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04/05/2026, 09:15
Title:
Pure extension of the theta divisor on a family of abelian varietiesAbstract
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A symmetric line bundle L on an abelian variety has the useful property that pulling it back along the `multiplication by n’ map is the same as raising it to the n-th tensor power; we say L has pure weight 2. In particular this holds for a symmetric ample line bundle representing a polarisation. Such a... -
04/05/2026, 11:00
Title: The Taylor expansion of the Torelli map and applications to intersection theory
Abstract: Using results of Hu, Norton '18 and Yamada '80, we can deduce the full Taylor expansions of the Torelli map and the Prym map at the boundary in terms of plumbing coordinates. We use the Taylor expansion to determine the scheme structure for the fiber product of the Torelli map $t: M_g^{ct}...
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04/05/2026, 16:00
Title: Fourier-Mukai transforms and log geometry.
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Abstract:
I will review progress in our understanding of the intersection theory of degenerating families of abelian schemes, namely the compactified Jacobians and Mumford's canonical partial compactification of the moduli space of principally polarized abelian varieties, parametrizing degenerations of torus rank at most one. I will state... -
04/05/2026, 17:45
Title: Lines in the plane
Abstract: I will discuss intersection theory on the moduli space of lines in the plane — the 2-dimensional generalization of stable pointed rational curves. I will present a few different paths to compact moduli spaces of these objects, touching on work of many others, including KSBA, Kapranov, Lafforgue, and Kennedy-Hunt. One path leads to a space with a virtual...
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05/05/2026, 09:15
Title: A tale of two Fourier transforms: universal Jacobians and hyper-Kähler varieties
Abstract: Fourier transforms for abelian varieties have been studied for decades since the work of Beauville in the 80s. The purpose of this talk is to explain how these ideas can be applied to the study of two different types of geometric objects: universal compactified Jacobians and hyper-Kähler...
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05/05/2026, 11:00
Title: GW/PT correspondence for toric pairs
Abstract: I will discuss work with Dhruv Ranganathan, in which we prove the primary and descendent GW/PT correspondence for snc pairs (X,D) where X is a toric threefold and D is a union of toric divisors. Even when D is empty, where everything has been known for a while, I’ll try to explain how the log approach gives a new proof and even...
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05/05/2026, 16:00
Title: Weight calculations and the tautological ring
Abstract: Most questions about the intersection theory of the toroidal compactifications of A_g are unanswered. In this talk, I will explain how we can solve most of these for the simplest compactification given by torus rank 1 degenerations. The main technique is an extended theory of weights. We can compute these explicitly in the...
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05/05/2026, 17:45
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06/05/2026, 09:15
Title: Families of G-curves and maximal monodromy
Abstract: Maximality results for the monodromy of families of algebraic varieties are widely studied in algebraic geometry. In this talk, we study the monodromy of families of Galois coverings of curves. The natural action of the Galois group G on cohomology induces a decomposition of the associated variation of Hodge structures, and under a...
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06/05/2026, 11:00
Title: The low degree cohomology of compactifications of $A_g$
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Abstract:
I will report on joint work with Samir Canning and Dan Petersen
determining which irreducible Galois representations can occur in the
low degree cohomology of any smooth toroidal compactification of $A_g$
or $X_{g,s}$, the $s$-fold fiber product of the universal abelian
variety. -
06/05/2026, 16:00
TITLE: On the classification of modular compactification of the universal Jacobian
ABSTRACT: I will first report on a joint work with M. Fava and N. Pagani in which we give a complete classification of all the modular compactifications of the universal Jacobian over the moduli stack of pointed stable curves. Then, I will discuss the relationship between these modular compactifications and...
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06/05/2026, 17:45
Title: On the elliptic genera of Quot schemes of zero dimensional quotients on curves
Abstract: We study Quot schemes of rank zero quotients on smooth projective curves. For quotients of a vector bundle of even rank, we present a formula for the level 2 elliptic genus. We also propose a conjectural generalization to higher level elliptic genera and provide supporting evidence.
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07/05/2026, 09:15
Title: Perspectives on the stable cohomology of compactifications of A_g
Abstract: By classical work of Borel, it is well known that the rational
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cohomology of the moduli space A_g of principally polarized abelian
varieties of dimension g stabilizes in degree k<g, In this talk, I would
like to review stability results on compactifications of A_g, such as
the Satake compactification and... -
07/05/2026, 11:00
Title: Curve-Jacobian correspondence
Abstract: By the Riemann-Roch theorem, when m> 2g-2, the m-th symmetric product of a smooth projective curve is a projective bundle over its Jacobian. It is natural to ask whether this relationship extends to families of curves that may have singularities.In this talk, I will describe a correspondence between algebraic cycles on the universal...
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07/05/2026, 12:30
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08/05/2026, 09:15
Title: Non-trivial cohomology of strata of differentials
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Abstract: A stratum of differentials is the moduli space of complex curves together with a meromorphic form with prescribed multiplicities of zeros and poles. The strata are phase spaces of an action of SL(2, R) and thus the central object of study in Teichmuller dynamics. On the other hand, they give natural high codimension... -
08/05/2026, 10:45
Title: Matroids and the integral Hodge conjecture
Abstract: Associated to any regular matroid of rank g on k elements, one can associate a multivariable semistable degeneration of principally polarized abelian g-folds over a k-dimensional base. I will discuss joint work with de Gaay Fortman and Schreieder, proving that a combinatorial invariant of the matroid obstructs the algebraicity of...
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