Organizers

Hyungryul Baik (KAIST),
Sang-hyun Kim, Sanghoon Kwak, Javier de la Nuez-González, Carl-Fredrik Nyberg-Brodda (KIAS)

How to join

Zoom https://kimsh.kr/vz

Meeting ID: 822 3235 0014

Passcode: 7998

Time Generally, Tuesdays or Thursdays 11 am KST

Length is typically for one-hour unless noted otherwise, although it's often extended by questions etc.

Mailing list Please contact one of the organizers to subscribe.

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2024

November 5th 2024  (Tuesday), 4 pm - 5 pm (Online)

Zoom https://kimsh.kr/vz

Hokuto Konno (Tokyo)
Diffeomorphism group and gauge theory

The dimension 4 is special in the classification theory of manifolds, as it exhibits phenomena that occur exclusively in this dimension. It is now well-known that gauge theory, which involves the study of partial differential equations derived from physics on 4-dimensional manifolds, is a powerful tool for discovering and exploring such phenomena. In recent years, there has been rapid progress in the "gauge theory for families", which is the application of gauge theory to families of 4-dimensional manifolds, leading to new insights into the diffeomorphism groups of 4-manifolds. Specifically, it has turned out that, similar to the classification theory of manifolds, the diffeomorphism groups of 4-manifolds exhibit phenomena that are unique to this dimension. In this talk, I will provide an overview of these recent developments.

KIAS--Springer Lectures

Prologue
November 13th 2024,
4:00 pm ~ 5:00 pm

In person KIAS 1503 & Zoom https://kimsh.kr/vz

Carl-Fredrik Nyberg-Brodda (KIAS)
Title:  A brief history of one-relator groups

Abstract: I’ll give an overview of the key moments in the history of one-relator group theory between around 1910-1970, and by extension all combinatorial group theory. I’ll start with free groups, knot groups, and surface groups and the work of Dehn, Dyck, Gieseking, Nielsen, and Schreier. Following this, I’ll present Magnus’  three remarkable articles from 1930, 1931, and 1931, including his solution to the word problem in all one-relator groups. I’ll discuss the “lull phase” where few results appeared, and the end of this phase in 1960, resulting in a flurry of results proved and key conjectures posed (now very recently resolved) in the 1960s.

Main lectures
November 18th 2024,
10:00 am ~ 10:50 am | 11:00 am ~ 11:50 am (Two lectures)

In person KIAS 1423 & Zoom https://kimsh.kr/vz

Marco Linton (ICMAT)
Title:  An overview of recent progress in the theory of one-relator groups

Abstract: One-relator groups form a fascinating class of groups which, despite many fundamental questions about them remaining virtually untouched, admit enough structure to be afforded a theory. In fact, the theory of one-relator groups has had a very long and fruitful history, originating in 1930 with Magnus' proof of the famed Freiheitssatz. For the majority of the last century, the tools used to study one-relator groups have mostly been combinatorial. In the last decade, exciting new ideas coming from geometry, topology and homological algebra have had a huge impact on the theory, often resulting in surprising results and resolutions of old problems that previously seemed intractable. In this series of talks I will give an overview of this recent progress, focusing on work of Andrei Jaikin-Zapirain, Lars Louder, Henry Wilton, Dani Wise and myself. I will also discuss some open problems and further directions for future research.

Epilogue

November 20-22, 2024
KIAS workshop on One RElator groups and other Aspects of GGT (registration closed)
A minicourse by Marco Linton (ICMAT)
https://kimsh.kr/dgt5