Number theory is a particularly active field in the study of algebraic structures. It focuses on integers and uses tools derived from algebra to solve elaborate number theory problems.

There is no shortage of topics to investigate in astrophysics—we have so much left to explore. Researchers at Laval study the formation, structure, and evolution of stars, including white dwarfs, neutron stars, and stellar black holes. Others focus on solar physics, the sun’s magnetic activity cycle, and the physical mechanisms that cause significant fluctuations in its amplitude and duration. Some astronomers are passionate about exoplanets and brown dwarfs, which they observe using new infrared astronomical instruments. The stellar and gaseous structure, dynamics, and evolution of galaxies also keep many astronomers busy, especially those who are looking to better understand dark matter.

Behavioural ecology is the study of animal behaviour under natural conditions. Researchers in the field use sampling, comparative analysis, and field observation to study basic animal behaviours such as finding food, mating, and group living that are crucial to individual reproductive success and population establishment in a given territory.

Genomics is the study of a species’ genome, i.e., all of the genetic material encoded in its DNA. A genome’s coding sequence dictates how its cells function biologically. Studying these sequences provides a better understanding of the roles played by environment, lifestyle, and genetic makeup in the development of chronic diseases. Biologists use genomics to estimate the abundance of species in lakes, manage wildlife populations, and select more disease-resistant or faster-growing species, among other things. In basic science, genomics is used to understand and document the origin of species and the formation of new ones.

Geochemistry uses the concepts and tools of chemistry to study the earth and sediments. Geochemists identify and characterize chemical, mechanical, and mineralogical processes that modify the chemical composition of materials. On a larger scale, they work to determine the composition of the Earth’s layers, from the atmosphere to the inner core. It also uses geochronology to determine the age of rocks and events that have affected the Earth.

Geophysics is the study of the earth, its gaseous envelope, and its magnetic and gravitational fields using physics methods. It is situated at the intersection of geology, physics, mathematics, and computer science. A distinction is made between internal geophysics, boundary layer geophysics, and external geophysics.

Analysis is the field of mathematics which studies continuous phenomena. It involves developing and studying the concepts of limits and convergence of sequences and functions, and then those of derivatives and integrals. Analytical research is divided into several fields, the main ones being complex analysis, harmonic analysis, functional analysis, and the theory of partial differential equations. Analysis is ubiquitous in mathematics because it forms the basis for several other branches of mathematics, including dynamic systems and differential geometry. Analysis is also very important for the development of other sciences. For example, partial differential equations are the main language used to state the laws and models that describe nature.

The fundamental character of mathematics, both as a field of knowledge and as a language and tool in many realms of application, has given rise to a long tradition of reflection and research on its teaching and learning. Several distinguished mathematicians contributed to this movement, such as Felix Klein, George Pólya or Hans Freudenthal, thus furthering the emergence of works on the pedagogical difficulties specific to mathematical knowledge and its acquisition. An important part of this research focuses on the mathematical education of teachers, especially at the primary and secondary levels.

Quantum chemistry is a branch of theoretical chemistry that applies quantum mechanics to molecular systems to study chemical processes and properties. The electrical and nuclear behaviour of molecules responsible for chemical properties can be described using quantum motion and other basic assumptions of quantum mechanics. Quantum mechanics has led to the development of digital calculation methods that have advanced modern chemistry, both in terms of understanding phenomena and in applications (Wikipedia).

In the natural sciences, engineering, economics, and computer science, there exist systems with input and output data for which the superposition of two inputs results in the superposition of the corresponding outputs. These systems can be analyzed using complex analysis and spectral theory, the branch of mathematics that studies matrices and their eigenvalues, infinite-dimensional counterparts, operators, and spectra. Spectral theory has numerous applications for technology, including control systems, image compression, and the Google PageRank algorithm.

The purpose of physics is to understand what the universe is made of using the most advanced scientific instruments at our disposal. Physicists attempt to identify the laws of nature that explain cause-and-effect relationships using theories expressed in mathematical language. Examples include Newton’s theory of gravitation, Einstein’s theory of general relativity, and, more recently, the Standard Model, which was confirmed by the discovery of the Higgs boson. Elementary particles physics is one of the most ambitious branches of theoretical physics because it examines nature’s most fundamental components and interactions.