Dr Stephan Tornier

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 in order 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 stunning 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, 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.


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

  • 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
Postdoctoral Research Associate University of Newcastle
School of Mathematical and Physical Sciences
Australia

Academic appointment

Dates Title Organisation / Department
1/09/2017 - 31/12/2017 Teaching Assistant ETH Zurich
Department of Mathematics
Switzerland
1/01/2017 - 31/08/2017 SNSF Fellow University of Newcastle
School of Mathematical and Physical Sciences
Australia
1/06/2016 - 31/12/2016 Research Assistant University of Newcastle
School of Mathematical and Physical Sciences
Australia
1/05/2013 - 31/08/2016 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 Tornier S, Garrido A, Glasner Y, 'Automorphism groups of trees: generalities and prescribed local actions', New Directions in Locally Compact Groups, Cambridge University Press, Cambridge, UK 92-116 (2018)
DOI 10.1017/9781108332675

Journal article (2 outputs)

Year Citation Altmetrics Link
2018 Tornier S, 'Prime localizations of Burger¿Mozes-type groups', Journal of Group Theory, 21 229-240 (2018)
DOI 10.1515/jgth-2017-0036
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

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 3
Total funding $45,873

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


Highlighted grants and funding

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

20181 grants / $208

Trees, dynamics and locally compact groups$208

Travel contribution to attend the conference "Trees, dynamics and locally compact groups" in Düsseldorf, Germany, from June 25 to June 29, 2018.


Funding body: Universität Düsseldorf

Funding body Universität Düsseldorf
Scheme Travel Grant
Role Lead
Funding Start 2018
Funding Finish 2018
GNo
Type Of Funding C3212 - International Not for profit
Category 3212
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

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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Dr Stephan Tornier

Position

Postdoctoral Research Associate
School of Mathematical and Physical Sciences
Faculty of Science

Contact Details

Email stephan.tornier@newcastle.edu.au

Office

Room -
Building Mathematics Building
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