Schedule of talks:

Abstracts

(Aluffi): We will present a new approach to the computation of the Segre class of a subscheme of projective space, based on the construction of a suitable Newton-Okounkov body. The result may be viewed as a common generalization of results of Kaveh and Khovanskii and of an earlier result on Segre classes of monomial schemes. The construction of the Newton-Okounkov body is modeled on work of Lazarsfeld and Mustata.

(Tseng):

(Bejleri): A degree one del Pezzo surface is the blowup of P² at 8 general points. By the classical Cayley-Bacharach Theorem, there is a unique 9th point whose blowup produces a rational elliptic surface with a section. Via this relationship, we can construct a compactification by stable pairs of the moduli space of anti-canonically polarized degree one del Pezzo surfaces. The theory of stable pairs (X,D) is the natural extension to dimension 2 of the Deligne-Mumford-Knudsen theory of pointed stable curves. I will discuss the construction of the space of interest as a limit of spaces of weighted stable elliptic surface pairs and explain how it relates to some previous compactifications of the space of degree one del Pezzo surfaces. This is joint work with Kenny Ascher.

(Can): In this talk we will discuss the following question: If Y is a Schubert variety in G/B, then when does the action of the Levi factor of the stabilizer of Y in G acts spherically on Y? We will show that this happens for all smooth Schubert varieties in ADE types.

(Wang): One central question in Gromov-Witten (GW) theory is to relate the GW invariants of a hypersurface to the GW invariants of the ambient space such as smooth projective variety or orbifold. In genus zero, this is usually done by the so-called quantum hyperplane principle, which uses the twisted GW invariants of the ambient space. This is analogous to the classical theorem that the number of lines inside a cubic surface can be obtained by computing the Euler number of a certain vector bundle on the space of lines inside P³ (which is the Grassmannian G(2,4)). But this approach requires a technical assumption called convexity for the line bundle over the ambient space defining the hypersurface, which can fail for hypersurfaces in orbifolds. In this talk, I will present a way to obtain the genus zero GW invariants of a positive hypersurface in Toric stacks for which the convexity may fail. One key ingredient in the proof is to resolve the genus zero quasimap Wall-Crossing (WC) conjecture proposed by Ionuţ Ciocan-Fontaine and Bumsig Kim, where we don't require the target to be carried with a good torus action as opposed to all previously proven WC examples (or hypersurfaces for which the convexity holds thereof).

(Kutler): We associate to any matroid a motivic zeta function. If the matroid is representable by a complex hyperplane arrangement, then this coincides with the motivic Igusa zeta function of the arrangement. We show that this zeta function is rational and satisfies a functional equation. Moreover, it specializes to the topological zeta function introduced by van der Veer. We compute the first two coefficients in the Taylor expansion of this topological zeta function, answering two questions of van der Veer. This is joint work with Dave Jensen and Jeremy Usatine.

Past Seminars

Ohio State University Algebraic Geometry Seminar-Year 2018-2019

Ohio State University Algebraic Geometry Seminar-Year 2017-2018

Ohio State University Algebraic Geometry Seminar-Year 2016-2017

Ohio State University Algebraic Geometry Seminar-Year 2015-2016

Ohio State University Algebraic Geometry Seminar-Year 2014-2015

Ohio State University Algebraic Geometry Seminar-Year 2013-2014

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