DRAFT: This module has unpublished changes.

  Beginners Explorations in Algebraic Geometry (formerly Elementary Algebraic Geometry) is a Graduate Center seminar for students and faculty in a form of a problem session. Contact Malgorzata Marciniak (mmarciniak@lagcc.cuny.edu) for questions and schedule.

 

DURING FALL 2017 WE WILL MEET ON TUESDAYS 12:30-1:30 PM IN GC 4214.03. "Tea time" is scheduled for 12 pm and 1:30 pm.

 

 The first (organizational) meeting is scheduled on September 12 and the last meeting on December 5, excluding September 19 and November 21 for irregular schedules.
We will follow Chapter 1, 2, and 4 from the book by Joseph Silverman The Arithmetic of Dynamical Systems, Graduate Texts in Mathematics 241, 2007
We will use CoCalc (SAGE) or another software to solve and illustrate problems that we pose or find in the book. All presentations are “hands-on” with the emphasis on posing questions and making attempts.

 

THERE IS THE SCHEDULE


September 12: organization and schedule of presentations
September 19: no meeting, Thursday schedule at GC, Friday schedule at LaGCC
September 26: Introduction to CoCalc (Johann Thiel, confirmed)

 

October 3: Introduction to Classic Dynamics: projective line, rational maps, critical points, periodic points (Shenglan Yuan, confirmed)

October 10: Introduction to CoCalc, part II (Johann Thiel, confirmed)
October 17: Chapter 1. Julia set, Fatou set, dynamical systems (Shenglan Yuan, confirmed)
October 24: Review of Congruent Numbers and Elliptic Curves (Malgorzata Marciniak, confirmed)

October 31: Chapter 2. Dynamics over local fields: nonarchimedean metric, periodic points (Shenglan Yuan, confirmed)

 November 7: Generalized congruent numbers and elliptic curves (Malgorzata)

November 14: Weakly congruent numbers and elliptic curves (Jonathan Sondow, confirmed)

November 21: no meeting, Friday schedule at Grad Center

November 28: The J-invariant of an elliptic curve (Malgorzata, confirmed)

December 5: summary of the semester, plans for spring, lunch in Franchia, 12 Park Avenue

 

Spring Semester:

 Chapter 4. Families of dynamical systems: dynatomic polynomials

 Chapter 4. The space of rational functions, the moduli space of dynamical systems

 

 

 

 

DRAFT: This module has unpublished changes.