Algebraic Geometry Seminar
Spring 2026
Regular Day: Tuesday
Regular Time: 3:30PM - 4:30PM
Regular Location: LCB 215
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January 6 |
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January 13 |
Javier Carvajal-Rojas
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How much of the geometry of a positive characteristic variety is encoded in its Frobenius? I'll give exact answers to this vague question in the toric case. For this, I'll introduce a Frobenius-theoretic cone sitting inside the pseudo-effective cone whose interaction with the other nef/ample/big cones determines the type of extremal contractions a variety can undergo. This leads to a geometric characterization of when the kernel of the Frobenius trace is; respectively, big, ample, and nef. This talk is based on my joint work with Emrezavci (EPFL), arXiv:2506.02994.
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February 5 Thursday |
Aaron Bertram
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Reider's Theorem is a remarkably precise criterion for very ampleness
of line bundles of the form K_S + D on an algebraic surface. By using Bridgeland
stability conditions and various theorems about the moduli spaces of stable objects, we
can extract information about the birational geometry of the blow-up of
the projective space |K_S + D|^vee along the surface, analogous to results of Thaddeus
in the curve case. This is part of a program that I am working on with my graduate students
in Utah and Macri's laboratory in Paris.
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February 10 |
TBA
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February 17 |
Marta Benozzo
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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 instance of such a formula is Kodaira's canonical bundle formula for surfaces which admit a fibration with elliptic fibres. It describes the relation between the canonical bundles in terms of the singularities of the fibres and their j-invariants. In higher dimension, we do not have an equivalent of the j-invariant, but we can still define a moduli part. Over fields of characteristic 0, positivity properties of the moduli part have been studied using variations of Hodge structures. Recently, the problem has been addressed with the minimal model program for foliations, which is known to fail in positive characteristic. In this talk I will explain an approach to the canonical bundle formula which adapts these methods in positive characteristic.
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February 24 |
TBA
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March 3 |
TBA
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March 10 |
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March 17 |
TBA
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March 24 @4pm |
Zhijia Zang
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Let X be a variety carrying a generically free regular action from a group G. We say X is G-unirational if there exists a dominant G-equivariant rational map from a linear G-representation V to X. This notion is
closely related to unirationality over non-closed fields and the group cohomology of G. In this talk, I will
explain these relations and study G-unirationality on some Fano threefolds and toric threefolds. This is joint
work with Yuri Tschinkel and Ivan Cheltsov.
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March 31 |
TBA
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April 2 Colloquium @4pm in LCB 215 |
Vasudevan Srinivas
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April 3 Joint Seminar with CA @2pm in LCB 222 |
Vasudevan Srinivas
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This talk will discuss some results on etale fundamental groups of varieties over an algebraically closed field of characteristic p > 0, based on joint work with Hélène Esnault and other coauthors. One result, along with Mark Schusterman, is that the tame fundamental group is finitely presented for such a variety which is the complement of an SNC divisor in a smooth projective variety. A second, along with Jakob Stix, is to give an obstruction for a smooth projective variety to admit a lifting to characteristic 0, in terms of the structure of its etale fundamental group as a profinite group. We will finally touch on some open questions.
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April 7 @4pm |
Y.P. Lee
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Among the generalized cohomology theories associated to 1-dimensional (formal) groups are ordinary cohomology (G_a), complex K-theory (G_m),
and elliptic cohomology (elliptic curve). In the late 1980s and early 1990s, physicists initiated quantum cohomology (Gromov-Witten theory) as the
enumerative geometry associated with ordinary cohomology. A decade later, A. Givental and I established quantum K-theory. In this joint work with E.
Bouaziz and I. Huq-Kuruvilla, I will report on recent (small) progress regarding the definition of the enumerative geometry of elliptic cohomology.
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April 14 |
TBA
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April 21 |
TBA
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