# Research: Number Theory

## Summer School 2020: Ergodic Theory with Applications to Continued Fractions

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From May 18 to May 22 2020 the University of North Carolina Greensboro will host the UNCG Summer School in Computational Number Theory and Algebra: **Ergodic Theory with Applications to Continued Fractions**. The summer school will take place in a live online format. The hours of the school will be during the daytimes of the Eastern Daylight Time Zone (EDT, i.e. UTC -4h, see schedule below).

Ergodic theory is the study of the long term behavior of points and sets under iterations of a measure preserving transformation. What better way to learn the subject than see it in action through its applications to number theory ?

This program is targeted primarily at early stage graduate students in mathematics with an interest in dynamical systems and number theory.

Questions? Email us at uncg2020summerschool@gmail.com

### Speakers

- Daniel Glasscock, UMass Lowell
- Claire Merriman, Ohio State University
- Donald Robertson, University of Manchester
- Clifford Smyth, UNCG

### Lecture Notes

UNCG_Ergodic_Theory_Summer_School_2020

Lecture-6-Computational-Experiments-with-Mathematica.nb (Mathematica Notebook)

### Current Schedule

The hours of the school will be during the daytimes of the Eastern Daylight Time Zone (EDT, i.e. UTC -4h).

Monday, 5/18

09:00 Introductions

09:30 Lecture I

10:00 Problem Session I

11:30 Discussion Session I

12:00 End of session

13:00 Lecture II

13:30 Problem Session II

15:00 Discussion Session II

15:30 End of day

Tuesday, 5/19

09:00 Lecture III

09:30 Problem Session III

11:00 Discussion Session III

11:30 End of session

13:00 Lecture IV

13:30 Problem Session IV

15:00 Discussion Session IV

15:30 End of day

Wednesday, 5/20

09:00 Lecture V

09:30 Problem Session V

11:00 Discussion Session V

11:30 End of session

13:00 Lecture VI

13:30 Problem Session VI

15:00 Discussion Session VI

15:30 End of day

16:00 Social session

17:00 End social session

Thursday, 5/21

09:00 Lecture VII

09:30 Problem Session VII

11:00 Discussion Session VII

11:30 End of session

13:00 Lecture VIII

13:30 Problem Session VIII

15:00 Discussion Session VIII

15:30 Talk: Sideways Dynamics, by Karl Petersen, UNC Chapel Hill, retired

Friday, 5/22

09:00 Lecture IX

09:30 Problem Session IX

11:00 Discussion Session IX

11:30 End of session

13:00 Lecture X

13:30 Problem Session X

15:00 Discussion Session X

15:30 Closing remarks

16:00 End of summer school

Non-participants are welcome to listen and participate in lectures, but not in the breakout/problem sessions. The breakout sessions are deliberately kept small in order to be manageable.

### Organizers

Talia Fernos, Sebastian Pauli, Filip Saidak, Clifford Smyth, Brett Tangedal, Dan Yasaki

### Acknowledgements

The summer school in computational number theory is supported by UNCG and the NSF.