Research Group — Zero-Dimensional Symmetry |
Date | Time | Room | Speaker | Title |
---|---|---|---|---|
18.12.2018 | 14.00 | MC LG17 | Max Carter, Peter Groenhout | Summer Projects |
11.12.2018 | 14.00 | MC G29 | Davide Spriano | Convexity and generalization of hyperbolicity |
Almost by definition, the main tool and goal of Geometric Group Theory is to find and exploit correspondences between geometric and algebraic features of groups. Following this philosophy, I will focus on the question: what does it mean for a sub(space/group) to "sit nicely" inside a bigger (space/group)?
Focusing on groups, for a subgroup H of a group G, possible answers for the above question are when the subgroup H is: quasi-isometrically embedded, undistorted, normal/malnormal, finitely generated, geometrically separated...
Many of the above are equivalent when H is a quasiconvex subgroup of a hyperbolic group G, providing very successful correspondences between geometric and algebraic properties of subgroups. The goal of this talk is to review quasiconvexity in hyperbolic spaces and try to generalize several of those features in a broader setting, namely the class of hierarchically hyperbolic groups (HHG). This is a joint work with Hung C. Tran and Jacob Russell. | ||||
04.12.2018 | all week | Adelaide | AustMS Meeting | |
27.11.2018 | 14.00 | MC LG17 | Alejandra Garrido | Hausdorff dimension and normal subgroups of free-like pro-$p$ groups |
Hausdorff dimension has become a standard tool to measure the "size" of fractals in real space. However, it can be defined on any metric space and therefore can be used to measure the "size" of subgroups of, say, pro-$p$ groups (with respect to a chosen metric). This line of investigation was started 20 years ago by Barnea and Shalev, who showed that $p$-adic analytic groups do not have any "fractal" subgroups, and asked whether this characterises them among finitely generated pro-$p$ groups. I will explain what all of this means and report on joint work with Oihana Garaialde and Benjamin Klopsch in which, while trying to solve this problem, we ended up showing an analogue of a theorem of Schreier in the context of pro-$p$ groups of positive rank gradient: any finitely generated infinite normal subgroup of a pro-$p$ group of positive rank gradient is of finite index. I will also explain what "positive rank gradient" means, and why pro-$p$ groups with such a property are "free-like". | ||||
20.11.2018 | 14.00 | MC 110 | Thibaut Dumont | Cocycles on trees and piecewise translation action on locally compact groups |
In the first part of this seminar, I will present some geometric cocycles associated to trees and ways to compute their norms. Similar construction exists for Euclidean buildings but no satisfactory estimates of the norm is currently known. In the second part, I will discuss some ongoing research with Thibaut Pillon on actions the infinite cyclic group by piecewise translations on locally compact group. Piecewise translation actions have been well studied for finitely generated groups, e.g. by Whyte, and provide positive answers to the von-Neumann-Day problem or the Burnside problem. The generalization to LC-groups was introduced by Schneider. The topic seems to have interesting implications for tdlc-groups. | ||||
13.11.2018 | all day | X 602 | EViMS Workshop | |
12.11.2018 | 14.00 | MC G29 | Anne Thomas | Divergence in right-angled Coxeter groups |
The divergence of a pair of geodesics in a metric space measures how fast they spread apart. For example, in Euclidean space all pairs of geodesics diverge linearly, while in hyperbolic space all pairs of geodesics diverge exponentially. In the 1980s Gromov proved that in symmetric spaces of non-compact type, the only possible divergence rates are linear or exponential, and he asked whether the same dichotomy holds in CAT(0) spaces. Soon afterwards, Gersten used these ideas to define a quasi-isometry invariant, also called divergence, which measures the "worst" rate of divergence. Gersten and others have since found many examples of finitely generated groups with quadratic divergence. We study divergence in right-angled Coxeter groups with triangle-free defining graphs. Using the structure of certain flats in the associated Davis complex, which is a CAT(0) square complex, we characterise such groups with linear and quadratic divergence, and construct examples of right-angled Coxeter groups with divergence polynomial of arbitrary degree. This is joint work with Pallavi Dani (Louisiana State University). | ||||
06.11.2018 | all day | U Sydney | Group Actions Seminar held at the University of Sydney | |
30.10.2018 | 14.00 | MC LG17 | Reading Group | |
23.10.2018 | all day | U Sydney | Group Actions Seminar held at the University of Sydney | |
16.10.2018 | 14.00 | MC LG17 | Alejandra Garrido | Maximal subgroups of some groups of intermediate growth |
Given a group one of the most natural things one can study about it is its subgroup lattice, and the maximal subgroups take a prominent role. If the group is infinite, one can ask whether all maximal subgroups have finite index or whether there are some (and how many) of infinite index. After telling some historical developments on this question, I will motivate the study of maximal subgroups of groups of intermediate growth and report on joint work with Dominik Francoeur where we give a complete description of all maximal subgroups of some "siblings" of Grigorchuk's group. | ||||
09.10.2018 | 14.00 | MC LG17 | Dave Robertson | Algebraic theory of self-similar groups |
I will describe the relationship between self-similar groups, permutational bimodules and virtual group endomorphisms. Based on chapter 2 of Nekrashevych’s book. | ||||
02.10.2018 | 14.00 | MC LG17 | Alex Bishop | The Group Co-Word Problem |
In this talk, we will introduce a class of tree automorphism groups known as bounded automata. From this definition, we will see that many of the interesting examples of self-similar groups in the literature are members of this class. A problem in group theory is classifying groups based on the difficulty of solving their co-word problems, that is, classifying them by the computational difficulty to decide if a word is not equivalent to the identity. Some well-known results in this study are that a group has a co-word problem given by a regular language if and only if it is finite, a deterministic context-free language if and only if it is virtually free, and a deterministic one-counter machine if and only if it is virtually cyclic. Each of these language classes corresponds to a natural and well-studied model of computation. We will show that the class of bounded automata groups has a co-word problem given by an ET0L language – a class of formal language which has recently gained popularity in areas of group theory. This strengthens a recent result of Holt and Röver (who showed this result for a less restrictive class of language) and extends a result of Ciobanu-Elder-Ferov (who proved this result for the first Grigorchuk group). | ||||
25.09.2018 | 14.00 | MC LG17 | Timothy Bywaters | Spaces at infinity for hyperbolic totally disconnected locally compact groups |
Every compactly generated t.d.l.c. group acts vertex transitively on a locally finite graph with compact open vertex stabilisers. Such a graph is called a rough Cayley graph and, up to quasi-isometry, is an invariant for the group. This allows us to define Gromov hyperbolic t.d.l.c. groups and their Gromov boundary in a way analogous to the finitely generated case.
The space of directions of a t.d.l.c. group is a metric space 'at infinity' obtained by analysing the action of the group on the set of compact open subgroups. It is particularly useful for detecting flat subgroups, think subgroups that look like $\mathbb{Z}^n$.
In my talk, I will introduce these two concepts of boundary and give some new results which relate them. Time permitting, I may also give details about the proofs. | ||||
10.09.2018 | 14.00 | MC G29 | Colin Reid | Endomorphisms of profinite groups |
Given a profinite group $G$, we can consider the semigroup $\mathrm{End}(G)$ of continuous homomorphisms from $G$ to itself. In general $\lambda \in\mathrm{End}(G)$ can be injective but not surjective, or vice versa: consider for instance the case when $G$ is the group $F_p[[t]$ of formal power series over a finite field, $n$ is an integer, and $\lambda_n$ is the continuous endomorphism that sends $t^k$ to $t^{k+n}$ if $k+n \ge 0$ and $0$ otherwise. However, when $G$ has only finitely many open subgroups of each index (for instance, if $G$ is finitely generated), the structure of endomorphisms is much more restricted: given $\lambda \in\mathrm{End}(G)$, then $G$ can be written as a semidirect product $N \rtimes H$ of closed subgroups, where $\lambda$ acts as an automorphism on $H$ and a contracting endomorphism on $N$. When $\lambda$ is open and injective, the structure of $N$ can be restricted further using results of Glöckner and Willis (including the very recent progress that George told us about a few weeks ago). This puts some restrictions on the profinite groups that can appear as a '$V_+$' group for an automorphism of a t.d.l.c. group. | ||||
03.09.2018 | 14.00 | MC G29 | Stephan Tornier | An introduction to self-similar groups |
We introduce the notion of self-similarity for groups acting on regular rooted trees as well as their description using automata and wreath iteration. Following the definition of Grigorchuk's group we show that it is an infinite, finitely generated $2$-group. The proof illustrates the use of self-similarity. | ||||
27.08.2018 | 14.00 | MC G29 | George Willis | The tree representation theorem and automorphism groups of rooted trees |
(joint work with R. Grigorchuk ad D. Horadam) The tree representation theorem represents a certain group associated with the scale of an automorphism of a t.d.l.c. group as acting by symmetries of a regular (unrooted) tree. It shows that groups acting on regular trees are a fundamental part of the theory of t.d.l.c. groups.
There is also an extensive theory of self-similar and self-replicating groups of symmetries of rooted trees which has developed from the discovery (or creation) of examples such as the Grigorchuk groups. It will be seen in this talk that these two branches of research are studying essentially the same groups. | ||||
20.08.2018 | 14.00 | MC G29 | George Willis | Locally pro-p contraction groups are nilpotent |
A contraction group is a pair $(G,\alpha)$ in which $G$ is a locally compact group and $\alpha$ is an automorphism of $G$ such that $\alpha^n(x)\to 1$ as $n\to\infty$. In joint work with H. Glöckner, it is shown that every contraction group is the direct sum of closed subgroups $$ G = D\oplus T $$ with $D$ divisible, i.e. for every $x\in D$ and $n>0$ there is $y\in D$ with $y^n =x$ and $T$ torsion, i.e. there is $n>0$ such that $x^n = 1$ for every $x\in T$. Furthermore, $D$ is the direct sum $$ D = \bigoplus_{i=1}^k D_{p_i} $$ of $p_i$-adic analytic nilpotent contraction groups for some prime numbers $p_1,\ldots, p_k$. The torsion subgrou $T$ may also be written as a composition series of simple contraction groups. In the case when all the composition factors are of the form $\mathbb{F}_p(\!(t)\!), \alpha$ with $\alpha$ being the automorphism of multiplication by $p$, it follows easily that $G$ is a solvable group. These ideas will be explained in the talk and a sketch will be presented of a proof that $G$ is in fact nilpotent in this case. | ||||
13.08.2018 | 14.00 | MC G29 | Michal Ferov | Separating cyclic subgroups in graph products of groups |
(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. | ||||
06.08.2018 | 14.00 | MC G29 | Stephan Tornier | Totally disconnected, locally compact groups from transcendental field extensions |
(joint work with Timothy Bywaters) Let E over K be field extension. Then the group of automorphisms of E which pointwise fix K is totally disconnected Hausdorff when equipped with the permutation topology. We study examples, aiming to establish criteria for this group to be locally compact, non-discrete and compactly generated. | ||||
30.07.2018 | 14.00 | MC G29 | Ben Brawn | Voltage and derived graphs and their relation to the free product of graphs |
We look at a classical construction known as ordinary voltage graphs and their derived graphs. We show how to construct the free product of graphs as the derived graph of a voltage graph whose base graph is the Cartesian product of the given graphs with a specific voltage assignment. We find that the voltage group is always a free group and give the number of generators needed. | ||||
23.07.2018 | 14.00 | MC G29 | Colin Reid | A lemma for group actions on zero-dimensional spaces |
I present a lemma concerning a group action on a locally compact zero-dimensional spaces, where the group has a 'small' (compact, say) generating set, relating invariant compact sets with orbit closures. A typical example to have in mind is a compactly generated tdlc group acting on itself by conjugation, where we use conditions on closures of conjugacy classes to deduce the existence of compact normal subgroups. The idea of the lemma has appeared several times in the literature but does not appear to have been given explicitly in this form. I will discuss various applications depending on time. | ||||
12.06.2018 | 14.00 | V 206 | Dave Robertson | Topological full groups - Part II |
For an action of a group G on the Cantor set, we can construct a group of transformations of the Cantor set that are constructed 'piecewise' from elements of G. This is called the topological full group of G. Examples include the topological full groups associated to a minimal homeomorphism of the Cantor set considered by Giordano, Putnam and Skau, and Neretin's group of spheromorphisms. I will describe the construction using groupoids, and show how certain examples admit a totally disconnected locally compact topology. This is based on work in progress with Alejandra Garrido and Colin Reid. | ||||
05.06.2018 | 14.00 | V 206 | Dave Robertson | Topological full groups - Part I |
For an action of a group G on the Cantor set, we can construct a group of transformations of the Cantor set that are constructed ' piecewise' from elements of G. This is called the topological full group of G. Examples include the topological full groups associated to a minimal homeomorphism of the Cantor set considered by Giordano, Putnam and Skau, and Neretin's group of spheromorphisms. I will describe the construction using groupoids, and show how certain examples admit a totally disconnected locally compact topology. This is based on work in progress with Alejandra Garrido and Colin Reid. | ||||
29.05.2018 | 14.00 | V 206 | Michal Ferov | Profinite words and inverse limits of finite state automata |
In the case of finitely generated discrete groups, the problem of deciding whether a product of a sequence of generators and their inverses represents the trivial element is known as the word problem. Somewhat surprisingly, the complexity of word problem is tightly connected to the structure and geometry of the group: a classical result of Anisimov states that a group has word problem decidable by finite-state automaton if and only if the group is finite; similarly, result of Muller and Shupp states that a group has word problem is decidable by push-down automaton if and only if the group is virtually-free. In my talk, I will define inverse limits of finite-state automata and discuss how it might be useful for studying totally-disconnected locally-compact groups. | ||||
22.05.2018 | 14.00 | V 206 | Thomas Murray | On automorphism groups of regular rooted groups |
Starting with the automorphism group of a regular, locally finite tree the tree representation theorem leads us to groups acting on a regular, rooted tree. Furthermore these groups satisfy a property called R and are profinite. As a result, the study of these groups may be reduced to those that act on a finite depth regular rooted tree with corresponding finite version of property R. We introduce the idea of studying such groups with geometric objects in order to study trees of higher valency and investigate conjectures made for the binary rooted tree. | ||||
15.05.2018 | 14.00 | LSTH 100 | George Willis | School Seminar — Zero-Dimensional Symmetry |
The pleasure and utility of observing symmetry in nature may be found in the mathematics of symmetry, which is known as group theory. Zero-dimensional symmetry is the symmetry of networks and relationships, such as a family tree. In contrast, physical objects, such as a sphere, have positive-dimensional symmetry. While positive-dimensional symmetry has been well understood for more than a century (and is applied in physics) it is only in the last 25 years that our understanding of zero-dimensional symmetry has begun to catch up. Even though great progress is being made, we still aren’t sure how close we are to having the full picture. | ||||
08.05.2018 | 14.00 | V 206 | Thomas Taylor | Automorphisms of Cayley graphs for right-angled Artin groups |
01.05.2018 | 14.00 | V 126 | George Willis | Project — Zero-Dimesional Symmetry |
The project on 0-dimensional symmetry, that is, totally disconnected locally compact groups, is organised around four themes, namely, ‘Structure theory’, ‘Geometries’, ‘Local structure and commensurators’ and ‘Representations and computation’. These themes relate to the scale function on a t.d.l.c. group as follows. The scale itself is defined directly in terms of commensuration and the tidying procedure enables computation of the scale. Tidy subgroups can also be characterised geometrically, and the scale behaves naturally under structural decompositions of groups. | ||||
24.04.2018 | 14.00 | V 205 | Ben Brawn | On quasi-label-regular trees and their classification |
We introduce almost isomorphisms of locally-finite infinite graphs and in particular trees. We introduce a type of infinite tree, dubbed label-regular, and consider trees that are label-regular except at a finite number of vertices, which we call quasi-label-regular trees. We show how to determine if two quasi-label-regular trees are almost isomorphic or not. We count the number of equivalence classes of quasi-label-regular trees under almost isomorphisms and find this number ranges from finite to infinite. | ||||
17.04.2018 | 14.00 | V 205 | Stephan Tornier | Groups acting on trees with non-trivial quasi-center |
We highlight the role of the quasi-center of a t.d.l.c. group in Burger-Mozes theory and present new results concerning the types of automorphisms that the quasi-center of a non-discrete subgroup of the automorphism group of a regular tree may contain in terms of its local action. A theorem which shows that said result is sharp is also presented. We include a proof of the fact that a non-discrete, locally transitive subgroup of the automorphism group of a regular tree does not contain a quasi-central involution. | ||||
10.04.2018 | 14.00 | V 205 | Stephan Tornier | An introduction to Burger-Mozes theory |
We recall the types of automorphisms of trees and introduce the notion of local action. After an excursion into permutation group theory, specifically the notions of transitivity, semiprimitivity, quasiprimitivity, primitivity and 2-transitivity, we give an introduction to Burger-Mozes theory of closed, non-discrete subgroups of the automorphism group of a (regular) tree which are locally quasiprimitive. | ||||
05.04.2018 | 14.00 | V 205 | Colin Reid | Totally disconnected, locally compact groups |
I give an overview of totally disconnected, locally compact (t.d.l.c.) groups: what they are and in what contexts they arise. In particular, t.d.l.c. groups encompass many classes of automorphism groups of structures, and also occur as completions of groups that have commensurated subgroups. I then discuss some techniques and approaches for studying them, particularly with an eye to general structural questions, and the recent progress that has been made. |
We investigate the structure of topological groups and, in particular, symmetry groups of discrete structures such as networks, combinatorial graphs and complexes. The topology on these symmetry groups is locally compact and totally disconnected; such spaces are also called 0-dimensional. The overall goal of our research is to achieve a complete description of 0-dimensional groups that says how a given group may be broken down into simpler ones; classifies the simple ones; relates the global structure of the groups to their local structure; and says how they may be represented geometrically, algebraically and computationally.
Our research may be contrasted with theory of connected locally compact groups, which was largely completed in the 1950s with the solution of Hilbert's Fifth Problem. Building on the earlier foundational work of Sophus Lie, Elie Cartan, Emmy Noether and Hermann Weyl, this theory was vital in twentieth century physics because 4-dimensional space-time, the equations of the quantum atom, and the strong nuclear force all have connected symmetry groups. Whereas they are symmetry groups of physical space, the totally disconnected groups we seek to understand are the symmetry groups of networks, or cyberspace.
Experimental calculations with finite groups guide many aspects of this research. Our longer term aim is to convert theorems into algorithms and to develop computational and visualisation tools for infinite groups which will be made available online. Since the groups are topological, using approximation to reduce the calculations to finite groups will be an important aspect of achieving that aim (p-adic analysis is a particular but restricted case where this approximation is understood).
0-dimensional groups have links with combinatorics, number theory, finite and profinite group theory, geometric group theory, Lie groups, harmonic analysis, descriptive set theory and logic. International research on 0-dimensional groups has grown rapidly in the past decade or so and much of this new activity has been stimulated by breakthroughs made at the University of Newcastle. Our researchers continue to make ground-breaking advances in collaboration with mathematicians from America, Europe and Asia. This research is being supported by Australian Research Council funds of $2.8 million in the period 2018-22.
Our research may be contrasted with theory of connected locally compact groups, which was largely completed in the 1950s with the solution of Hilbert's Fifth Problem. Building on the earlier foundational work of Sophus Lie, Elie Cartan, Emmy Noether and Hermann Weyl, this theory was vital in twentieth century physics because 4-dimensional space-time, the equations of the quantum atom, and the strong nuclear force all have connected symmetry groups. Whereas they are symmetry groups of physical space, the totally disconnected groups we seek to understand are the symmetry groups of networks, or cyberspace.
Experimental calculations with finite groups guide many aspects of this research. Our longer term aim is to convert theorems into algorithms and to develop computational and visualisation tools for infinite groups which will be made available online. Since the groups are topological, using approximation to reduce the calculations to finite groups will be an important aspect of achieving that aim (p-adic analysis is a particular but restricted case where this approximation is understood).
0-dimensional groups have links with combinatorics, number theory, finite and profinite group theory, geometric group theory, Lie groups, harmonic analysis, descriptive set theory and logic. International research on 0-dimensional groups has grown rapidly in the past decade or so and much of this new activity has been stimulated by breakthroughs made at the University of Newcastle. Our researchers continue to make ground-breaking advances in collaboration with mathematicians from America, Europe and Asia. This research is being supported by Australian Research Council funds of $2.8 million in the period 2018-22.
Ben Brawn | Michal Ferov | Alejandra Garrido |
Thomas Murray | Colin Reid | Dave Robertson |
Thomas Taylor | Stephan Tornier | George Willis |
PhD Scholarship
A PhD scholarship opportunity is available for students to investigate totally disconnected, locally compact groups under the supervision of ARC Laureate Professor George Willis. The students will join a team seeking to bring our understanding of these groups to a level comparable to that of finite.Summer Projects 2018/19
The following student research projects are related to the Australian Research Council project on 0-Dimensional Symmetry. While they are independent, each one gives a different view on the overall project. Another, more technical, description of this research is that it concerns totally disconnected, locally compact groups. An overview which attempts to explain the broader research project to non-experts may be seen here.
An essential step towards understanding $0$-dimensional symmetry is to describe the totally disconnected, locally compact (t.d.l.c.) groups which are simple. Simple groups are those which cannot be factored into smaller pieces and they are sometimes called the 'atoms of symmetry', or said to be analogues of the prime numbers in number theory. This project investigates t.d.l.c. groups of infinite matrices. It is suspected that these groups will be found to be simple and we will aim to show that by first studying corresponding groups of $n\times n$ matrices which are known to be simple. Students taking this project will extend their knowledge of algebra, analysis and number theory. 'Totally disconnected', 'locally compact' and '$0$-dimensional' are topological notions; 'group' and 'simple' are algebraic ones; and the matrix entries are numbers modulo a prime number $p$. |
The notion of a solvable group originated with the work of É. Galois (1832), who showed that a polynomial equation has a solution by radicals if and only if its group of symmetries is solvable. For example, the formula $x=-b\pm\sqrt{b^{2}-4ac}/2a$ is the solution of a quadratic equation by radicals and symmetries of the equation swap the $+$ and $-$ signs. (A group that is not solvable has some factors which are simple.) Groups of upper triangular $n\times n$ real matrices are solvable and also have the topological property of being connected. It may be shown that these are essentially all the connected solvable groups. This project investigates solvable totally disconnected, locally compact groups. Our starting point is groups of upper triangular matrices having integer entries. These groups have the property of being nilpotent, which is stronger than solvability. Students taking this project will extend their knowledge of algebra, analysis and number theory. 'Totally disconnected' and 'locally compact' are topological notions; 'group', 'solvable and 'nilpotent' are algebraic ones; and the integer matrices embed into matrices over the real numbers as well as over other number fields. |
Symmetries of networks (or graphs) are '$0$-dimensional', and such symmetries are investigated through the algebraic technique of totally disconnected, locally compact groups. We are interested in highly symmetric, infinite graphs and one way to form such graphs is by gluing together infinitely many copies of finite graphs according to some regular instructions. This project investigates the symmetry groups of examples of graphs formed in this way and compares them with the symmetry groups of infinite regular trees, which are the most basic type of infinite regular graph. The aim is to determine whether the symmetry groups obtained in this way are simple and new. Students taking this project will extend their knowledge of algebra, analysis and combinatorics. 'Totally disconnected' and 'locally compact' are topological notions; 'group' and 'simple' are algebraic ones; and 'graphs' are a combinatorial concept. |
The word 'symmetry' brings to mind visual images and geometry. It has a broader meaning in mathematics, where we think of regularly repeating patterns and invariance under transformations as displaying symmetry, and where the language of algebra is used to describe symmetry. Visualising the patterns or the dynamics of the transformations remains an effective tool for understanding the algebra however. This project aims to develop software for visualising various aspects of $0$-dimensional symmetry, which is the symmetry of infinite networks and arises in number theory and other parts of algebra as well. The aim is to produce software which may be used by researchers and which will be made available on web-pages of the $0$-Dimensional Symmetry project. Students taking this project will extend their knowledge of algebra, analysis, mathematical software and coding skills. 'Totally disconnected' and 'locally compact' are topological notions; 'group' is an algebraic one; and other concepts will be met in the course of the project. |
Date | Time | Room | Speaker | Title |
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06.06.2018 | 14.00 | V 206 | George Willis | Free products of graphs - Part II |
30.05.2018 | 14.00 | V 206 | George Willis | Free products of graphs - Part I |
Date | Time | Room | Speaker | Title |
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17.12.2018 | 14.00 | MC G29 | Stephan Tornier | Haar measures |
10.12.2018 | 14.00 | MC G29 | Dave Robertson | Haar measures |
04.12.2018 | all week | Adelaide | AustMS Meeting | |
03.12.2018 | all week | Adelaide | AustMS Meeting | |
27.11.2018 | 9.00 | MC G29 | Dave Robertson | Haar measures |
26.11.2018 | 14.00 | MC G29 | CARMA Retreat | |
20.11.2018 | 9.00 | MC G29 | Dave Robertson | Haar measures |
19.11.2018 | 14.00 | MC G29 | Dave Robertson | Haar measures |
13.11.2018 | 9.00 | MC G29 | EViMS Workshop | |
12.11.2018 | 14.00 | MC G29 | Weekly Seminar | |
06.11.2018 | 9.00 | MC G29 | Group Actions Seminar held at the University of Sydney | |
05.11.2018 | 14.00 | MC G29 | Exercise Session | |
30.10.2018 | 14.00 | MC G29 | Stephan Tornier | Semidirect products and restricted direct products |
30.10.2018 | 9.00 | MC G29 | Michal Ferov | Locally finite graphs |
29.10.2018 | 14.00 | MC G29 | Michal Ferov | Locally finite graphs |
22.10.2018 | 14.00 | MC G29 | Michal Ferov | Topological Isomorphism Theorems |
16.10.2018 | 9.00 | MC G29 | Michal Ferov | Topological structure of t.d.l.c. Polish groups |
15.10.2018 | 14.00 | MC G29 | Michal Ferov | Van Dantzig's theorem |
Dates | Place | Event | Participants | |
---|---|---|---|---|
September 22-27, 2019 | Heidelberg, Germany |
Heidelberg Laureate Forum | ||
August 5-9, 2019 | Sydney, Australia |
Flags, Galleries and Reflection Groups | ||
May 26-30, 2019 | Tel Aviv, Israel |
Geometric and Asymptotic Group Theory with Applications |
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March 24-29, 2019 | Dagstuhl, Germany |
Algorithmic Problems in Group Theory | ||
January 22-25, 2019 | Zurich, Switzerland |
Groups, spaces, and geometries on the occasion of Alessandra Iozzi's 60th birthday |
Colin Reid, Stephan Tornier | |
January 21-25, 2019 | Sydney, Australia |
The Asia-Australia Algebra Conference 2019 | Michal Ferov, Alejandra Garrido, George Willis | |
January 16-18, 2019 | Auckland, New Zealand |
Groups and Geometries | ||
December 4-7, 2018 | Adelaide, Australia |
Meeting of the Australian Mathematical Society | Alejandra Garrido, Colin Reid, Dave Robertson, Stephan Tornier, George Willis | |
November 14-16, 2018 | Newcastle, Australia |
AMSI-CARMA workshop on Mathematical Thinking | George Willis | |
November 13, 2018 | Newcastle, Australia |
Effective Visualisation in the Mathematical Sciences | Alejandra Garrido, Colin Reid, Dave Robertson, Stephan Tornier, George Willis | |
November 9-11, 2018 | Newcastle, Australia |
Diagrammatic Reasoning in Higher Education | Dave Robertson, Stephan Tornier | |
September-December, 2018 | Bonn, Germany |
Logic and Algorithms in Group Theory | Michal Ferov, George Willis | |
September 21, 2018 | London, England |
Hausdorff Dimension | Alejandra Garrido | |
September 11-13, 2018 | Geneva, Switzerland |
Spectra and L^{2} - invariants | Alejandra Garrido | |
September 3-7, 2018 | Oxford, England |
Groups, Geometry and Representations | Alejandra Garrido | |
June 25-29, 2018 | Düsseldorf, Germany |
Trees, dynamics and locally compact groups | Michal Ferov, Alejandra Garrido, Colin Reid, Stephan Tornier, George Willis | |
June 11-14, 2018 | St. Andrews, England |
British Mathematical Colloquium | Colin Reid | |
January 23-26, 2018 | Auckland, New Zealand |
Groups and Geometry | Michal Ferov, Colin Reid, George Willis |
The Group Actions Seminar held regularly at The University of Sydney
The Geometry and Topology Seminar held regularly at The University of Sydney