Dr Stephan Tornier

Dr Stephan Tornier

ARC DECRA Fellow

School of Information and Physical Sciences

Career Summary

Biography

Having completed high school with a focus on mathematics, physics and geography in Northern Germany, I moved to Munich in Southern Germany to carry out my civilian service.

With an interest in astronomy and theoretical physics at the time, I decided to study mathematics at ETH Zurich, Switzerland. My Bachelor studies included a stay at the Australian National University in Canberra as an exchange student. In terms of mathematics, I soon developed an interest in algebra, specifically group theory, and completed my Bachelor studies with a thesis on low-dimensional group cohomology.

Taking advantage of the excellent, broad mathematical education at ETH Zurich I pursued my passion for group theory during my Master's. Intensive studies in Lie groups and, more generally, locally compact groups added a topological twist to the groups I had been studying and motivated me to write a Master thesis on rigidity phenomena associated to Property (T) and amenability.

The research frontier finally in sight, I started a PhD program at the same institution under the supervision of Marc Burger who introduced me to striking analogues between Lie theory and groups acting on trees with certain local properties. Lying at the opposite end of the spectrum of locally compact groups as far as connectedness is concerned, they quickly became my primary focus. Several research stays at The University of Newcastle, notably enabled by a fellowship award from the Swiss National Science Foundation, allowed me to connect my work to other research in the field, pursue new approaches to the overarching classification goal of totally disconnected locally compact groups, and to collaborate.

From the last year of my Bachelor's onwards I worked as a teaching assistant at both ETH Zurich and, later on, The University of Newcastle in parallel to my studies. Challenged with the conduction of weekly recitation classes, occasional lecturing and content creation for courses ranging from Bachelor to PhD level in fields as diverse as Algebra, Differential Geometry and Lie Groups, I also developed a passion for teaching mathematics.

Upon completion of my PhD with a thesis concerning groups acting on trees, I started a full-time position as postdoctoral research associate at The University of Newcastle in April 2018 in the research group on zero-dimensional symmetry led by Laureate Professor George Willis. Over three years I was able to follow my interest in groups acting on trees and benefit from the superb atmosphere in this research group as well as the broader research centre CARMA. Ultimately, this led to the award of a DECRA through the Australian Research Council which allows me to propel the field further ahead.


Qualifications

  • Doctor of Science, Swiss Federal Institute of Technology - Zurich
  • Bachelor of Science (Mathematics), Swiss Federal Institute of Technology - Zurich
  • Master of Science (Mathematics), Swiss Federal Institute of Technology - Zurich

Keywords

  • Computational algebra
  • Group theory

Languages

  • German (Mother)
  • English (Fluent)
  • Spanish (Working)
  • French (Working)

Fields of Research

Code Description Percentage
490405 Group theory and generalisations 100

Professional Experience

UON Appointment

Title Organisation / Department
Casual Academic University of Newcastle
School of Information and Physical Sciences
Australia

Academic appointment

Dates Title Organisation / Department
1/1/2017 - 31/8/2017 SNSF Fellow University of Newcastle
School of Mathematical and Physical Sciences
Australia
1/6/2016 - 31/12/2016 Research Assistant University of Newcastle
School of Mathematical and Physical Sciences
Australia
1/5/2013 - 31/8/2016 Teaching Assistant ETH Zurich
Department of Mathematics
Switzerland
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Chapter (1 outputs)

Year Citation Altmetrics Link
2018 Garrido A, Glasner Y, Tornier S, 'Automorphism groups of trees: generalities and prescribed local actions', New Directions in Locally Compact Groups, Cambridge University Press, Cambridge, UK 92-116 (2018) [B1]
DOI 10.1017/9781108332675
Citations Scopus - 4

Journal article (4 outputs)

Year Citation Altmetrics Link
2020 Carter M, Tornier S, Willis G, 'On free products of graphs', Australasian Journal of Combinatorics, 78 154-176 (2020) [C1]
Co-authors Max Carter, George Willis
2019 Bywaters T, Tornier S, 'Willis theory via graphs', Groups, Geometry, and Dynamics, 13 1335-1372 (2019) [C1]
DOI 10.4171/ggd/525
2018 Tornier S, 'Prime localizations of Burger-Mozes-type groups', Journal of Group Theory, 21 229-240 (2018)

This article concerns Burger-Mozes universal groups acting on regular trees locally like a given permutation group of finite degree. We also consider locally isomorphic generaliza... [more]

This article concerns Burger-Mozes universal groups acting on regular trees locally like a given permutation group of finite degree. We also consider locally isomorphic generalizations of the former due to Le Boudec and Lederle. For a large class of such permutation groups and primes p we determine their local p-Sylow subgroups as well as subgroups of their p-localization, which is identified as a group of the same type in certain cases.

DOI 10.1515/jgth-2017-0036
Citations Scopus - 1
2018 Bywaters T, Glöckner H, Tornier S, 'Contraction groups and passage to subgroups and quotients for endomorphisms of totally disconnected locally compact groups', Israel Journal of Mathematics, 227 691-752 (2018) [C1]
DOI 10.1007/s11856-018-1750-9
Citations Scopus - 1Web of Science - 2
Show 1 more journal article

Thesis / Dissertation (2 outputs)

Year Citation Altmetrics Link
2018 Tornier S, Groups Acting on Trees and Contributions to Willis Theory, ETH Zurich (2018)
DOI 10.3929/ethz-b-000265512
2013 Tornier S, On a theorem of Shalom, ETH Zurich (2013)
DOI 10.3929/ethz-a-010590629
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Grants and Funding

Summary

Number of grants 4
Total funding $452,979

Click on a grant title below to expand the full details for that specific grant.


20211 grants / $405,314

Effective classification of closed vertex-transitive groups acting on trees$405,314

Symmetry is a fundamental organising principle in mathematics and human endeavour. This project aims to
advance our knowledge of zero-dimensional symmetry, a frontier in symmetry research. In the longer term,
advancements in fundamental knowledge in this area have the potential to inform the usage and development of
digital structures in more practical contexts, such as data networks and information processing. The project is
expected to develop new tools of both theoretical and computational nature that will accelerate ongoing research
across the field and enable new approaches. This will cement Australia's position at the forefront of research in
symmetry and its use in the digital age.

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Doctor Stephan Tornier, Doctor Stephan Tornier
Scheme Discovery Early Career Researcher Award (DECRA)
Role Lead
Funding Start 2021
Funding Finish 2023
GNo G1901376
Type Of Funding C1200 - Aust Competitive - ARC
Category 1200
UON Y

20201 grants / $2,000

SISP Program: What is Symmetry?$2,000

Development of an educational video "What is Symmetry?" for the NSW Department of Education and Training's STEM Industry School Partnerships Program, aimed at year 5-11 students.

Funding body: Department of Education and Training, NSW

Funding body Department of Education and Training, NSW
Scheme SISP Program
Role Lead
Funding Start 2020
Funding Finish 2020
GNo
Type Of Funding C1600 - Aust Competitive - StateTerritory Govt
Category 1600
UON N

20172 grants / $45,665

Closure of projections of lattices in products of trees$45,000

Two of the most exciting developments in 20th century mathematics that have gained considerable attention in recent years are the structure theory of locally locally compact groups and the theory of lattices in locally compact groups. Thanks to many important contributions over the years, the structure theory of locally compact groups can, to a large extent, be reduced to the case of groups acting on trees. This research combines the two above-mentioned research streams by studying projection closures of lattices in products of trees.

Funding body: Swiss National Science Foundation (SNSF)

Funding body Swiss National Science Foundation (SNSF)
Project Team

Stephan Tornier

Scheme Doc.Mobility
Role Lead
Funding Start 2017
Funding Finish 2017
GNo
Type Of Funding C3212 - International Not for profit
Category 3212
UON N

Workshop: Group actions and cohomology in non-positive curvature$665

This workshop is the closing event of the semester-long program "Non-positive curvature, Group Actions, and Cohomology".

Funding body: Swiss Mathematical Society

Funding body Swiss Mathematical Society
Project Team

Stephan Tornier

Scheme Travel Grant
Role Lead
Funding Start 2017
Funding Finish 2017
GNo
Type Of Funding C3212 - International Not for profit
Category 3212
UON N
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Research Supervision

Number of supervisions

Completed0
Current3

Current Supervision

Commenced Level of Study Research Title Program Supervisor Type
2021 PhD Exploring Smith’s Construction to Generate Local Isomorphism Classes PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle Co-Supervisor
2021 Masters Unitary Representations of Automorphism Groups of Label-Regular Trees M Philosophy (Mathematics), College of Engineering, Science and Environment, The University of Newcastle Co-Supervisor
2019 PhD A Finer Invariant for Locally Compact Totally Disconnected Groups PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle Co-Supervisor
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Dr Stephan Tornier

Positions

ARC DECRA Fellow
School of Information and Physical Sciences
College of Engineering, Science and Environment

Casual Academic
School of Information and Physical Sciences
College of Engineering, Science and Environment

Contact Details

Email stephan.tornier@newcastle.edu.au

Office

Room .
Building Mathematics Building
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