Additive Combinatorics - NDMI109

• Title: Additive Combinatorics
• Guaranteed by: Department of Applied Mathematics (32-KAM)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2020
• Semester: summer
• E-Credits: 5
• Hours per week, examination: summer s.:2/2, C+Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Guarantor: prof. RNDr. Martin Loebl, CSc.
• Teacher(s): Mykhaylo Tyomkyn, Ph.D.
• Class: DS, diskrétní modely a algoritmy; Informatika Mgr. - Diskrétní modely a algoritmy
• Classification: Informatics > Discrete Mathematics

Annotation

The course deals with problems at the interface of Combinatorics, Number Theory and Analysis.

Last update: Klimošová Tereza, Mgr., Ph.D. (07.05.2020)

Literature

T. Tao and V. Vu: Additive Combinatorics, Cambridge University Press; 1

edition (2009) ISBN: 978-0521136563

T. Gowers: Generalizations of Fourier analysis, and how to apply them,

preprint. arXiv:1608.04127

Last update: Klimošová Tereza, Mgr., Ph.D. (07.05.2020)

Syllabus

Discrete Fourier analysis, Arithmetic progressions in the

integers and finite abelian groups (Roth's theorem), sum-product

estimates, the Littlewood-Offord problem, Sets with small sumsets

(Freiman's theorem).

Last update: Klimošová Tereza, Mgr., Ph.D. (07.05.2020)