Кто читает:: Факультет математики

Статус:: Курс обязательный

Когда читается:: 1-й курс, 3, 4 модуль

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 systems
Collatz conjecture (3n + 1 conjecture). Furstenberg conjecture. Margulis conjecture. MLC conjecture – Is the Mandelbrot set locally connected? Weinstein conjecture. Arnold–Givental conjecture.
Algebra
Finite 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.

Assessment Elements

active participation at the seminar
own talk at the seminar

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

Магистерская программа «Математика»

Research Seminar of Master’s Programme 2

Course Syllabus