# Manchester Algebra Seminar - Alex Levine

Dates: | 8 November 2022 |
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Times: | 13:00 - 14:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, Current University students |

Speaker: Alex Levine

Title: Languages, group equations, and quadratic equations in integers

Abstract: In 2015, Duchin, Liang and Shapiro proved that there is an algorithm that takes as input an equation in the Heisenberg group, and outputs whether or not it admits a solution. They proved this by showing that such an equation can be expressed as a quadratic equation in the ring of integers. They then used a theorem of Siegel, which states that it is decidable whether single quadratic equations in integers admit a solution, thus completing their proof. We investigate language properties of the set of solutions to equations in one variable in the Heisenberg group, and how this relates to the language properties of two-variable quadratic equations in the ring of integers. Place: Frank Adams (this term the seminar will not be streamed online)

Tea and biscuits 12:45 in the foyer