The following is our current schedule, but see here for previous talks.

Speaker: Sebastian Opper
Date: 20 October 2025, 4pm CET
Title: Derived Picard groups and Lie theory

Abstract

We discuss how to compute derived Picard groups (enhanced autoequivalence groups) of Fukaya categories of surfaces after Bocklandt and Haiden-Katzarkov-Kontsevich, and the related nodal stacky curves. I will also explain how solving this problem naturally leads to a very general analogy between Lie groups, Lie algebras, derived Picard groups and Hochschild cohomology.

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Speaker: Calum Crossley
Date: 3 November 2025, 4pm CET
Title: Categorical resolutions from geometry
slides | video

Abstract

This will be a survey on categorical resolutions, in the context of conjectures relating derived categories to birational geometry. Examples using matrix factorizations give a geometric perspective, shedding light on various aspects of these resolutions: crepancy and minimality, null categories, and relations to singular equivalences.

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Speaker: Céline Fietz
Date: 17 November 2025, 4pm CET
Title: Categorical resolutions of cuspidal singularities

Abstract

In this talk I will explain that there exists a particularly small (“crepant”) categorical resolution of the derived category of a projective variety with an isolated A_2/cuspidal singularity. More importantly, one can describe generators of its kernel in a very explicit way: In the case of an even dimensional variety with an isolated A_2 singularity, the kernel can be generated by two 2-spherical objects, which are related to spinor sheaves on a nodal quadric and induce autoequivalences on the categorical resolution.

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Speaker: Prashanth Sridhar
Date: 8 December 2025, 4pm CET
Title: Differential Graded Noncommutative Geometry
slides

Abstract

Pioneering work of Artin-Tate-Van den Bergh-Zhang extends important aspects of projective geometry to the noncommutative (nc) setting. In particular, the derived category of such a nc scheme shares many features with the derived category of a classical one. In this talk, I'll discuss extensions of some classical and modern results in the theory of nc projective geometry to nc spaces associated to dg-algebras. The focus will be on applications to projective varieties: for instance, this approach results in an analog of a landmark theorem of Orlov concerning the derived category of a complete intersection for any projective variety.

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Speaker: Aporva Varshney
Date: 15 December 2025, 4pm CET
Title: Stringy Kähler moduli of flops using GIT
slides

Abstract

According to predictions coming from physicists and mirror symmetry, the fundamental group of the "stringy Kahler moduli space" of a variety acts on the derived category by autoequivalences. However, it is unclear how to compute or even define this space in full generality. I will discuss two approaches given in the literature, one using Bridgeland stability manifolds and the other based in GIT and window subcategories. We will see that these two approaches agree for single curve threefold flops of lengths one and two. This is based on work in arxiv:2508.05285.

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