Research Group — Zero-Dimensional Symmetry

Date Time Room Speaker Title
05.02.2019 12.00 MC G29 Alastair Anderberg, Max Carter, Peter Groenhout
William Roland-Batty, Chloe Wilkins
Summer Projects Dress Rehearsal

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.

Ben Brawn Michal Ferov Alejandra Garrido
Thomas Murray Colin Reid Dave Robertson
Thomas Taylor Stephan Tornier George Willis
Come along to one of our seminars or get in touch via e-mail to learn more about our research!

Symmetry in Newcastle (SIN)

This is a series of meetings with the aim of bringing together mathematicians working on Symmetry -- broadly understood -- that are based around Newcastle -- also broadly understood. Topics of interest include all aspects of group theory and connections to computer science, dynamics, graph theory, logic, number theory, operator algebras, topology.

All interested are warmly invited to attend. It's also a great opportunity to discover why Newcastle is Australia's coolest coastal town!

The mailing list carries updates and reminders as new seminars are announced. To be added to or removed from the mailing list, or for any other information, please contact Alejandra Garrido.

Upcoming Events

Date Time Room Speaker Title
01.03.2019 12.00-13.00 MC 102 Marcelo Laca TBA
14.00-15.00 MC 102 Zahra Asfar TBA
15.30-16.30 MC 102 Aidan Sims TBA

15.03.2019 12.00-13.00 TBA Mathai Varghese TBA
14.00-15.00 TBA Fedor Sukochev TBA
15.30-16.30 TBA George Willis TBA

05.04.2019 12.00-13.00 TBA Arnaud Brothier TBA
14.00-15.00 TBA Murray Elder TBA
15.30-16.30 TBA Lawrence Reeves TBA

Past Events

No past events yet.
Date Time Room Speaker Title
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
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,
Heidelberg Laureate Forum

August 5-9, 2019 Sydney,
Flags, Galleries and Reflection Groups

May 26-30, 2019 Tel Aviv,
Geometric and Asymptotic Group Theory
with Applications

March 24-29, 2019 Dagstuhl,
Algorithmic Problems in Group Theory

January 22-25, 2019 Zurich,
Groups, spaces, and geometries
on the occasion of Alessandra Iozzi's 60th birthday
Colin Reid, Stephan Tornier

January 21-25, 2019 Sydney,
The Asia-Australia Algebra Conference 2019 Michal Ferov, Alejandra Garrido, George Willis

January 16-18, 2019 Auckland,
New Zealand
Groups and Geometries

January 1, 2019 London,
Geometric Group Theory meeting at Royal Holloway Colin Reid

December 4-7, 2018 Adelaide,
Meeting of the Australian Mathematical Society Alejandra Garrido, Colin Reid, Dave Robertson, Stephan Tornier, George Willis

November 14-16, 2018 Newcastle,
AMSI-CARMA workshop on Mathematical Thinking George Willis

November 13, 2018 Newcastle,
Effective Visualisation in the Mathematical Sciences Alejandra Garrido, Colin Reid, Dave Robertson, Stephan Tornier, George Willis

November 9-11, 2018 Newcastle,
Diagrammatic Reasoning in Higher Education Dave Robertson, Stephan Tornier

September-December, 2018 Bonn,
Logic and Algorithms in Group Theory Michal Ferov, George Willis

September 21, 2018 London,
Hausdorff Dimension Alejandra Garrido

September 11-13, 2018 Geneva,
Spectra and L2 - invariants Alejandra Garrido

September 3-7, 2018 Oxford,
Groups, Geometry and Representations Alejandra Garrido

June 25-29, 2018 Düsseldorf,
Trees, dynamics and locally compact groups Michal Ferov, Alejandra Garrido, Colin Reid, Stephan Tornier, George Willis

June 11-14, 2018 St. Andrews,
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