Level sets of prevalent Hölder functions
R. Anttila, B. Bárány, A. Käenmäki (2024). Level sets of prevalent Hölder functions. To appear in Proc. Am. Math. Soc.
CV
Education
- Ph.D. in Mathematics, University of Oulu, 2025 (expected)
- Advisors: Ville Suomala, Antti Käenmäki
- M.S. in Mathematics, University of Oulu, 2021
- Master’s thesis: On multifractal analysis and local dimensions of measures
- B.S in Mathematics, University of Oulu, 2020
- Bachelor’s thesis: Normal numbers
Work experience
- May 2021 - Aug 2021: Trainee
- Nokia
- Duties included: Test automation development using Python. Maintenance of existing web APIs, and data parsing, formatting and visualization using the pandas library for python.
- Tools and technologies: Python, Django, Git, Linux, Docker, ElasticSearch
- Sep 2020 - Mar 2021: Teaching Assistant
- University of Oulu
- Duties included: Teaching exercise classes in courses Introduction to Mathematical Deduction, Functions and Limits, and Integral.
- Jun 2020 - Aug 2020: University Trainee
- University of Oulu
- Duties included: I participated in in independent research in the Fractal Geometry Research Group at the Department of Mathematical Sciences. The results are published.
- Suprevisor: Ville Suomala
- Apr 2017 - June 2017, May 2019 - June 2019: Substitute Teacher
- Oulainen High School
- Duties included: Preparing and teaching lessons in mathematics and physics. In 2017 I taught three full courses in trigonometric functions and integration, thermodynamics, and electromagnetism, and in 2019 I taught three weeks of lessons in thermodynamics and geometry. I also prepared and graded the exams.
Teaching
I have lectured the following course at the University of Oulu.
- Matrix Theory (800693S), Summer 2024
I have been a teaching assistant in the following courses at the University of Oulu.
- Real Numbers and Limits (802302A), Fall 2024
- Differential Calculus (800101P), Fall 2023
- Functions and Approximation (802102P), Spring 2023
- Algebraic structures (802355A), Fall 2021, Fall 2022
- Linear algebra (802320A), Spring 2022
- Integral (800318A), Spring 2021
- Introduction to Mathematical Deduction (802151P), Fall 2020
- Functions and Limits (800119P), Fall 2020
- Matrices and Optimization for Economists (802160P), Spring 2019
- Mathematics for Economists (802158P), Spring 2019
Grants
Vilho, Yrjö and Kalle Väisälä foundation 2023
Travel grant for a research visit to the University of St. Andrews (4 400€)
Magnus Ehrnrooth foundation 2023
Doctoral training grant (48 000€)
Magnus Ehrnrooth foundation 2022
Doctoral training grant (24 000€)
UniOGS travel grant 2022
A travel grant (1000€) for the conference Fractals and Related Fields IV.
Academic Responsibilities
- ERF: Vice President, 2024-
- Acting Vice President of ERF, the Early career Research Forum for the PhD students and postdocs of the Research Unit of Mathematical Sciences at the University of Oulu
- Geometry and Fractals under the Midnight Sun: Co-organizer, 2024
- Co-organized a conference in fractal geometry and related fields at the University of Oulu
Publications
Multifractal analysis for the pointwise Assouad dimension of self-similar measures
R. Anttila, V. Suomala (2024). Multifractal analysis for the pointwise Assouad dimension of self-similar measures. To appear in Indiana Univ. Math. J.
Slices of the Takagi function
R. Anttila, B. Bárány, A. Käenmäki, (2023). Slices of the Takagi function. Ergod. Theory Dyn. Syst., 44 (2024), no. 9, 2361-2398
Pointwise Assouad dimension for measures
R. Anttila, (2022). Pointwise Assouad dimension of measures. Proc. R. Soc. Edinb. Sect. A, Math., 153 (2022), no. 6, 2053-2078
Local entropy and Lq-dimensions of measures in doubling metric spaces
R. Anttila (2020). Local Entropy and Lq-Dimensions of Measures in Doubling Metric Spaces. The PUMP Journal of Undergraduate Research, 3, 226-243.