Calf Seminar
About the Calf
Calf is the junior COW, an algebraic geometry seminar group primarily aimed at PhD students.
The organisers for academic year 2024/25 are Heath Pearson (Nottingham), Siao Chi Mok (Cambridge), and Alexander Fruh (Birmingham), as well as an extensive network of local organisers at different universities. Calf announcements are made using the COW mailing list. If you would like to get involved in the organisation, or suggest your institution as the next venue, please contact any of the people named above.
The COW seminar has some funding for travel expenses, and information on reimbursement can be found on the main COW webpage.
About the Calf
Calf is the junior COW, an algebraic geometry seminar group primarily aimed at PhD students.
The organisers for academic year 2024/25 are Heath Pearson (Nottingham), Siao Chi Mok (Cambridge), and Alexander Fruh (Birmingham), as well as an extensive network of local organisers at different universities. Calf announcements are made using the COW mailing list. If you would like to get involved in the organisation, or suggest your institution as the next venue, please contact any of the people named above.
The COW seminar has some funding for travel expenses, and information on reimbursement can be found on the main COW webpage.
Upcoming Meeting:
University of Nottingham, Wednesday 26th March 2025
Room A17, School of Mathematical Sciences, 13:00 - 18:00
13:00: Hamdi Dërvodeli (University of Warwick)
Title: Reducible varieties and tropical geometry
Abstract: The factoring locus of a polynomial is a list of conditions on its coefficients under which the polynomial factors. The aim of this talk is to explore connections tropical geometry has with this factoring locus. More generally, we want to know if the reducibility of a classical variety is detected by the tropicalization of its defining ideal. We wonder the same about the singular locus of a classical variety.
14:10: Jingxiang Ma (University of Sheffield)
Title: Mirror symmetry for ADE resolutions
Abstract: I will discuss two constructions associated with ADE Dynkin diagrams. The first is the quantum cohomology of minimal resolutions of du Val singularities, which admit an ADE classification. The second is a family of curves on a one-dimensional extension of the Cartan subalgebra, arising purely from a representation of the corresponding Lie algebra. I will explain how this second construction provides mirrors for all ADE resolutions and discuss potential applications. This talk is based on recent joint work with Andrea Brini and Ian Strachan.
17:00: Parth Shimpi (University of Glasgow)
Title: Heart-to-heart on rational curves
Abstract: Bounded hearts on derived categories have been an indispensable homological tool for studying equivalences of categories in algebra and geometry. Neighbourhoods of rational curves provide a natural playground where algebra and geometry collide and interact— the categories of coherent sheaves are derived equivalent to finite dimensional algebras and we find machinery from both worlds at our disposal. I will talk through some of the story, and explain recent work on classification of all possible hearts in such a category.
University of Nottingham, Wednesday 26th March 2025
Room A17, School of Mathematical Sciences, 13:00 - 18:00
13:00: Hamdi Dërvodeli (University of Warwick)
Title: Reducible varieties and tropical geometry
Abstract: The factoring locus of a polynomial is a list of conditions on its coefficients under which the polynomial factors. The aim of this talk is to explore connections tropical geometry has with this factoring locus. More generally, we want to know if the reducibility of a classical variety is detected by the tropicalization of its defining ideal. We wonder the same about the singular locus of a classical variety.
14:10: Jingxiang Ma (University of Sheffield)
Title: Mirror symmetry for ADE resolutions
Abstract: I will discuss two constructions associated with ADE Dynkin diagrams. The first is the quantum cohomology of minimal resolutions of du Val singularities, which admit an ADE classification. The second is a family of curves on a one-dimensional extension of the Cartan subalgebra, arising purely from a representation of the corresponding Lie algebra. I will explain how this second construction provides mirrors for all ADE resolutions and discuss potential applications. This talk is based on recent joint work with Andrea Brini and Ian Strachan.
17:00: Parth Shimpi (University of Glasgow)
Title: Heart-to-heart on rational curves
Abstract: Bounded hearts on derived categories have been an indispensable homological tool for studying equivalences of categories in algebra and geometry. Neighbourhoods of rational curves provide a natural playground where algebra and geometry collide and interact— the categories of coherent sheaves are derived equivalent to finite dimensional algebras and we find machinery from both worlds at our disposal. I will talk through some of the story, and explain recent work on classification of all possible hearts in such a category.
Recent Meeting:
University of Cambridge, Friday 17th January 2025
MR4, Centre for Mathematical Sciences, 13:00 - 17:00
13:00: Terry Song (University of Cambridge)
Title: Genus one stable maps and Vakil—Zinger moduli space
Abstract: In this talk I will introduce the Kontsevich space of genus one stable maps and desingularisation of its main component, which is constructed by Vakil—Zinger and admits an interpretation in logarithmic geometry by Ranganathan—Santos-Parker—Wise. If time permits, I will present calculations on Euler characteristics and Betti numbers that offer a quantitative comparison between the two moduli spaces. Partly based on joint work with Siddarth Kannan.
14:30: Patience Ablett (University of Warwick)
Title: Gotzmann's persistence theorem for smooth projective toric varieties
Abstract: Gotzmann's persistence theorem is a useful tool for finding equations of the Hilbert scheme parameterising subschemes of projective space. From the commutative algebra perspective, there is a natural way to generalise such Hilbert schemes to any smooth projective toric variety. A key example we will discuss is the Hilbert scheme parameterising subschemes of the product of projective spaces. We will see how Gotzmann's persistence theorem generalises to this setting.
16:00: Thamarai Valli Venkatachalam (UCL)
Title: Complete intersections in toric varieties
Abstract: Toric varieties, with their rich combinatorial structure, simplify computations, and their complete intersections inherit these advantages. In this talk, I will introduce toric varieties as GIT quotients and explore complete intersections within these varieties, along with their combinatorial properties. We will also examine how these properties aid in classifying Fano varieties. If time permits, I will discuss my ongoing work on the classification of Fano complete intersections in toric varieties.
University of Cambridge, Friday 17th January 2025
MR4, Centre for Mathematical Sciences, 13:00 - 17:00
13:00: Terry Song (University of Cambridge)
Title: Genus one stable maps and Vakil—Zinger moduli space
Abstract: In this talk I will introduce the Kontsevich space of genus one stable maps and desingularisation of its main component, which is constructed by Vakil—Zinger and admits an interpretation in logarithmic geometry by Ranganathan—Santos-Parker—Wise. If time permits, I will present calculations on Euler characteristics and Betti numbers that offer a quantitative comparison between the two moduli spaces. Partly based on joint work with Siddarth Kannan.
14:30: Patience Ablett (University of Warwick)
Title: Gotzmann's persistence theorem for smooth projective toric varieties
Abstract: Gotzmann's persistence theorem is a useful tool for finding equations of the Hilbert scheme parameterising subschemes of projective space. From the commutative algebra perspective, there is a natural way to generalise such Hilbert schemes to any smooth projective toric variety. A key example we will discuss is the Hilbert scheme parameterising subschemes of the product of projective spaces. We will see how Gotzmann's persistence theorem generalises to this setting.
16:00: Thamarai Valli Venkatachalam (UCL)
Title: Complete intersections in toric varieties
Abstract: Toric varieties, with their rich combinatorial structure, simplify computations, and their complete intersections inherit these advantages. In this talk, I will introduce toric varieties as GIT quotients and explore complete intersections within these varieties, along with their combinatorial properties. We will also examine how these properties aid in classifying Fano varieties. If time permits, I will discuss my ongoing work on the classification of Fano complete intersections in toric varieties.
