일정

김신영

제목: Complex Algebraic Groups 1 and 2

초록: Algebraic group is a group and variety with operators are morphisms. In this lecture, we study basics of complex algebraic groups: mainly we will consider algebraic linear groups and Borel fixed point theorem. Main reference is chapter 3 of the book " Lie groups and Algebraic groups" written by Vinberg and Onishchik. We will not discuss Lie algebras and root system.

김영락

제목: Vanishing resonance in algebraic geometry

초록: The notion of resonance can be found in several places including hyperplane arrangements and cohomology jumping loci, and is introduced by Papadima and Suciu in algebraic setting brought together with the notion of Koszul modules. There are fruitful applications of them including a proof of generic Green's conjecture by Aprodu-Farkas-Papadima-Raicu-Weyman. The purpose of this 2-hour talk is to survey on recent works about the resonance varieties, particularly on the resonance varieties associated to vector bundles.

References

1. S. Papadima, A. Suciu, Vanishing resonance and representations of Lie algebras, J. Reine Angew. Math. (2015)

2. M. Aprodu, G. Farkas, C. Raicu, J. Weyman, Koszul modules with vanishing resonance in algebraic geometry, Selecta Math. (2024)

3. M. Aprodu, C. Spiridon, Linear sections of Grassmannians and resonance of vector bundles, arXiv:2510.09195 (2025)

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