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 2022/23 are, Girtrude Hamm (Nottingham), James Jones (Loughborough), and Patrick Kennedy-Hunt (Cambridge), 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.
The Calf will maintain a hybrid approach to delivering the seminar, with talks delivered in person and with the option for those who cannot make the seminar in person to join via Zoom. The link to join will be in an email announcement made via the COW mailing list. If you do not have the link and wish to attend, please email one of the organisers.
About the Calf
Calf is the junior COW, an algebraic geometry seminar group primarily aimed at PhD students.
The organisers for academic year 2022/23 are, Girtrude Hamm (Nottingham), James Jones (Loughborough), and Patrick Kennedy-Hunt (Cambridge), 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.
The Calf will maintain a hybrid approach to delivering the seminar, with talks delivered in person and with the option for those who cannot make the seminar in person to join via Zoom. The link to join will be in an email announcement made via the COW mailing list. If you do not have the link and wish to attend, please email one of the organisers.
Recent Meeting:
Cambridge 21/11/22
Marta Benozzo (University College London)
Title: A canonical bundle formula in positive characteristic
Abstract: An important problem in birational geometry is trying to relate in a meaningful way the canonical bundles of the source and the base of a fibration. The first result in this area is Kodaira’s canonical bundle formula for elliptic fibrations on surfaces. Until recent developments, in characteristic 0 more general results had been established only thanks to Hodge theory which is a tool that we cannot use in positive characteristic. One of the main differences between characteristic 0 and positive characteristic is the presence of purely inseparable maps. The Frobenius can be an enemy of algebraic geometers, giving counterexamples to many conjectures, but it can also be a powerful tool. During the talk, we will see how we can exploit the Frobenius to get a canonical bundle formula in positive characteristic, following the work of Das-Schwede.
Sebastian Schlegel Mejia (University of Edinburgh)
Title: On BPS cohomology
Abstract: Since its inception 20 years ago as an enumerative theory of sheaves on Calabi-Yau 3-folds, Donaldson-Thomas theory has evolved and reached far beyond its original domain with applications in subjects such as quantum groups, cluster algebras, and nonabelian Hodge Theory. A key role in many of these applications is played by BPS invariants and BPS cohomology which intuitively are a count of simple objects in certain abelian categories of homological dimension no more than 3. My talk is an introduction to BPS cohomology. There will be examples and computations. Time permitting I will talk about the (mostly conjectural) chi-independence phenomenon for BPS cohomology and its applications.
George Cooper (University of Oxford)
Title: Compactified Universal Jacobians over Stacks of Stable Curves via GIT
Abstract: Associated to any smooth projective curve C is its degree d Jacobian variety, parametrising isomorphism classes of degree d line bundles on C. Letting the curve vary as well, one is led to the universal Jacobian stack. This stack admits several compactifications over the stack of marked stable curves, depending on the choice of a stability condition. In this talk I will introduce these compactified universal Jacobians, and explain how their moduli spaces can be constructed using Geometric Invariant Theory (GIT).
Recent Meeting:
Cambridge 21/11/22
Marta Benozzo (University College London)
Title: A canonical bundle formula in positive characteristic
Abstract: An important problem in birational geometry is trying to relate in a meaningful way the canonical bundles of the source and the base of a fibration. The first result in this area is Kodaira’s canonical bundle formula for elliptic fibrations on surfaces. Until recent developments, in characteristic 0 more general results had been established only thanks to Hodge theory which is a tool that we cannot use in positive characteristic. One of the main differences between characteristic 0 and positive characteristic is the presence of purely inseparable maps. The Frobenius can be an enemy of algebraic geometers, giving counterexamples to many conjectures, but it can also be a powerful tool. During the talk, we will see how we can exploit the Frobenius to get a canonical bundle formula in positive characteristic, following the work of Das-Schwede.
Sebastian Schlegel Mejia (University of Edinburgh)
Title: On BPS cohomology
Abstract: Since its inception 20 years ago as an enumerative theory of sheaves on Calabi-Yau 3-folds, Donaldson-Thomas theory has evolved and reached far beyond its original domain with applications in subjects such as quantum groups, cluster algebras, and nonabelian Hodge Theory. A key role in many of these applications is played by BPS invariants and BPS cohomology which intuitively are a count of simple objects in certain abelian categories of homological dimension no more than 3. My talk is an introduction to BPS cohomology. There will be examples and computations. Time permitting I will talk about the (mostly conjectural) chi-independence phenomenon for BPS cohomology and its applications.
George Cooper (University of Oxford)
Title: Compactified Universal Jacobians over Stacks of Stable Curves via GIT
Abstract: Associated to any smooth projective curve C is its degree d Jacobian variety, parametrising isomorphism classes of degree d line bundles on C. Letting the curve vary as well, one is led to the universal Jacobian stack. This stack admits several compactifications over the stack of marked stable curves, depending on the choice of a stability condition. In this talk I will introduce these compactified universal Jacobians, and explain how their moduli spaces can be constructed using Geometric Invariant Theory (GIT).
This page is maintained by Chris Seaman.
