
Dr Stephan Tornier
Postdoctoral Research Associate
School of Mathematical 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
- Bachelor of Science (Mathematics), Swiss Federal Institute of Technology - Zurich
- Master of Science (Mathematics), Swiss Federal Institute of Technology - Zurich
Keywords
- Amenability
- Automorphism groups of trees
- Cohomology
- Property (T)
- Rigidity
- Structure theory of locally compact groups
- Totally disconnected locally compact groups
Languages
- German (Mother)
- English (Fluent)
- Spanish (Working)
- French (Working)
Fields of Research
Code | Description | Percentage |
---|---|---|
010105 | Group Theory and Generalisations | 100 |
Professional Experience
UON Appointment
Title | Organisation / Department |
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Academic appointment
Dates | Title | Organisation / Department |
---|---|---|
1/5/2013 - 31/8/2016 | Teaching Assistant | ETH Zurich Department of Mathematics Switzerland |
1/1/2017 - 31/8/2017 | SNSF Fellow | University of Newcastle School of Mathematical and Physical Sciences Australia |
1/9/2017 - 31/12/2017 | Teaching Assistant | ETH Zurich Department of Mathematics Switzerland |
1/6/2016 - 31/12/2016 | Research Assistant | University of Newcastle School of Mathematical and Physical Sciences Australia |
Publications
For publications that are currently unpublished or in-press, details are shown in italics.
Chapter (1 outputs)
Year | Citation | Altmetrics | Link | |||||
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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]
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Journal article (4 outputs)
Year | Citation | Altmetrics | Link | ||
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2020 |
Carter M, Tornier S, Willis G, 'On free products of graphs', Australasian Journal of Combinatorics, 78 154-176 (2020) [C1]
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2019 |
Bywaters T, Tornier S, 'Willis theory via graphs', Groups, Geometry, and Dynamics, 13 1335-1372 (2019) [C1]
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2018 |
Tornier S, 'Prime localizations of Burger Mozes-type groups', Journal of Group Theory, 21 229-240 (2018)
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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]
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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)
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2013 |
Tornier S, On a theorem of Shalom, ETH Zurich (2013)
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Grants and Funding
Summary
Number of grants | 4 |
---|---|
Total funding | $448,140 |
Click on a grant title below to expand the full details for that specific grant.
20211 grants / $400,475
Effective classification of closed vertex-transitive groups acting on trees$400,475
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
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
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
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 |
News
Four Newcastle researchers selected for funding boost
November 23, 2020
Special Semester at the Bernoulli Center
June 4, 2019
Dr Stephan Tornier
Position
Postdoctoral Research Associate
School of Mathematical and Physical Sciences
Faculty of Science