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 Warwick 29th November 2024
Room B1.01, Zeeman Building, 14:00 - 18:00
Local Organiser: Marc Truter
14:00: Menelaos Zikidis (University of Sheffield)
Title: Joyce Structures on Spaces of Bridgeland Stability Conditions
Abstract: In this lecture I will try to convey the essence behind the notion of a Joyce structure, concentrating on fundamental examples. Joyce structures are geometric structures on spaces of Bridgeland stability conditions Stab(D) aiming to encode geometrically Donaldson-Thomas invariants of triangulated Calabi-Yau 3 categories D. The theory can be made explicit in a large class of examples where Stab(D) is identified with the moduli of meromorphic quadratic differentials on algebraic curves. In this case the geometric structure arises, via isomonodromic deformations of Stokes-Riemann-Hilbert data, as a family of non-linear Ehresmann connections on a modulispace parametrizing wild algebraic curves, wild parabolic bundles, irregular Higgs fields and flat connections. Such a Joyce structure equips this space of irregular objects with a Complex Hyperkähler structure and an associated Twistor space.
15:30: James Jones (Loughborough University)
Title: Type II Degenerations of Degree 4 K3 Surfaces
Abstract: Moduli spaces of K3 surfaces have long been studied, beginning with the proof of the Torelli theorem for K3s in the 70s. The most well-known compactification of this moduli space is still probably the Baily-Borel compactification, whose boundary components consist of Type II and Type III degenerations. Meanwhile, the GIT compactification is able to explicitly describe its boundary components, often by equations as studied by Shah in the 80s and more recently by Laza and O'Grady. In this talk we provide the requisite definitions of degenerations, giving examples along the way. The punchline of the talk is an explicit classification of all Type II degenerations of degree 4 K3 surfaces.
17:00: Aporva Varshney (University College London)
Title: The Derived Category of a Singular Variety
Abstract: When varieties become singular, they wreak havoc on the derived category. Nonetheless, we must reckon with singularities in some way: since we started caring about things like minimal models and moduli spaces, they’ve become all too prevalent, and derived categories can be a very useful tool to study geometry. I’ll give a (hopefully) accessible introduction on how we can reconcile these two foes: first we’ll look at an example of a nodal curve and explore what goes wrong in the derived category. This will lead us to the idea of “categorical absorption” (following work of Kuznetsov-Shinder) which breaks down the derived category into a smooth component and a singular component. Importantly for nodal varieties, this singular component behaves nicely under smoothings. Time permitting, we’ll also look at a small generalization to non-isolated singularities.
University of Warwick 29th November 2024
Room B1.01, Zeeman Building, 14:00 - 18:00
Local Organiser: Marc Truter
14:00: Menelaos Zikidis (University of Sheffield)
Title: Joyce Structures on Spaces of Bridgeland Stability Conditions
Abstract: In this lecture I will try to convey the essence behind the notion of a Joyce structure, concentrating on fundamental examples. Joyce structures are geometric structures on spaces of Bridgeland stability conditions Stab(D) aiming to encode geometrically Donaldson-Thomas invariants of triangulated Calabi-Yau 3 categories D. The theory can be made explicit in a large class of examples where Stab(D) is identified with the moduli of meromorphic quadratic differentials on algebraic curves. In this case the geometric structure arises, via isomonodromic deformations of Stokes-Riemann-Hilbert data, as a family of non-linear Ehresmann connections on a modulispace parametrizing wild algebraic curves, wild parabolic bundles, irregular Higgs fields and flat connections. Such a Joyce structure equips this space of irregular objects with a Complex Hyperkähler structure and an associated Twistor space.
15:30: James Jones (Loughborough University)
Title: Type II Degenerations of Degree 4 K3 Surfaces
Abstract: Moduli spaces of K3 surfaces have long been studied, beginning with the proof of the Torelli theorem for K3s in the 70s. The most well-known compactification of this moduli space is still probably the Baily-Borel compactification, whose boundary components consist of Type II and Type III degenerations. Meanwhile, the GIT compactification is able to explicitly describe its boundary components, often by equations as studied by Shah in the 80s and more recently by Laza and O'Grady. In this talk we provide the requisite definitions of degenerations, giving examples along the way. The punchline of the talk is an explicit classification of all Type II degenerations of degree 4 K3 surfaces.
17:00: Aporva Varshney (University College London)
Title: The Derived Category of a Singular Variety
Abstract: When varieties become singular, they wreak havoc on the derived category. Nonetheless, we must reckon with singularities in some way: since we started caring about things like minimal models and moduli spaces, they’ve become all too prevalent, and derived categories can be a very useful tool to study geometry. I’ll give a (hopefully) accessible introduction on how we can reconcile these two foes: first we’ll look at an example of a nodal curve and explore what goes wrong in the derived category. This will lead us to the idea of “categorical absorption” (following work of Kuznetsov-Shinder) which breaks down the derived category into a smooth component and a singular component. Importantly for nodal varieties, this singular component behaves nicely under smoothings. Time permitting, we’ll also look at a small generalization to non-isolated singularities.
Recent Meeting:
University of Bath 16th May 2024
Room 1.1, 6 West 13:00-17:00
16:00: Oliver Daisey (Durham University)
Title: A Laurent Phenomenon for the Cayley Plane
Abstract: I will describe a Laurent phenomenon for the Cayley plane, which is the homogeneous variety associated to the cominuscule representation of E_6. The corresponding Laurent phenomenon algebra has finite type and appears in a natural sequence of LPAs indexed by the E_n Dynkin diagrams for n<7. I will introduce a conjecture on the existence of a further finite type LPA, associated to the Freudenthal variety of type E_7. This is a joint work with Tom Ducat.
14:30: Rhiannon Savage (Oxford University)
Title: A Representability Theorem for Stacks in Derived Geometry Contexts
Abstract: The representability theorem for stacks, due to Artin in the underived setting and Lurie in the derived setting, gives conditions under which a stack is representable by an n-geometric stack. In recent work of Ben-Bassat, Kelly, and Kremnizer, a new theory of derived analytic geometry has been proposed as geometry relative to the ∞-category of simplicial commutative Ind-Banach R-modules, for R a Banach ring. In this talk, I will present a representability theorem which holds in a very general context, encompassing both the derived algebraic geometry context of Toën and Vezzosi and these new derived analytic geometry contexts.
13:00: Yannik Schuler (University of Sheffield)
Title: Tangents to Nodal Cubic
Abstract: Given a plane nodal cubic D, how many straight lines are there meeting D in exactly one point? This question can be treated using classical techniques in Algebraic Geometry which return the correct answer (three). However, just a slight generalisation of this exercise (e.g. the enumeration of higher degree and higher genus parametrised curves maximally tangent to D) renders standard techniques essentially useless. In my talk I will present a correspondence which translates questions about maximally tangent curves to D phrased in the framework of logarithmic Gromov-Witten theory to the Gromov-Witten theory of local P1 which is solved completely by the topological vertex. This is joint work with Michel van Garrel and Navid Nabijou.
University of Bath 16th May 2024
Room 1.1, 6 West 13:00-17:00
16:00: Oliver Daisey (Durham University)
Title: A Laurent Phenomenon for the Cayley Plane
Abstract: I will describe a Laurent phenomenon for the Cayley plane, which is the homogeneous variety associated to the cominuscule representation of E_6. The corresponding Laurent phenomenon algebra has finite type and appears in a natural sequence of LPAs indexed by the E_n Dynkin diagrams for n<7. I will introduce a conjecture on the existence of a further finite type LPA, associated to the Freudenthal variety of type E_7. This is a joint work with Tom Ducat.
14:30: Rhiannon Savage (Oxford University)
Title: A Representability Theorem for Stacks in Derived Geometry Contexts
Abstract: The representability theorem for stacks, due to Artin in the underived setting and Lurie in the derived setting, gives conditions under which a stack is representable by an n-geometric stack. In recent work of Ben-Bassat, Kelly, and Kremnizer, a new theory of derived analytic geometry has been proposed as geometry relative to the ∞-category of simplicial commutative Ind-Banach R-modules, for R a Banach ring. In this talk, I will present a representability theorem which holds in a very general context, encompassing both the derived algebraic geometry context of Toën and Vezzosi and these new derived analytic geometry contexts.
13:00: Yannik Schuler (University of Sheffield)
Title: Tangents to Nodal Cubic
Abstract: Given a plane nodal cubic D, how many straight lines are there meeting D in exactly one point? This question can be treated using classical techniques in Algebraic Geometry which return the correct answer (three). However, just a slight generalisation of this exercise (e.g. the enumeration of higher degree and higher genus parametrised curves maximally tangent to D) renders standard techniques essentially useless. In my talk I will present a correspondence which translates questions about maximally tangent curves to D phrased in the framework of logarithmic Gromov-Witten theory to the Gromov-Witten theory of local P1 which is solved completely by the topological vertex. This is joint work with Michel van Garrel and Navid Nabijou.
