Solving semidecidable problems in group theory

Abstract: Group theory is littered with undecidable problems. A classic example is the word problem: there are groups for which there exists no algorithm that can decide if a product of generators represents the trivial element or not. Many problems (the word problem included) are at least semidecidable, meaning that there is a correct algorithm guaranteed to terminate if the answer is "yes", but with no guarantee on how long one has to wait. I will discuss strategies to try and tackle various semidecidable problems computationally with the key example being the discovery of a counterexample to the Kaplansky unit conjecture.

Biography: Giles Gardam is a research associate at the University of Münster working in geometric group theory. He studied mathematics and computer science at the University of Sydney, receiving his Bachelor's degree in 2012, and completed his doctorate at Oxford in 2017. He was then a postdoc at the Technion before starting at Münster in 2019.

commutative algebraalgebraic geometryanalysis of PDEsalgebraic topologydifferential geometrygeneral topologygeometric topologymetric geometryoperator algebrasquantum algebrarings and algebrassymplectic geometry

Audience: researchers in the topic

( slides | video )

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Algebra Seminar (presented by SMRI)

Series comments: Algebra Seminar:

'Homological comparison of resolution and smoothing'

Will Donovan (Tsinghua University)

Friday Sep 23, 12:00-1:00PM

Online via Zoom

Register here: uni-sydney.zoom.us/meeting/register/tZEpd-isqD0iGdLoqtmNEEQKxmg0xlakSdCq

Abstract: A singular space often comes equipped with (1) a resolution, given by a morphism from a smooth space, and (2) a smoothing, namely a deformation with smooth generic fibre. I will discuss work in progress on how these may be related homologically, starting with the threefold ordinary double point as a key example.

Biography: Will Donovan is currently an Associate professor at Yau MSC, Tsinghua University, Beijing. He is also a member of the adjunct faculty at BIMSA, Yanqi Lake, Huairou, Beijing and a visiting associate scientist at Kavli IPMU, University of Tokyo. He received his PhD in Mathematics in 2011 from Imperial College London. His interests are algebraic geometry, noncommutative geometry, representation theory, string theory and symplectic geometry.

www.maths.usyd.edu.au/u/AlgebraSeminar/

Note: These seminars will be recorded, including participant questions (participants only when asking questions), and uploaded to the SMRI YouTube Channel www.youtube.com/c/SydneyMathematicalResearchInstituteSMRI

Other upcoming SMRI events can be found here: mathematical-research-institute.sydney.edu.au/news-events/

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