KNU Mathematics Intensitve Lecture Series

Introduction to Sheaves on Manifolds

given by

Prof. Youngho Yoon (Chungbuk National University)

August 19–22, 2024

Abstract

This lecture series introduces graduate students to sheaf theory’s key concepts and applications on manifolds. We will cover the basics of sheaves and presheaves, sheaf cohomology, constructible and perverse sheaves, and the Riemann-Hilbert correspondence. Emphasis is placed on understanding theoretical insights and practical examples to provide a comprehensive understanding of sheaf theory in modern mathematics.

Lectures

August 19(Mon)

Lecture 1. Introduction: Basic Concepts and History, 10:00 – 11:30
Lecture 2. Presheaves, Sheaves, and Sheafification, 14:00 – 15:30
Lecture 3. Sheaf Operations, 16:00 – 17:30

August 20(Tue)

Lecture 4. Basics of Sheaf Cohomology, 10:00 – 11:30
Lecture 5. Cech Cohomology and Derived Functors, 14:00 – 15:30

August 21(Wed)

Lecture 6. Constructible Sheaves, 10:00 – 11:30
Lecture 7. Perverse Sheaves: Introduction, 14:00 – 15:30
Lecture 8. Perverse Sheaves: Examples and Applications, 16:00 – 17:30

August 22(Thu)

Lecture 9. The Riemann–Hilbert Correspondence, 10:00 – 11:30
Lecture 10, Applications of Sheaf Theory, 14:00 – 15:30

Lecture Notes

Note

Venue

#102, College of Natural Sciences, Kyungpook National University, Daegu, Korea

Participants

Byunghee An (Kyungpook National University)
Jinju Choi (Pusan Bational University)
Woohyuk Choi (POSTECH)
Kiryong Chung (Kyungpook National University)
Jinyoung Huh (Kyungpook National University)
Jeonghoon Joo (Pusan National University)
Junho Jung (Chungbuk National University)
Hyunsoo Kim (Kyungpook National University)
Inseo Kim (Chungbuk National University)
Jeongsoo Kim (Chungbuk National University)
Hyunwoo Lee (Kyungpook National University)
Sungwoo Lee (Kyungpook National University)
Jihoon Park (Kyungpook National University)
Youngho Yoon (Chungbuk National University)