IMSA Seminar
Bruno De Oliveira
University of Miami & IMSA
Surface Quotient Singularities and Big Cotangent Bundle
Thursday, December 22, 2022, 11:00am
Ungar 528B
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Abstract: Surfaces with big cotangent bundle have hyperbolic properties, e.g. they satisfy the Green-Griffiths-Lang conjecture. The GGL-conjecture states that a variety of general type X has a proper subvariety Z such that all entire curves of X are contained in Z. We present a bigness criterion for resolutions of orbifold surfaces and obtain as a corollary the canonical model singularities criterion that can be applied to all surfaces of general type. We describe how the CMS-criterion improves upon other known criteria, such as the Rouseau-Rolleau criterion. The CMS-criterion involves an analytical based invariant of surface singularities that we calculate for A_n singularities. We then apply this criterion to the problem of finding what are the degrees $d$ (what is the minimal such d?) for which the deformation equivalence class of a smooth hypersurface of degree d in P^3 has a representative with big cotangent bundle.
IMSA Seminar
Jiachang Xu
University of Miami & IMSA
Motivic Integration for Non-Archimedean Analytic Spaces I
Wednesday, October 5, 2022, 5:00pm
Ungar 528B
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Abstract: In the first talk, I will introduce the theory of motivic integration for rigid varieties over a complete discrete valued field follows the works of François Loeser and Julien Sebag, which could be considered as a possible to develop a theory of motivic integration for Berkovich spaces over a complete discrete valued field. Also, I will also discuss some potential generalization to logarithmic geometry.
IMSA Seminar
Enrique Becerra
University of Miami & IMSA
Basics on Motivic Integration
Wednesday, September 28, 2022, 5:00pm
Ungar 528B
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Abstract: In this talk, I will expose some basic ideas on motivic integration. The goal will be to define the notion of motivic volume and show some simple computational examples.
IMSA Seminar
Yixian Wu
University of Miami & IMSA
Schön Varieties and Decomposition of a Semi-algebraic Set
Wednesday, September 21, 2022, 5:00pm
Ungar 528B
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Abstract: Tropicalization provides us with a way to study varieties using its limit under degenerations. Schön varieties are those whose initial degenerations are smooth. They are the first cases whose motivic volumes are defined in Nicaise-Payne-Schroeter. In this talk, I will introduce Schön varieties, the tropical fan of them and how we decompose a semi-algebraic set into pieces where each of them can be treated as a Schön case.
IMSA Seminar
Yixian Wu
University of Miami & IMSA
Tropical Curve Counting and Correspondence Theorem
Wednesday, September 14, 2022, 5:00pm
Ungar 528B
Abstract: In the first talk, I will give an introduction to tropical geometry. I will set up the curve counting problems in both algebraic geometry and tropical geometry. In the case of toric surfaces, I will give a proof of the correspondence theorem that relates these two counts.
