During Fall 2025, we meet on Thursdays at 10:15 at MA B1 524.

Oct 02- Alapan Mukhopadhyay

Generic Local Duality and Purity Exponents 

Oct 09- Raymond Cheng

Obstructions to unirationality for product-quotient surfaces over F_p 

Oct 16- Linus Eric Rösler

Asymtotic Samuel Functions and Applications 

Oct 23- Holiday

Oct 30- Léo Navarro Chafloque

Quasi F splitting of smooth weak del Pezzos in mixed characteristics 

Nov 06- Archi Kaushik

Title: Moduli of sheaves on the blow-up of a surface.

Abstract: The Hilbert Scheme of n points of a smooth complex surface S, denoted by Hilb_n(S), is an important moduli space that parameterises dim 0 sub-schemes of S of length n. One notes that Hilb_n(-) is not a functor, for example: Let p: Bl_p S -> S be the blow-up of a point on S, then p induces a birational map between the Hilbert schemes which doesn't extend to a morphism. In our talk we examine this birational map from the point of view of the MMP and enumerative invariants ie. singular cohomology and the derived category of coherent sheaves.

First, we discuss a classical wall-crossing construction of Nakajima and Yoshioka [https://arxiv.org/abs/0806.0463]. They realise both Hilb(S) and Hilb^{n}(Bl_p S) as moduli spaces of so-called perverse coherent sheaves on the blow-up of a surface with different stability parameters and are in particular able to relate the Betti numbers of the two spaces by an elegant formula. Then we discuss recent works of Koseki (https://arxiv.org/pdf/1907.08885 and https://arxiv.org/pdf/2110.08315), who shows that the wall crossing construction mentioned above realises an MMP for Hilb(Bl_p S) terminating at Hilb(S) for S=A^2. Furthermore, Koseki computes a semi-orthogonal decomposition of the derived category of Hilbert scheme of the blow-up thereby categorifying the Betti numbers formula of Nakajima and Yoshioka.

........................................................................................................................................................................................

Nov 13- Emre Alp Özavci

Antiampleness and ampleness of the Frobenius Kernel 

Nov 20- Zsolt Patakfalvi

Nov 27- Basel, EPFL, Neuchatel, Dijon, Zurich meeting

Dec 04- Domenico Valloni

Dec 11- Nikolaos Tsakanikas

Dec 18- Jefferson Baudin