Trevor Hyde / Notes

Slides from research talks

• 7. Existence of periodic points and Sharkovsky's theorem

  Slides from a talk given at Summer@ICERM 2019.

• 6. Factorization Statistics, Representation Stability, and the Growing Gaps Principle

  Slides for a talk given at the Midwest Representation Stability Research Meeting on April 28th, 2019.

• 5. Cyclotomic Factors of Necklace Polynomials

  Slides for a talk given at the University of Michigan graduate student recruitment on March 16th, 2019 and at the Emerging Connections in Number Theory special session at the AMS Spring Central and Western Joint Sectional Meeting on March 24th, 2019.

• 4. Polynomial Factorization Statistics and Point Configurations in R^3

  Slides for a talk given at the CANT 2018 conference on May 22nd, 2018, at the FPSAC 2018 conference on July 17th, 2018, and the University of Michigan Combinatorics Seminar on February 1st, 2019.

• 3. Orbits visiting finite sets

  Slides for a talk given in the Arithmetic Dynamics Special Session of the AMS Spring Easter Sectional Meeting on April 22nd, 2018.

• 2. An arithmetic dynamical Mordell-Lang theorem

  Slides for a talk given at the Joint Math Meetings, January 2018.

• 1. Reduction stability and iterate decomposition stability

  Slides from talk at 2016 Field's Institute Workshop.

Slides from Math Club talks at the University of Michigan

• 5. Exploring the Topograph

  February 14th, 2019.

• 4. Blockchains

  September 13th, 2018.

• 3. Down the Rabbit Hole: An introduction to p-adic numbers

  February 15th, 2018.

• 2. Combinatorial species and generating functions

  February 9th, 2017.

• 1. How does a parabola look on the horizon?

  October 6th, 2016.

Math Circle Handouts

• 1. Too Many Pigeons

  • Pigeonhole Principle Problems
  • Pigeonhole Principle Solutions

Expository notes

• 10. Normal elements in finite fields,
  arXiv preprint 1809.02155.
• 9. Collusions in Teichmüller expansions
  arXiv preprint 1704.07940.
• 8. Circulant q-Butson Hadamard matrices,
  with Joe Kraisler. arXiv preprint 1701.08871.

• 7. Differential note

  Note on a simple algebraic method for solving a general family of differential equations.

• 6. A dynamical proof of the Cantor-Bernstein theorem

  Note giving a simple proof of the Cantor-Bernstein theorem from the perspective of discrete dynamics.

• 5. Cyclotomic Integers

  Short note on fundamental facts about cyclotomic integers. Includes a non-standard calculation of the discriminant.

• 4. FI-modules and representation stability

  Lecture notes from a talk given in the Student Representation Theory Seminar, Spring 2016.

• 3. Realizing regular polytopes over Q

  Note solving the problem of which regular polytopes can be constructed with vertices having rational coordinates.

• 2. Wan's Theorem

  An exposition of Wan's theorem with generalizations.

• 1. Power-full polynomials over finite fields

  Note on the number of polynomials over a finite field divisible by a non-trivial dth power, with a new proof extending an idea of Zieve in the case d = 2.