Academy postdoc researcher

University of Helsinki

Biography

I am an academy postdoc researcher at the University of Helsinki. Between 2019-2022 I was a postdoc at SISSA. I completed my PhD in 2019 at the University of Jyväskylä under the supervision of Enrico Le Donne.

My work mainly deals with sub-Riemannian geometry and computational mathematics. On the sub-Riemannian side of things I am particularly interested in Carnot groups and everything related to the so called abnormal curves, whose properties are the topic of interest of open problems such as the regularity of geodesics and the Sard problem. Within the computational realm I am mainly interested in applications within pure mathematics such as exact computation (e.g. in real algebraic geometry) or developing methods and tools to aid in finding new and interesting examples. My computer algebra system of choice is the free open-source project SageMath.

Interests

  • Sub-Riemannian geometry
  • Computational mathematics
  • Lie theory
  • Carnot groups
  • Metric geometry
  • Control theory

Education

  • Doctor of philosophy, 2019

    University of Jyväskylä

  • Pedagogical studies in education (mathematics subject teacher), 2016

    University of Jyväskylä

  • Master of science, 2015

    University of Jyväskylä

  • Bachelor of science, 2013

    University of Jyväskylä

Publications

Eero Hakavuori, Enrico Le Donne (2023). Blowups and blowdowns of geodesics in Carnot groups. J. Differential Geom.

PDF Journal of Differential Geometry arXiv

Eero Hakavuori, Ville Kivioja, Terhi Moisala, Francesca Tripaldi (2022). Gradings for nilpotent Lie algebras. J. Lie Theory.

PDF Code Journal of Lie Theory arXiv Online

Andrei Ardentov, Eero Hakavuori (2022). Cut time in the sub-Riemannian problem on the Cartan group. ESAIM: COCV.

PDF ESAIM: COCV arXiv

Eero Hakavuori (2021). ODE trajectories as abnormal curves in Carnot groups. J. Differential Equations.

PDF Code Journal of Differential Equations arXiv Online

Eero Hakavuori (2020). Infinite geodesics and isometric embeddings in Carnot groups of step 2. SIAM J. Control Optim.

PDF SIAM Journal on Control and Optimization arXiv Online

Eero Hakavuori (2019). Sub-Riemannian geodesics (thesis).

JYX archive

Eero Hakavuori, Enrico Le Donne (2016). Non-minimality of corners in subriemannian geometry. Invent. Math.

PDF Inventiones Mathematicae arXiv

Talks

Extendability of sub-Riemannian geodesics
Jan 5, 2024 15:00 Helsinki
Sub-Riemannian manifolds and their abnormal curves
Dec 1, 2022 12:15 Helsinki
Sub-Riemannian abnormal extremals
Dec 1, 2021 16:45 Online
Carnot groups and abnormal dynamics
Nov 3, 2020 16:00 Online
Infinite geodesics in Carnot groups
Feb 25, 2020 14:00 Paris, France
See all talks

Misc projects

Alexander maps

A visualization of how Alexander maps wrap a triangulated region of the plane onto the unit sphere.
Alexander maps

Infinite jigsaw

An infinite jigsaw puzzle using An aperiodic set of 11 Wang tiles by Jeandel and Rao.
Code
Infinite jigsaw

Lie algebra central extensions

A basic drag-and-drop type editor to build nilpotent and graded Lie algebras by repeated central extensions.
Code
Lie algebra central extensions

Teaching

Current:

Previous courses at University of Jyväskylä:

Previous teaching assistant duties at University of Jyväskylä:

  • MATA114 Differentiaaliyhtälöt (Summer 2016)
  • MATP170 Approbatur 3 (Spring 2014)
  • MATP121 Lineaarinen algebra ja geometria 1 (Fall 2013)
  • MATY010 Matematiikan propedeuttinen kurssi (Fall 2013)

In the 2015–2016 academic year I completed a formal 60 ECTS credit qualification for mathematics subject teachers at the University of Jyväskylä. This consisted of both theoretical pedagogy studies and practical experience of planning and giving courses and individual lessons. During this time I taught mathematics for:

  • Elementary school students in grades 7–9 (ages 13–16)
  • High school students (ages 16–19)
  • JAMK University of applied sciences

Contact