### Fall 2019: Matilde Lalin (University of Montreal) and David Krumm (Reed College)

Date: Saturday, November 23, 2019
Location: University of Oregon
Room: Fenton 110

Program:

• 11:00-12:00 -- Matilde Lalin (University of Montreal), Lecture I: The Mahler measure of multivariable polynomials
• 12:20-1:30 -- Lunch
• 1:30-2:30 -- David Krumm (Reed College): Algebraic preperiodic points of entire transcendental functions
• 3:00-4:00 -- Matilde Lalin (University of Montreal), Lecture II: The mean values of cubic L-functions

Abstracts:

• Matilde Lalin, Lecture I: The Mahler measure of multivariable polynomials

• Matilde Lalin, Lecture II: The mean values of cubic L-functions

• David Krumm: Algebraic preperiodic points of entire transcendental functions

Motivated by questions in transcendental number theory, K. Mahler asked in 1976 whether there exists an entire transcendental function $f:\mathbb {C}\to\mathbb{C}$ with the property that $f(\overline{\mathbb{Q}})\subseteq\overline{\mathbb{Q}}$ and $f^{-1}(\overline{\mathbb{Q}})\subseteq\overline{\mathbb{Q}}$. Mahler's question was answered in the affirmative by Marques and Moreira in 2016. In this talk we will discuss some dynamical properties of this type of function $f$, in particular the structure of the directed graph of algebraic preperiodic points of $f$

### Registration

If you plan to attend this meeting, please register by filling out this webform.

### Funding

A very limited amount of funding may be available for regional graduate students. To apply for funding to attend the next meeting, please fill out the above registration webform.

### Previous meetings:

Spring 2019 (Portland State University):
• Chantal David (Concordia University), Lecture I: Explicit Sato-Tate conjecture and other equidistribution conjectures for elliptic curves
• Chantal David (Concordia University), Lecture II: Distributions for elliptic curves over finite fields
• Neha Prabhu (Queen's University): The error term in the Sato-Tate law of Birch

Winter 2019 (Oregon State University):
• John Voight (Dartmouth College) Lecture I, Definite quaternion orders with stable cancellation (lecture slides)
• John Voight (Dartmouth College) Lecture II, Computing Belyi maps (lecture slides)
• Piper H (University of Hawaii at Manoa), Lecture I: Equidistribution of shapes of (certain) number fields
• Piper H (University of Hawaii at Manoa), Lecture II: How to Become a Liberated Mathematician in 13 Painful Years
• Poster presentations by Allison Arnold-Roksandich (Oregon State University), Charles Camacho (Oregon State University), Sarah Frei (University of Oregon), Matthew Jobrack (Washington State University), Manar Riman (University of Washington), and Joe Webster (University of Oregon)

Spring 2018 (Portland State University):
• Rachel Pries (Colorado State University) Lecture I, Newton polygons of cyclic covers of the projective line. (video of this lecture)
• Rachel Pries (Colorado State University) Lecture II, Generalizing a Galois action on the homology of the Fermat curve. (video of this lecture)
• Özlem Ejder (Colorado State University): Sporadic points on X_1(n). (video of this lecture)

Winter 2018 (Oregon State University):
• Ken Ono (Emory University) Lecture I, Polya's Program for the Riemann Hypothesis and Related Problems (lecture slides)
• Ken Ono (Emory University) Lecture II, Can you feel the Moonshine? (lecture slides)
• Asif Zaman (Stanford University), A new formulation of the Chebotarev density theorem
• Posters presented by Jetjaroen Klangwang (Oregon State University), Peter Cho-Ho Lam (Simon Frasier University), and Daniel Reiss (University of Idaho)

Fall 2017 (University of Oregon):
• Kirsten Eisenträger (Penn State University) Lecture I, Undecidability in number theory. (video of this lecture)
• Kirsten Eisenträger (Penn State University) Lecture II, Existentially and universally definable subsets of global fields. (video of this lecture)
• Travis Scholl (University of Washington), Isolated elliptic curves in cryptography.

### Support has been provided by:

 National Science Foundation Pacific Institute for the Mathematical Sciences Number Theory Foundation College of Arts and Sciences, University of Oregon Oregon State University College of Science and Department of Mathematics College of Liberal Arts and Sciences, Portland State University

### Organizers

 Shabnam Akhtari University of Oregon Derek Garton Portland State University Clay Petsche Oregon State University Holly Swisher Oregon State University Email: oregonnumbertheorydays@gmail.com