INTERACTIONS OF HARMONIC ANALYSIS, COMBINATORICS AND NUMBER THEORY
CATEGORY THEORY
Date
April 25th – May 19th, 2017
Registration
No fee.
Universitat de Barcelona (UB)
The main purpose of this course is to explore several applications of Fourier analytic techniques in number theory and combinatorics, as well as their interactions. The course is designed to be of interest for a wide variety of graduate students with different backgrounds and motivations, including students in the area of analysis, discrete mathematics and number theory.
April 25th – May 19th, 2017
No fee.
Universitat de Barcelona (UB)
The main purpose of this course is to explore several applications of Fourier analytic techniques in number theory and combinatorics, as well as their interactions. The course is designed to be of interest for a wide variety of graduate students with different backgrounds and motivations, including students in the area of analysis, discrete mathematics and number theory.
Joaquim Ortega-Cerdà (BGSMath/UB)
Email: jortega@ub.edu
Juanjo Rué (BGSMath/UPC)
Email: juan.jose.rue@upc.edu
Jorge Jímenez (BGSMath/UPC)
Email: jjimenez@ma4.upc.edu
Oriol Serra (BGSMath/UPC)
Email: juan.jose.rue@upc.edu
Pablo Candela (UAM)
Email: pablo.candela@uam.edu
Schedule
Week 1: Joaquim Ortega-Cerdà: Harmonic analysis and applications
Week 2: Juanjo Rué: Interactions of harmonic analysis and combinatorics
Week 3: Jorge Jímenez: Interactions of harmonic analysis and analytic number theory
Week 4: Oriol Serra i Pablo Candela: Interactions of harmonic analysis and combinatorial number theory
Summari
The main purpose of this course is to explore several applications of Fourier analytic techniques in number theory and combinatorics, as well as their interactions. The course is designed to be of interest for a wide variety of graduate students with different backgrounds and motivations, including students in the area of analysis, discrete mathematics and number theory.
Contents
Week 1 (Joaquim Ortega-Cerdà), 4 hours:
– Session 1 (2 hours, 15:30h-17:30h Tuesday 25/04, Main room IMUB): Introduction
– Session 2 (2 hours, 15:30h-17:30h, Wednesday 26/04, Room T2, UB): tilings on groups and Fuglede Conjecture
Week 2 (Juanjo Rué), 5 hours:
– Session 1 (2,5 hours, 15:30h-18:00h, Wednesday 3/05, Room T2, UB): Boolean functions
– Session 2 (2,5 hours, 16h:18:30h, Friday 5/05, Main Room IMUB): Further combinatorial results
Week 3 (Jorge Jiménez), 6 hours:
– Session 1 (2 hours,15:30h-17:30h, Monday 8/05, Main Room IMUB): Exponential sums
– Session 2 (2 hours, 15:30h-17:30h, Wednesday 10/05, Room T2, UB): The circle Method
– Session 3 (2 hours, 15:30h-17:30h, Friday 12/05, Main Room IMUB): Applications
Week 4 (Oriol Serra and Pablo Candela), 7 hours:
– Session 1 (2 hours,15:30h-17:30h, Monday 15/05, Main Room IMUB ) Roth Theorem (I)
– Session 2 (2 hours, 15:30h-17:30h, Wednesday 17/05 Room T2, UB) Roth Theorem (II) and Chang’s Lemma
– Session 3 (1,5 hours, 15:30-17:00 h), Thursday 18/05, Main Room IMUB) Higher order Fourier analysis: Gowers norms (I)
– Session 4 (1,5 hours, 15:30h-17:00h, Friday 19/05, Main Room IMUB) Higher order Fourier analysis: Gowers norms (II)