## Michaelmas Term

**PhD Talks: Poset Saturation Problems & Algebraic Geometry** by *Maria Ivan and Patrick Kennedy-Hunt*

*Tuesday, 24th November, 18:00*

The final Adams Society Talk of the term is happening on Tuesday! We’ll have the chance to hear from two of our very own PhD Students: Maria Ivan and Patrick Kennedy-Hunt. They’ll both be giving short talks on their research areas, Poset Saturation Problems and Algebraic Geometry respectively, aimed at an undergraduate audience.

It promises to be a great chance to hear from mathematicians who were in your shoes not very long ago!

Title: “Poset Saturation Problems” – Maria Ivan

Abstract: “A poset is short for a partially ordered set. The most common example of a poset is the power set of [n] with the partial relation given by inclusion. Given a fixed poset P we say that a family F of subsets of [n] is P-free if there is no induced copy of P formed by elements of F. We further say that F is P-saturated if it is P-free and, for any other set X subset of [n], the family F\cup \{X\} contains an induced copy of P. The size of the smallest P-saturated family is called the induced saturation number of P, denoted by sat^*(n,P).The natural question is can we determine the saturation number for simple posets, or at least their order of magnitude? The posets that have been actively researched are the antichain, the diamond (one maximal element, one minimal element and two incomparable elements), and the butterfly (two maximal and two minimal elements). Until recently, the questions for all these three posets were open, despite substantial improvements. In 2020 the butterfly question was completely solved by two independent papers, the first of which I am the author of and proves the lower bound of n+1, with the second providing an example of size about 6n. These two papers combined give that the saturation number for the butterfly is of order n.In this talk I will introduce the audience to the field of poset saturation and focus on the butterfly poset, especially on the key ideas of my proof for the lower bound. There will be lots of diagrams which will hopefully make all the steps natural and easy to follow. I am looking forward to seeing you all there.

Title: “Algebraic Geometry” – Patrick Kennedy-Hunt

Abstract: Algebraic Geometry is an important area of modern pure maths in which we study the zero sets of polynomial equations. In this talk I will describe a visual construction in the relatively new tropical algebraic geometry. These `tropical curves’ are easier to think about than polynomials but remember lots of key information. We will use our construction and a result of Milkhalkin to sketch an unusual take on (which will not quite amount to a proof) Bezout’s theorem. Bezout’s theorem is one of the most famous results in algebraic geometry: it says two polynomials of degree d and e share d\times e common zeroes in projective space.

**Algebra and Geometry in the Tropics**,** **by *Dr Dhruv Ranganathan*

*Tuesday, 10th November, 18:00*

We are pleased to announce our second talk of the term, this time by Dr Dhruv Ranganathan. The title is “Algebra and Geometry in the Tropics”, abstract below:*There is a remarkable collection of ideas, with roots in high energy theoretical physics, that links the world of manifolds, polynomials, and string theory to the world of polygons, combinatorics, and graph theory. The bridge is ultimately based on the notion of an absolute value. While all of us understand the concept of absolute values of numbers, the ideas of tropical geometry give us an absolute value of geometry itself. We’ll explore what on earth this might mean, and stare at a large number of poorly drawn pictures to understand what makes this odd sounding concept a powerful new tool in modern mathematics.*

As before, we will hold the talk on zoom on **Tuesday, 10th November **at **6pm**. The link to the meeting will be sent in a reminder email and posted in the facebook event which you can find here.

**On Conway’s Numbers and Games**,** **by *Dr Jessica Fintzen*

*Tuesday, 27th October, 18:00*

Our first talk of the term will be by Dr Jessica Fintzen and hosted on zoom. If you would like to attend, please sign up for the facebook event here and we will send you further details closer to the date.

**Fresher’s Squash,** by *the Adams Society *

*Tuesday, 13th October 2020, 16:00-17:30*

Join as at **Gazebo 3** (in Merton Court next to Cripps) for an opportunity for the new members to meet and greet the other mathmos in college.

As you’re all probably very bored of by now, there are various of restrictions which we need to abide by, so please through the following guidelines and stick to them:

- 1m distancing at all times
- Wear a mask
- Do not attend if you have symptoms of COVID-19

## Easter Term

**Quiz night**, by *the Adams Society*

*Monday, 4th May 2020, 7pm*

A mathematical themed quiz on zoom. A chance to chat with your fellow mathematical friends at St John’s from home.

### About Us

The Adams Society is the mathematics society of St John’s college, Cambridge. We host numerous events each year including mathematical talks and socials.

### Talks

Free admission to all talks. Refreshments are served in the foyer before each talk.

Our talks usually take place in the Fisher Building, St John’s College.

### Contact

Get in touch through our committee members or email theadamssociety@gmail.com