**Mathematical Sciences Jamboree**

The Mathematical Sciences Jamboree gives an opportunity for PhD students in our department whose primary research area is in pure or applied mathematics or statistics to tell us about their research. Each talk will be half an hour in length.

The first jamboree will take place at **2 June from ****14:15-16:30** in **Room 745.**

The speakers, titles and abstracts are:

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**Speaker: ** Emilio Pierro

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**Title:** The Generation Game

**Abstract:** Various problems in finite group theory involve the determination of finding a generating structure for a group, G, subject to certain conditions. We discuss a few cases of interest from which these conditions arise, and various techniques for finding such generating triples, focussing on the case of the finite simple groups of Lie type.

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**Speaker:** Angela Aguele

**Title: **Thin Plate Spline Interpolation on the Unit Interval.

**Abstract: **It is known that the unique thin plate spline interpolant to a function f ∈ C^{3}(R) sampled at the scaled integers hZ converges at an optimal rate of h^{3} . In this paper we present results from a recent numerical investigation of the case where the function is sampled at equally spaced points on the unit interval. In this setting the known theoretical error bounds predict a drop in the convergence rate from h^{3} to h. However, numerical experiments show that the usual rate of convergence is h^{3/2} and that the deterioration occurs near the end points of the interval. We show that there exists functions which enjoy an even faster order of convergence of h^{5/2}.

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**Speaker: **Amal Sbeiti Clarke

**Title: **Commuting Involution Graphs for Affine Weyl Groups

**Abstract: **In this talk, I will give a brief description of Coxeter groups, the commuting graphs of involution conjugacy classes in the affine Weyl groups, and verify that the diameter of all such connected graphs is at most (n + 2).

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**Speaker: **Chimere Stanley Anabanti

**Title: ** On locally maximal sum-free sets in finite groups

**Abstract: **We begin with an introduction to sum-free sets in three folds: first is a brief discussion of result of Schur (1917), then maximal sum-free sets “MSFS for short” from the approach of Erdos (1965), Diananda and Yap (1969) up to Green and Ruzsa (2005), and finally, locally maximal sum-free sets “LMSFS” from the approach of Street and Whitehead (1974) up to Giudici and Hart (2009). In this talk, we determine all finite groups containing a LMSFS of size 3. Furthermore, we classify small LMSFS in 2-groups of coclass 1. Then conclude with a counter example to the 1974 conjecture of Street and Whitehead on filled dihedrals.