Arithmetic Algebraic Geometry at the University of Arizona

In summary, this report is a summary of a lecture series at the Southwestern Center for Arithmetic Algebraic Geometry discussing the potential connections between number theory and dynamical systems on foliated spaces. The material is based on previous papers, but has been streamlined and updated. The author hopes it will be of interest to readers. Additionally, the conversation refers to a different resource discussing similar topics.
  • #1
wolram
Gold Member
Dearly Missed
4,446
558
http://www.arxiv.org/abs/math.NT/0505354

Authors: C. Deninger
Subj-class: Number Theory; Dynamical Systems
MSC-class: 11-02; 11R42; 34C25; 37C27; 53C12; 58B34

This report on the topics in the title was written for a lecture series at the Southwestern Center for Arithmetic Algebraic Geometry at the University of Arizona.It may serve as an introduction to certain conjectural relations between number theory and the theory of dynamical systems on foliated spaces. The material is based on streamlined and updated versions of earlier papers on this subject.

Far beyond me, hope it interests someone.
 
Physics news on Phys.org
  • #3


Thank you for sharing this report on Arithmetic Algebraic Geometry at the University of Arizona. It is great to see that the university is offering a lecture series on this topic, which is a fascinating and important area of mathematics. The authors have provided a clear and concise overview of the connections between number theory and the theory of dynamical systems on foliated spaces, making it accessible to a wider audience. Their updated versions of previous papers also showcase the ongoing research and developments in this field. Overall, this report is a valuable resource for anyone interested in exploring these conjectural relationships and I hope it attracts more interest in this exciting area of mathematics.
 

Related to Arithmetic Algebraic Geometry at the University of Arizona

1. What is Arithmetic Algebraic Geometry?

Arithmetic Algebraic Geometry is a branch of mathematics that combines concepts from algebraic geometry and number theory. It studies the geometry of solutions to polynomial equations with coefficients in number fields, and uses techniques from algebraic geometry to understand the behavior of these solutions.

2. What is the focus of the Arithmetic Algebraic Geometry program at the University of Arizona?

The Arithmetic Algebraic Geometry program at the University of Arizona focuses on studying the arithmetic properties of algebraic varieties, with an emphasis on applications to number theory and cryptography. This program also offers opportunities for research in areas such as Diophantine equations, elliptic curves, and Galois representations.

3. What background is required to study Arithmetic Algebraic Geometry at the University of Arizona?

Students interested in studying Arithmetic Algebraic Geometry at the University of Arizona should have a strong background in mathematics, including courses in algebra and geometry. Familiarity with abstract algebra and number theory is also recommended. Programming skills and knowledge of computer algebra systems are helpful for research in this field.

4. What research opportunities are available in Arithmetic Algebraic Geometry at the University of Arizona?

The University of Arizona offers a variety of research opportunities in Arithmetic Algebraic Geometry, including opportunities to work with faculty on their research projects. Students can also participate in seminars, workshops, and conferences focused on this field. Additionally, the university has collaborations with other institutions and offers opportunities for students to participate in research programs abroad.

5. What career paths can one pursue with a degree in Arithmetic Algebraic Geometry from the University of Arizona?

Graduates of the Arithmetic Algebraic Geometry program at the University of Arizona can pursue careers in academia, industry, and government. Some common career paths include research positions in universities and research institutes, data science and analytics roles in the private sector, and cryptography and security positions in government agencies. Graduates may also choose to pursue further education, such as a PhD in mathematics or a related field.

Similar threads

  • General Math
Replies
1
Views
1K
  • Sticky
  • Science and Math Textbooks
Replies
10
Views
5K
  • Poll
  • Science and Math Textbooks
Replies
4
Views
5K
  • Beyond the Standard Models
Replies
2
Views
4K
  • STEM Academic Advising
Replies
3
Views
947
  • STEM Academic Advising
Replies
13
Views
2K
  • Poll
  • Science and Math Textbooks
Replies
1
Views
5K
  • Science and Math Textbooks
2
Replies
62
Views
52K
  • STEM Academic Advising
Replies
5
Views
2K
  • STEM Academic Advising
Replies
17
Views
3K
Back
Top