# Pure Maths Colloquium: Dimitra Kosta

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

Where: | Lecture Theatre C |

When: | Feb 27 2020 @ 16.00 |

Video: | Not recorded |

Speaker: | Dimitra Kosta University of Glasgow |

Title: | Unboundedness of Markov complexity of monomial curves in A^n for n ≥ 4 |

Computing the complexity of Markov bases is an extremely challenging problem; no formula is known in general and there are very few classes of toric ideals for which the Markov complexity has been computed. A monomial curve \(C\) in \(\mathbb{A}^3\) has Markov complexity \(m(C)\) two or three. Two if the monomial curve is complete intersection and three otherwise. Our main result shows that there is no \(d\in \mathbb{N}\) such that \(m(C) \leq d\) for all monomial curves \(C\) in \(\mathbb{A}^4\). The same result is true even if we restrict to complete intersections. We extend this result to all monomial curves in \(\mathbb{A}^n, n \geq 4\).