# Doctoral School of Exact Sciences

## Disciplines

#### Training in the Doctoral School of Exact Sciences is provided in the following disciplines:

**Astronomy**

Astronomy is a discipline of science dedicated to the knowledge and understanding of the Universe. It studies both the Universe as a whole (cosmology) and the physical objects that exist within it - from galaxy clusters to free atoms and molecules in space. It also deals with our Earth seen as one of the planets and the human creations orbiting around it - artificial satellites.

Observational astronomy uses telescopes that cover a wide range of the electromagnetic spectrum (from radio telescopes to gamma ray detectors); both ground-based and space-based, cosmic ray particle detectors and, more recently, gravitational wave detectors.

Theoretical astronomy is closely related to mathematics (celestial mechanics) and physics (astrophysics).

The Poznań Astronomical Observatory began its over one hundred year history as a centre focused on classical astronomy - first and foremost astrometry (determination of coordinates on the celestial sphere). The present Institute of Astronomical Observatory is a significant centre of research on small bodies of the Solar System (asteroids, comets and meteoroids) and the motion of artificial satellites, including "space junk". In recent decades, astrophysical topics have also developed, including the study of binary and multiple star systems and star-forming processes in galaxies. Both theoretical and observational studies are carried out. The latter use not only its own modern telescopes located in Poland (Borówiec, Chalin) and abroad (Winer Observatory in Arizona), but also telescopes on Earth and in space belonging to international consortia.

**Computer Science**

A scientific discipline concerned with the processing of information using computers; includes computer theories, the construction of computer systems (including programming), the construction and operation of computer hardware, the application of computer methods in various fields of human activity. Computer theories deal with the study of phenomena related to information handling - its representation, storage, acquisition, ordering and processing. The laws governing these phenomena underlie the construction of computer science tools, which are physical objects (mainly computers) and logical objects (e.g. algorithms, programming languages, programs, data structures). Thanks to the application of computer science methods, many different fields of human activity have been improved, e.g. administration and management, scientific calculations, control of technological processes, preparation of texts (text editor), publishing works (DTP), sending messages (electronic mail), design (CAD, CAM), medical diagnostics (e.g. computed tomography). Recently emerging fields of computer science are also developing, including artificial intelligence and computer graphics.

**Mathematics**

A deductive science, a branch of knowledge whose purpose can be described as the study of the consequences of accepted assumptions. Modern mathematics is characterised on the one hand by being highly abstract and formalised and on the other by a rapidly growing range of applications, covering not only the technical and natural sciences, but also economics and some branches of the humanities. The history of mathematics goes back to the beginnings of civilisation. In ancient Babylonia (c. 2000 BC), for example, the areas of certain shapes were calculated and certain calculations were performed - counting was based on various systems, mainly decimal. Thales of Miletus (c. 600 BC) marked the beginning of major developments in mathematics, especially in geometry (deductive reasoning); Eudoxus of Cnidus (4th c. BC) invented calculation methods similar to today's integral calculus, Euclid created the first axiomatic system of geometry, which he formulated in Elements, a work that for many years set a standard of mathematical accuracy. The 17th century was a turning point in the history of mathematics: R. Descartes created analytic geometry, I. Newton and G.W. Leibniz created differential and integral calculus; both disciplines immediately became powerful and effective tools for studying natural phenomena; probability calculus also crystallized at that time (P. Fermat, B. Pascal, Jacob Bernoulli). In the 18th century, variational calculus was developed, as well as the theory of differential equations. At the turn of the 18th and 19th centuries, mathematical analysis led to the development of theoretical mechanics (L. Euler, J. Lagrange, and P.S. Laplace). The nineteenth century saw intensive development of number theory (C.F. Gauss), the theory of analytic functions (A.L. Cauchy, K. Weierstrass), differential geometry (Gauss, G.F.B. Riemann). Projective geometry came into being (J.V. Poncelet, J. Steiner), N. Lobaczewski and J. Bolyai independently created the first non-Euclidean geometry, higher algebra developed dynamically, especially the theory of groups (N.H. Abel, É. Galois). At the end of the century, the theory of multiplicity was formed (G. Cantor), and at the turn of the 20th century, topology (the Polish school of mathematics played an important role in its development, e.g. W. Sierpiński, Z. Janiszewski, S. Mazurkiewicz, K. Kuratowski, K. Borsuk). The twentieth century saw the beginning of thorough research on the foundations of mathematics (D. Hilbert), the emergence of mathematical logic (G. Peano, G. Frege, K. Gödel); new branches of mathematics developed vigorously, such as the theory of integral equations (Hilbert, I. Fredholm), the theory of real functions (H. Lebesgue), functional analysis (D. Hilbert, S. Banach), mathematical foundations of the theory of relativity (H. Minkowski) were created and A. Kolmogorov contributed to the mathematics of probability theory.

**Chemical Sciences**

Chemistry is the science that studies the composition, structure and properties of substances, especially the transformations between them.

Research conducted at the Faculty of Chemistry covers all major fields of experimental and theoretical, organic, inorganic and physical chemistry. The scientific activity of our staff has been, and still is, closely connected with teaching – students write bachelor’s and master’s theses and doctoral dissertations, which constitute an important part of scientific research. Areas of chemistry in which the results obtained at the Faculty by research teams are particularly significant both nationally and internationally include: metal-organic chemistry and catalysis with metal-organic compounds including - synthesis and reactivity of organic derivatives containing silicon atoms as well as other heteroatoms; biocrystallography and roentgenographic studies of the structure of condensed phases; supramolecular chemistry in particular chemistry and physicochemistry of synthetic molecular receptors; synthesis of chiral organic compounds; synthesis and studies of fluoroorganic compounds with potential application in medicine, agriculture and obtaining new materials; synthesis, characterization, modification and studies of catalytic properties of zeolites and other porous materials; bioorganic chemistry and photochemistry, including studies of mechanisms of light-induced chemical processes with the use of ultrafast laser spectroscopy; analytical chemistry with particular emphasis on chemical methods for analysis and monitoring of environmental pollution; coordination chemistry and spectroscopic studies of lanthanides; theoretical chemistry, preparation and studies of photocatalytic activity and luminescence of nanomaterials containing rare earth elements.

A significant part of research topics is realised in cooperation with domestic and foreign centres, mainly in Europe, USA, Canada and Japan. The cooperation is conducted both within the framework of formal agreements and contracts between Adam Mickiewicz University and other universities as well as informal individual contacts between the Faculty staff and cooperating researchers from various domestic and foreign centres.

**Physical Sciences**

In the new classification of disciplines, physical sciences included traditional physics, biophysics (physics of living organisms) and geophysics (physics of the Earth). Research conducted at the Faculty of Physics focuses mainly on physics and biophysics. Physics is a discipline of sciences that deals with the description and explanation of phenomena and interactions occurring both on the smallest scale (quarks, particles, atoms) and on the largest scale (the Universe). The most general division includes theoretical and experimental physics. Theoretical physics allows for a precise description of phenomena or the prediction of new ones, for which it uses the precise language of mathematics. Experimental physics, on the other hand, involves the construction of measuring apparatus and conducting experiments with its use, which allows theoretical predictions to be verified experimentally or new physical phenomena to be described. Physics can also be divided according to the objects of research: for example particle physics, atomic physics, condensed matter physics etc. The study of specific phenomena, in turn, is dealt with by such branches of physics as acoustics, optics, mechanics, electrodynamics or thermodynamics. Physics also enters interdisciplinary research areas such as astrophysics, biophysics, medical physics, physical chemistry or material engineering. Research in the discipline of physical sciences conducted at the Faculty of Physics covers a wide range of research paths and is both theoretical and experimental in nature. Publications originating in the Faculty address not only the foundations of the micro-world (chromodynamics and quantum mechanics), magnetic properties, interaction of light with matter, nanostructures or complex particles in living cells, but also issues closer to everyday life, such as efficiency of photovoltaic cells, noise or sight and hearing defects. They look to the future, for example by considering the behaviour of quantum computers or the resistance of quantum money to counterfeiting and go back thousands of years with radiocarbon dating of the oldest excavations.

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