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A small workshop in Arithmetic Geometry for graduate students. Lectures in the morning and project groups in the afternoons
A small workshop in Arithmetic Geometry for graduate students. Lectures in the morning and project groups in the afternoons
August 3-7, 2026
August 3-7, 2026
University of North Texas
University of North Texas
Denton, Texas
Denton, Texas
Project Leaders and Descriptions:
Project Leaders and Descriptions:
Title: Lattice Point Counting in Arithmetic Statistics
Title: Lattice Point Counting in Arithmetic Statistics
Description: Many counting problems in number theory can be described in terms of counting lattice points in certain finite dimensional vector spaces. These parametrizations are interesting both algebraically (why are they true?) and analytically (how can you count the lattice points?), and this course will focus on the analytic side. I'll introduce tools such as Bhargava's averaging method and Sato-Shintani zeta functions, and explain how they get used in practice.
Project Assistants:
Project Assistants:
Title: Parametrizations in arithmetic statistics
Title: Parametrizations in arithmetic statistics
Description: This course will introduce fundamental tools in arithmetic statistics, such as ring and class group parametrizations. In recent years, these tools have been used to study number fields and class groups. Along the way, we'll see how these tools are also useful for traditional algebro-geometric problems (and have found applications in the study of covers of the projective line, special divisors on curves, etc.).
Project Assistants:
Project Assistants:
Schedule: Two talks each day Monday-Thursday. Other time for working groups.
Friday morning the groups present their findings.
Monday:
Lecture 1: 10:30am-11:20am (TBD, GAB 461)
Lecture 2: 11:30-12:20pm (TBD, GAB 461)
Working groups 1:30-5pm (TBD group: GAB 473, TBD group: GAB 461)
Tuesday:
Lecture 1: 10:30am-11:20am (TBD, GAB 461)
Lecture 2: 11:30-12:20pm (TBD, GAB 461)
Working groups 1:30-5pm (TBD group: GAB 473, TBD group: GAB 461)
Wednesday:
Lecture 1: 10:30am-11:20am (TBD, GAB 461)
Lecture 2: 11:30-12:20pm (TBD, GAB 461)
Working groups 1:30-5pm (TBD group: GAB 473, TBD group: GAB 461)
Thursday:
Lecture 1: 10:30am-11:20am (TBD, GAB 461)
Lecture 2: 11:30-12:20pm (TBD, GAB 461)
Working groups 1:30-5pm (TBD group: GAB 473, TBD group: GAB 461)
Friday:
Presentations: 10:30am-12:30pm (GAB 461)
To apply, please fill the form here. Applications completed by July 20 will receive priority. Most accepted applicants will be offered funding. For questions please email Lea Beneish (lea.beneish "at" unt.edu).
Results from projects initiated at workshop:
Coming soon!
Previous iterations of the workshop:
Arithmetic Geometry at UNT (2025): https://sites.google.com/view/arithmetic-geometry-at-unt/home
Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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