Short Courses and Seminars - Fall 2022

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.