Geometry Seminars: Lorenzo Sillari and Kirill Zaynullin

Topological and geometric aspects of almost complex 4-manifolds in the spirit of Enriques-Kodaira classification / Cohomology of a linear algebraic group: chasing the Hopf structure

Monday 15 December 2025, from 2 pm in Room U9-09 (U9 Building - Viale dell'Innovazione 10, Milano), Lorenzo Sillari (University of Parma) and Kirill Zaynullin (University of Ottawa) will give the following talks

 

Speaker: Lorenzo Sillari

Title: Topological and geometric aspects of almost complex 4-manifolds in the spirit of Enriques-Kodaira classification

Abstract: In this talk I am going to discuss the possibility of extending parts of Enriques-Kodaira classification of compact complex surfaces to compact almost complex 4-manifolds. I will start by giving a broad perspective on the standard classification and on the main invariants used in it: the Kodaira dimension and the plurigenera. I will later move on and discuss the difficulties of working with non-integrable structures. In this case, one has to combine in a clever way techniques from symplectic topology and differential geometry to prove interesting results. We will conclude by speculating on what could be a possible shape of the classification, especially in relation with some recent conjecture by Chen and Zhang.

 

Speaker: Kirill Zaynullin

Title: Cohomology of a linear algebraic group: chasing the Hopf structure

Abstract: In the talk we show how categorical methods (duoidal categories of bimodules) can be successfully applied to study geometric objects (algebraic/Lie groups). More precisely, we explain how to lift the classical Hopf structure on an oriented cohomology of a linear algebraic group to the bi-Hopf structure on the associated equivariant oriented cohomology of a flag variety. This is an overview of recent joint projects with Martina Lanini, Rui Xiong and Changlong Zhong.

 

All interested are invited to participate


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