- SYMMETRY IN NEWCASTLE
- Location: Room US321, (Callaghan Campus) The University of Newcastle
- Dates: Fri, 4th Mar 2022 - Fri, 4th Mar 2022
- Speaker: Dr Michal Ferov, CARMA, The University of Newcastle
- Title: Automorphism groups of Cayley graphs of Coxeter groups: when are they discrete?
- Abstract for Automorphism groups of Cayley graphs of Coxeter groups: when are they discrete?:
Group of automorphisms of a connected locally finite graph is naturally a totally disconnected locally compact topological group, when equipped with the permutation topology. It therefore makes sense to ask for which graphs is the topology not discrete. We show that in case of Cayley graphs of Coxeter groups, one can fully characterise the discrete ones in terms of the symmetries of the corresponding Coxeter system. Joint work with Federico Berlai.
- Speaker: Dr Jeroen Schillewaert, Department of Mathematics, The University of Auckland
- Title: The geometries of the Freudenthal-Tits magic square
- Abstract for The geometries of the Freudenthal-Tits magic square:
I will give an overview of a programme investigating projective embeddings of (exceptional) geometries which Hendrik Van Maldeghem and I started in 2010.
- Speaker: A/Prof James Parkinson, The University of Sydney
- Title: Automorphisms and opposition in spherical buildings
- Abstract for Automorphisms and opposition in spherical buildings:
The geometry of elements fixed by an automorphism of a spherical building is a rich and well-studied object, intimately connected to the theory of Galois descent in buildings. In recent years, a complementary theory has emerged investigating the geometry of elements mapped onto opposite elements by a given automorphism. In this talk we will give an overview of this theory. This work is joint primarily with Hendrik Van Maldeghem (along with others).
- Abstract for Automorphism groups of Cayley graphs of Coxeter groups: when are they discrete?:
Group of automorphisms of a connected locally finite graph is naturally a totally disconnected locally compact topological group, when equipped with the permutation topology. It therefore makes sense to ask for which graphs is the topology not discrete. We show that in case of Cayley graphs of Coxeter groups, one can fully characterise the discrete ones in terms of the symmetries of the corresponding Coxeter system. Joint work with Federico Berlai.
- Abstract for The geometries of the Freudenthal-Tits magic square:
I will give an overview of a programme investigating projective embeddings of (exceptional) geometries which Hendrik Van Maldeghem and I started in 2010.
- Abstract for Automorphisms and opposition in spherical buildings:
The geometry of elements fixed by an automorphism of a spherical building is a rich and well-studied object, intimately connected to the theory of Galois descent in buildings. In recent years, a complementary theory has emerged investigating the geometry of elements mapped onto opposite elements by a given automorphism. In this talk we will give an overview of this theory. This work is joint primarily with Hendrik Van Maldeghem (along with others).
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- ZERO-DIMENSIONAL SYMMETRY SEMINAR
- Speaker: Dr Michal Ferov, CARMA, The University of Newcastle
- Title: Separating cyclic subgroups in graph products of groups
- Location: Room MC102, McMullin (Callaghan Campus) The University of Newcastle
- Dates: Mon, 13th Aug 2018 - Mon, 13th Aug 2018
- Abstract:
(joint work with Federico Berlai) A natural way to study infinite groups is via looking at their finite quotients. A subset S of a group G is then said to be (finitely) separable in G if we can recognise it in some finite quotient of G, meaning that for every g outside of S there is a finite quotient of G such that the image of g under the canonical projection does not belong to the image of S. We can then describe classes of groups by specifying which types of subsets do we require to be separable: residually finite groups have separable singletons, conjugacy separable groups have separable conjugacy classes of elements, cyclic subgroup separable groups have separable cyclic subgroups and so on... We could also restrict our attention only to some class of quotients, such as finite p-groups, solvable, alternating... Properties of this type are called separability properties. In case when the class of admissible quotients has reasonable closure properties we can use topological methods.
We prove that the property of being cyclic subgroup separable, that is having all cyclic subgroups closed in the profinite topology, is preserved under forming graph products.
Furthermore, we develop the tools to study the analogous question in the pro-p case. For a wide class of groups we show that the relevant cyclic subgroups - which are called p-isolated - are closed in the pro-p topology of the graph product. In particular, we show that every p-isolated cyclic subgroup of a right-angled Artin group is closed in the pro-p topology and, consequently, we show that maximal cyclic subgroups of a right-angled Artin group are p-separable for every p.
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- CARMA COLLOQUIUM
- Speaker: Dr Michal Ferov, CARMA, The University of Newcastle
- Title: Groups, machines, algae and trees
- Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 4:00 pm, Tue, 4th Apr 2017
- Abstract:
In a way, mathematics can be seen as a language game, where we use symbols, together with some rewriting rules, to represent objects we are interested in and then ask what can be said about the sequences of symbols (languages) that capture certain phenomena. For example, given a group G with generators a and b, can we recognise (using a computer) the sequences of generators that correspond to non-trivial elements of G? If yes, how strong computer do we need, i.e. how complicated is the language we are studying?
There is a natural duality between various types of computational models and classes of languages that can be recognised by them. Until recently most problems/languages in group theory were classified within the Chomsky hierarchy, but there are more computational models to consider. In the talk I will briefly introduce L-systems, a family of classes of languages originally developed to model growth of algae, and show that the co-word problem in Grigorchuk's group, a group of particularly nice transformations of infinite binary tree, can be seen as a language corresponding to a fairly simple L-system.
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- CARMA GROUP THEORY RHD MEETING
- Speaker: Dr Michal Ferov, CARMA, The University of Newcastle
- Title: Galois theory
- Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 11:00 am, Thu, 23rd Feb 2017
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- CARMA GROUP THEORY RHD MEETING
- Speaker: Dr Michal Ferov, CARMA, The University of Newcastle
- Title: Galois theory for infinite algebraic extensions
- Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 11:00 am, Fri, 17th Feb 2017
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- CARMA GROUP THEORY RHD MEETING
- Speaker: Dr Michal Ferov, CARMA, The University of Newcastle
- Title: Separating cyclic subgroups in graph products
- Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 11:00 am, Thu, 17th Nov 2016
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- CSSE SEMINAR
- Speaker: Dr Michal Ferov, CARMA, The University of Newcastle
- Title: Enhancing LambdaMART Using Oblivious Trees
- Location: Room EF122, Engineering Building EF (Callaghan Campus) The University of Newcastle
- Time and Date: 2:00 pm, Fri, 28th Oct 2016
- Note change of date.
- Abstract:
Learning to rank is a machine learning technique broadly used in many areas such as document retrieval, collaborative filtering or question answering. We present experimental results which suggest that the performance of the current state-of-the-art learning to rank algorithm LambdaMART, when used for document retrieval for search engines, can be improved if standard regression trees are replaced by oblivious trees. This paper provides a comparison of both variants and our results demonstrate that the use of oblivious trees can improve the performance by more than 2:2%. Additional experimental analysis of the inuence of a number of features and of a size of the training set is also provided and confirms the desirability of properties of oblivious decision trees.
About the Speaker: Dr Michal Ferov is a Postdoctoral Research Fellow in the School of Mathematical and Physical Sciences,Faculty of Science and Information Technology.
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- CARMA GROUP THEORY RHD MEETING
- Speaker: Dr Michal Ferov, CARMA, The University of Newcastle
- Title: Separability properties and graph products of groups
- Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 11:00 am, Thu, 20th Oct 2016
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