Master
2018/2019
Research Seminar of Master’s Programme 2
Type:
Compulsory course (Mathematics)
Area of studies:
Mathematics
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1 year, 3, 4 module
Mode of studies:
offline
Master’s programme:
Mathematics
Language:
English
ECTS credits:
5
Contact hours:
84
Course Syllabus
Abstract
Research Seminar of Master’s Programme “Open Problems of Modern Mathematics” is compulsory and accessible to any first year student of the master’s program in mathematics, no special pre-requisite required. Each participant of the seminar give a talk about open problems in the area of his/her own research.
Learning Objectives
- The seminar is intended to introduce most popular open mathematical problems and known approaches to solve them. Also it offers the students an opportunity to prepare and give a talk.
Expected Learning Outcomes
- knows the current state of various branches of mathematics, which problems are open now and what is already done, improves presentation skills and ability to understand mathematics from each other
Course Contents
- Dynamical systemsCollatz conjecture (3n + 1 conjecture). Furstenberg conjecture. Margulis conjecture. MLC conjecture – Is the Mandelbrot set locally connected? Weinstein conjecture. Arnold–Givental conjecture.
- AlgebraFinite lattice representation problem. Hilbert's sixteenth problem. Hilbert's fifteenth problem. Hadamard conjecture. Jacobson's conjecture. Existence of perfect cuboids and associated cuboid conjectures. Zauner's conjecture: existence of SIC-POVMs in all dimensions. Köthe conjecture. Birch–Tate conjecture. Serre's conjecture II. Bombieri–Lang conjecture. Farrell–Jones conjecture. Bost conjecture. Rota's basis conjecture.
Interim Assessment
- Interim assessment (4 module)0.4 * active participation at the seminar + 0.6 * own talk at the seminar
Bibliography
Recommended Core Bibliography
- Connes, A., & Kouneiher, J. (2019). Sir Michael Atiyah, a Knight Mathematician A tribute to Michael Atiyah, an inspiration and a friend. https://doi.org/10.1090/noti1981
Recommended Additional Bibliography
- De Lellis, C. (2016). The masterpieces of John Forbes Nash Jr. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1606.02551