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 2023/24 are Ajith Urundolil-Kumaran (Cambridge), Austin Hubbard (Bath), and Josh Kimberley (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 2023/24 are Ajith Urundolil-Kumaran (Cambridge), Austin Hubbard (Bath), and Josh Kimberley (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:
Once a date is set, information regarding the next Calf meting will appear here.
Once a date is set, information regarding the next Calf meting will appear here.
Recent Meeting:
University of Cambridge 22nd November 2023
Room MR3, Centre for Mathematical Sciences 13:00-17:00
13:00: Shivang Jindal (University of Edinburgh)
Title: Quantum groups from Donaldson-Thomas theory
Abstract: In 2012, Schiffmann and Vasserot considered a Hall algebra type construction on the cohomology of moduli stack of sheaves supported on points on a plane and used it in their proof's of AGT conjecture. However due to the mysterious nature of the moduli of representations of pre-projective algebra, these algebras are very hard to study and are often highly non trivial. They are conjectured to be the same as Maulik-Okounkov Yangians which has further applications to Quantum Cohomology. In this talk, my goal is to explain how one can use tools from Cohomological DT theory to study these algebras. In particular, I will explain how for the case of cyclic quiver, this algebra turns out to be one half of the universal enveloping algebra of the Lie algebra of matrix differential operators on the torus, while its deformation turn out be one half of an explicit integral form of the Affine Yangian of gl(n).
14:30: Joseph Malbon (University of Edinburgh)
Title: Explicit K-Stability of Fano threefolds
Abstract: The construction of well-behaved moduli spaces of Fano varieties is a historically difficult one, the fundamental obstruction being that the space is not automatically separated, this being case with canonical polarised and Calabi-Yau varieties. In this talk, we will introduce the notion of K-stability, which within the last decade or so has recently been understood to offer the correct property for the objects parametrised to possess in order to overcome this difficulty. Our focus will be the explicit description of the K-stable objects within a deformation family of smooth Fano threefolds.
16:00: Siao Chi Mok (University of Cambridge)
Title: Logarithmic Fulton-MacPherson configuration spaces
Abstract: In 1994, Fulton and MacPherson constructed a compactification of the configuration space of points on a projective manifold. The compactification has excellent properties - it is smooth and projective with normal crossings boundary. As part of their foundational study, Fulton and MacPherson gave an explicit presentation of the cohomology ring of their spaces. In this talk, I will recall the construction of the Fulton--MacPherson spaces, and then explain the generalization of the construction to the simple normal crossings pair setting. Precisely, given a variety X and a normal crossings divisor D, I will explain how one can compactify the configuration space of n distinct points on X that lie away from D. I will also mention some of the properties that this compactification satisfies. Time permitting, we will discuss some future directions of this project. This is work in progress.
University of Cambridge 22nd November 2023
Room MR3, Centre for Mathematical Sciences 13:00-17:00
13:00: Shivang Jindal (University of Edinburgh)
Title: Quantum groups from Donaldson-Thomas theory
Abstract: In 2012, Schiffmann and Vasserot considered a Hall algebra type construction on the cohomology of moduli stack of sheaves supported on points on a plane and used it in their proof's of AGT conjecture. However due to the mysterious nature of the moduli of representations of pre-projective algebra, these algebras are very hard to study and are often highly non trivial. They are conjectured to be the same as Maulik-Okounkov Yangians which has further applications to Quantum Cohomology. In this talk, my goal is to explain how one can use tools from Cohomological DT theory to study these algebras. In particular, I will explain how for the case of cyclic quiver, this algebra turns out to be one half of the universal enveloping algebra of the Lie algebra of matrix differential operators on the torus, while its deformation turn out be one half of an explicit integral form of the Affine Yangian of gl(n).
14:30: Joseph Malbon (University of Edinburgh)
Title: Explicit K-Stability of Fano threefolds
Abstract: The construction of well-behaved moduli spaces of Fano varieties is a historically difficult one, the fundamental obstruction being that the space is not automatically separated, this being case with canonical polarised and Calabi-Yau varieties. In this talk, we will introduce the notion of K-stability, which within the last decade or so has recently been understood to offer the correct property for the objects parametrised to possess in order to overcome this difficulty. Our focus will be the explicit description of the K-stable objects within a deformation family of smooth Fano threefolds.
16:00: Siao Chi Mok (University of Cambridge)
Title: Logarithmic Fulton-MacPherson configuration spaces
Abstract: In 1994, Fulton and MacPherson constructed a compactification of the configuration space of points on a projective manifold. The compactification has excellent properties - it is smooth and projective with normal crossings boundary. As part of their foundational study, Fulton and MacPherson gave an explicit presentation of the cohomology ring of their spaces. In this talk, I will recall the construction of the Fulton--MacPherson spaces, and then explain the generalization of the construction to the simple normal crossings pair setting. Precisely, given a variety X and a normal crossings divisor D, I will explain how one can compactify the configuration space of n distinct points on X that lie away from D. I will also mention some of the properties that this compactification satisfies. Time permitting, we will discuss some future directions of this project. This is work in progress.
