the 18th century. In this talk I will introduce basic graph theory and Euler’s solution to this problem. Using the result, we will also explore other related puzzles and its application.

## 2/28 – Floyd Williams: If tractroids were black hole vacua, we would all be dead

The math club offers a pleasant place to take a break in busy exam weeks. Floyd Williams gives a talk for us. For the abstract, see below:

A tractroid ( or pseudosphere ) is a surface generated by revolving a special curve ( a tractrix ) about an axis. By a clever change of variables one can find a nice realization of this surface as a certain “vaccum space”, which mathematicians call an orbifold -the latter being defined by a simple relation between points. This vaccum space is similar in nature to a 2-dimensional black hole with mass degenerating to zero. Thankfully however these objects are “not” the same (otherwise there’s no life on earth ), and thankfully no knowledge of black holes is needed for the talk-which mainly involves calculus.