IMPRESSUM    DATENSCHUTZ
	Fakultät für Mathematik	Universität Regensburg
Hinweis Bitte informieren Sie sich auf den jeweiligen GRIPS-Seiten über den digitalen Ablauf der Lehrveranstaltungen. Note For our digital courses all relevant information can be found on the appropriate GRIPS sites. Differential Galois Theory Semester SoSe 2020 Lecturer Niko Naumann Type of course (Veranstaltungsart) Vorlesung Contents This course is an introduction to the Galois theory of (linear, homogeneous) differential equations. Similar to a polynomial equation in one variable, studied in every basic course in algebra, such an equation admits a Galois-group which captures essential information about the equation. The groups appearing are (linear) algebraic groups and there will be a parallel course by Ertl/Schäppi outlining their basic theory (which is not mandatory to follow this one). A first major application of classical Galois theory is the result that a general equation of degree at least 5 cannot be solved by radicals. Similarly in spirit, we will prove here that the indefinite integral \int exp(-x^2) dx does not admit an elementary solution. Time permitting, we will give an overview of further developments, e.g. to the foundations through Tannakian categories or about (algebraic) D-modules. Literature 1) Kolchin, E. R., Differential algebra and algebraic groups. Pure and Applied Mathematics, Vol. 54. Academic Press, New York-London, 1973.\\ 2) Magid, Andy R., Lectures on differential Galois theory. University Lecture Series, 7. American Mathematical Society, Providence, RI, 1994.\\ 3) Deligne, P., Catégories tannakiennes. The Grothendieck Festschrift, Vol. II, 111–195, Progr. Math., 87, Birkhäuser Boston, Boston, MA, 1990.\\ 4) Borel, A. et al. Algebraic D-modules. Perspectives in Mathematics, 2. Academic Press, Inc., Boston, MA, 1987 Recommended previous knowledge Linear algebra, algebra and commutative algebra. Time/Date Tuesday, 10 am. Location M101 Course homepage https://elearning.uni-regensburg.de/course/view.php?id=40884 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration Preliminary registration for the organisation of exercise classes: at the end of the previous semester via EXA or LSF (see announcement by the department) Registration for the exercise classes: in class Registration for course work/examination/ECTS: FlexNow Course work (Studienleistungen) Successful participation in the exercise classes: Examination (Prüfungsleistungen) Written exam: Duration: 120 minutes, Date: TBD, re-exam: Date: TBD Modules BAlg(2), BV, MV, MArGeo, LA-GyAlg ECTS 6

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