After successful completion of the course, students are able to present their chosen subject or field (for example a chapter of a textbook or monograph, or a scientific paper) at an introductory level.

Selection of topics during/after the preliminary discussion. Topics in integral geometry and stochastic geometry (topics in geometric analysis or optimal transport are also possible on request).

Discussion of the topic and the design of the presentation and the written paper with the course instructor.

Suggested topics (other topics can also be suggested):

• Buffon's needle problem; Steiner formula and intinsic volumes; kinematic and Crofton formula;...
  
  
• Sylvester's four-point problem; random polytopes; Blaschke--Petkantschin formula;...
  
  
• Betrand's paradox; random hyperplane tesselations;...

Literature references:

• Survey Paper: "Some Classical Problems in Random Geometry", P. Calka: https://catalogplus.tuwien.at/permalink/f/8agg25/TN_cdi_springer_books_10_1007_978_3_030_13547_8_1
  
  
• Book: "Stochastic and Integral Geometry", R. Schneider & W. Weil: https://catalogplus.tuwien.at/permalink/f/8agg25/TN_cdi_openaire_primary_doi_9af9e0ad8807643c22516de2fe3629a8
  
  
• Book: "Convex bodies : the Brunn-Minkowski theory", R. Schneider: https://catalogplus.tuwien.at/permalink/f/8j3js/UTW_alma5195146900003336
  
  
• Book: "Introduction to geometric probability", D.A. Klain & G.-C. Rota: https://catalogplus.tuwien.at/permalink/f/8j3js/UTW_alma2149269960003336

Presentation with discussion and written summary.

Depending on the subject.