Alexandra-Iulia Otiman

Project title

Conformal Geometry: metrics and cohomology

What is your project about?

My project is meant to make theoretical advances in the field of differential geometry and more precisely, it aims at understanding the shape of some special spaces in arbitrary high dimensions by using a particular way of measuring distances. Describing the shape of a space in dimension more than four is not a straightforward task. In order to achieve this, my team and I will use abstract theories coming from various sides and branches of mathematics, that will produce the appropriate tools and framework.

How did you become interested in your particular field of research?

My interest in mathematics and geometry came early on in childhood, and I grew up participating in mathematics contests and competitions such as the Mathematical Olympiad. I was always fascinated as a child by numbers and geometric patterns and shapes in two or three dimensions. This passion transformed into pursuing studies in differential geometry, which requires a leap of abstractization and imagination. I like to think that at the heart of this more advanced theory lies the same mathematical game.

What are the scientific challenges and perspectives in your project?

The challenges that we usually face in a theoretical branch of mathematics, such as differential geometry, always regard the way we shall use old and classic methods to solve new difficult problems and tackle new developments. As it is most often the case, we shall develop new tools and new instruments which will be beneficial and useful for the mathematical community. In the long run, these tools will generate new potential ideas and theories and serve as an effective measure of progress in the field.

What is your estimate of the impact, which your project may have to society in the long term?

Mathematics permeates modern society in many aspects, shapes and forms. The tools that we develop will not have short term concrete applications beyond building a much improved understanding of geometry from a theoretical perspective. However, history has taught us that the mathematical tools developed in this and neighbouring fields have made many of the inventions that we today take for granted, such as the GPS for instance. Through the use of metrics, geometry has nowadays a wide range of applications in practical fields such as biology and computer science, and the results we are aiming for in my project could potentially be of use in the long term in such areas.

Which impact do you expect the Sapere Aude programme will have on your career as a researcher?

It is a great honour to be a recipient of the Sapere Aude: DFF Starting-grant, which represents a big step forward in my career. Having just taken up a faculty position at Aarhus University, it will be central in building a group here, where we look forward to hiring talented young researchers from all over the world to work toward the goal of advancing part of the mathematics of geometry. It will also give me ample opportunities to enlarge my international network and enrich my research further through continued interaction with some of the world leading experts in the area.

Background and personal life

I am originally from Bucharest in Romania. After moving around Europe for my studies, including extended stays in particular in Germany and Italy, in 2022 I moved to Denmark to take up a faculty position at Aarhus University, alongside a 3-year fellowship at the Aarhus Institute of Advanced Studies. A lot of my spare time is currently defined by spending quality time with my husband and our one-year-old son. Together we like taking our electric bikes or the train to discover new places and new adventures.