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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
May 5-9, 2025
May 5-9, 2025
University of North Texas
University of North Texas
Denton, Texas
Denton, Texas
Project Leaders and Descriptions:
Project Leaders and Descriptions:
Title: Modular Curves and Galois Representations
Title: Modular Curves and Galois Representations
Description: Research concerning torsion points of elliptic curves exhibits an exciting interplay between algebra and geometry. For example, a famous theorem of Mazur implies that an elliptic curve over the rational numbers possesses a rational point of order N if and only if 1 ≤ N ≤ 10 or N=12. These are precisely the values for which the modular curve X_1(N) has genus 0. This course will introduce tools for studying torsion points, emphasizing Galois representations and modular curves, before surveying recent results and open problems in the field.
Project Assistants:
Project Assistants:
Title: Iwasawa Theory and its Applications
Title: Iwasawa Theory and its Applications
Description: This course will introduce some of the fundamental ideas, results, and techniques from Iwasawa theory, with an emphasis on recent progress in the Iwasawa theory of elliptic curves. We will see how Iwasawa theory can offer insights into more "mainstream" problems in arithmetic geometry, such as the distribution of ranks of elliptic curves and Hilbert's tenth problem.
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: 10am-10:50am (Bourdon, GAB 461)
Lecture 2: 11-11:50am (Hatley, GAB 461)
Working groups 1-5pm (Hatley group: GAB 464, Bourdon group: GAB 461)
Tuesday:
Lecture 1: 10am-10:50am (Hatley, GAB 473)
Lecture 2: 11-11:50am (Bourdon, GAB 473)
Working groups 1-5pm (Hatley group: GAB 439A, Bourdon group: GAB 461)
Wednesday:
Lecture 1: 10am-10:50am (Bourdon, GAB 61)
Lecture 2: 11-11:50am (Hatley, GAB 461)
Working groups 1-5pm (Hatley group: GAB 464, Bourdon group: GAB 461)
Thursday:
Working groups 10am-12noon (Hatley group: GAB 464, Bourdon group: GAB 439A)
Lecture 1: 1pm-1:50pm (Hatley, GAB 461)
Lecture 2: 2pm-2:50pm (Bourdon, GAB 461)
Working groups 3-5pm (Hatley group: GAB 464, Bourdon group: GAB 461)
Friday:
Presentations: 10am-12noon (GAB 461)
To apply, please fill the form here. Applications completed by March 25 will receive priority. Most accepted applicants will be offered funding. For questions please email Lea Beneish (lea.beneish "at" unt.edu).
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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