Home Page of Dylan Airey

I graduated May 2022 with a PhD in Mathematics from the Department of Mathematics at Princeton University under the supervision of Allan Sly. This is my CV [pdf].

Publications

My papers can all be found on arXiv.org here

Published papers

• A topological dynamical system with two different positive sofic entropies  (with L. Bowen and F. Lin), published in Trans. Amer. Math. Soc. Ser. B. Vol. 9, Iss. 2, pp. 35--98 (2022).
• Some complexity results in the theory of normal numbers (with S. Jackson and B. Mance), published in Canadian J. Math. Vol. 74, Iss. 1, pp. 170--198 (2022).
• Descriptive complexity in cantor series (with S. Jackson and B. Mance), published in J. Symb. Log. pp. 1--22 (2021).
• Hotspot lemma for noncompact spaces (with B. Mance), published in Math. Notes Vol 108, pp. 434--439 (2020).
• Borel complexity of sets of normal numbers via generic points in subshifts with specification (with S. Jackson, D. Kwietniak and B. Mance), published in Trans. Amer. Math. Soc. Vol 373, pp. 4561--4584 (2020).
• Unexpected distribution phenomenon resulting from Cantor series expansions (with B. Mance), published in Adv. Math. Vol. 279, pp. 372--404 (2015).
• On the Hausdorff dimension of some sets of numbers defined through the digits of their Q-Cantor series expansions (with B. Mance), published in J. Frac. Geom. Vol. 3, Iss. 2, pp. 163--186 (2016).
• Normality preserving operations for Cantor series expansions and associated fractals part I (with B. Mance), published in Illinois J. Math. Vol. 59, No. 3, pp. 531--543 (2015).
• Normality preserving operations for Cantor series expansions and associated fractals part II (with B. Mance and J. Vandehey), published in New York J. Math. Vol. 21, pp. 1311--1326 (2015).
• Normal equivalencies for eventually periodic basic sequences (with B. Mance), published in Indag. Math. Vol. 26, No. 3, pp. 476--484 (2015).
• Normal number constructions for Cantor series with slowly growing bases (with B. Mance and J. Vandehey), published in Czech. Math J. Vol. 66, Iss. 2, pp. 465--480 (2016).
• Normality of different orders for Cantor series expansions (with B. Mance), submitted.

Talks

• Gibbs measures on sparse random graphs, Dissertation defense, Princeton University, Princeton, NJ, Spring 2022
• Dynamical systems of algebraic origin, Graduate Student Seminar, Princeton University, Princeton, NJ, Fall 2019
• SL(n,R) has Property (T), Geometric Group Theory MSRI Summer Graduate School, Oaxaca, Mexico, Summer 2019
• Borel complexity of the set of generic points for dynamical systems with specification, Ergodic Theory & Statistical Mechanics seminar, Princeton University, Princeton, NJ, Spring 2018
• Entropy beyond amenable groups, Mathematics Graduate Student Seminar, Princeton University, Princeton, NJ, Spring 2018
• Borel complexity of generic points of dynamical systems with a weak specification property, Groups & Dynamics seminar, UT Austin, Austin, TX, Spring 2017
• Some complexity results in the theory of normal numbers, RTG Logic and Dynamics Seminar, University of North Texas, Denton, TX, Summer 2016
• Some complexity results in the theory of normal numbers, AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, FL, Summer 2016
• Some complexity results on sets related to normal numbers, Wrocław University of Technology, Summer 2016
• Some complexity results in the theory of normal numbers, University of Warmia and Mazury in Olsztyn, Summer 2016
• Some complexity results on sets related to normal numbers, University of Gdansk, Summer 2016
• Some complexity results on sets related to normal numbers, University of Warsaw, Summer 2016
• Some complexity results on sets related to normal numbers, Nicolaus Copernicus University, Torun, Summer 2016
• Some complexity results on sets related to normal numbers, Seminarium z Układów Dynamicznych IMPAN, IMPAN, Summer 2016
• Unexpected distribution phenomenon resulting from Cantor series expansions, Logic Seminar, California Institute of Technology, Fall 2015
• Normality preserving operations for Cantor series expansions and associated fractals, Young Mathematicians Conference, Ohio State University, Summer 2015
• Unexpected distribution phenomenon resulting from Cantor series expansions, Special Session on Fractal Geometry and Ergodic Theory, Spring Southeastern AMS Sectional Meeting, University of Alabama at Huntsville, Spring 2015
• The Hausdorff dimension of sets of numbers defined by their Q-Cantor series expansions, AMS Session on Number Theory II, Joint Mathematics Meetings, Spring 2015
• Unexpected distribution phenomenon resulting from Cantor series expansions, Special Session on Connections in Number Theory, Fall Southeastern AMS Sectional Meeting, University of North Carolina at Greensboro, Fall 2014
• Unexpected distribution phenomenon resulting from Cantor series expansions, Young Mathematicians Conference, Ohio State University, Summer 2014
• Unexpected distribution phenomenon resulting from Cantor series expansions, RTG Research Conference: Logic, Dynamics, and Their Interactions II, University of North Texas, Summer 2014
• Unexpected distribution phenomenon resulting from Cantor series expansions, RTG Logic and Dynamics Seminar, University of North Texas, Spring 2014
• Ergodic properties of different types of series expansions, Informal Mathematics Research Problem Session, University of North Texas, Spring 2014
• Uniform distribution in topological groups, Dynamical Systems Seminar, University of North Texas, Spring 2014
• Uniform distribution in topological groups, Texas Undergraduate Topology and Geometry Conference, University of Texas at Austin, Spring 2014
• Normal Numbers in a Variety of Number Systems, Normal Numbers Seminar, University of North Texas, Spring 2013
• Comparing two notions of normality for Cantor series expansions, RTG Logic and Dynamics Seminar, University of North Texas, Spring 2013
• Arithmetic progressions on Cantor-like sets, Informal Mathematics Research Problem Session, University of North Texas, Fall 2012

Conferences Attended

• Online Open Probability School, Online, Summer 2021
• Online Open Probability School, Online, Summer 2020
• Geometric Group Theory MSRI Summer Graduate School, Oaxaca, Mexico, Summer 2019
• Advances in Asymptotic Probability in Honor of Amir Dembo's 60th Birthday, Stanford, CA Winter 2019
• Current Trends in Dynamical Systems and the Mathematical Legacy of Rufus Bowen, Vancouver, Canada, Summer 2017
• AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, FL, Summer 2016
• New developments around x2 x3 conjecture, Cieplice, Poland, Summer 2016
• Young Mathematicians Conference, Columbus, OH, Summer 2015
• Spring Southeastern AMS Sectional Meeting, Huntsville, AL, Spring 2015
• Joint Mathematics Meetings, San Antonio, TX, Spring 2015
• Fall Southeastern AMS Sectional Meeting, Greensboro, NC, Fall 2014
• Young Mathematicians Conference, Columbus, OH, Summer 2014
• RTG Research Conference: Logic, Dynamics, and Their Interactions II, Denton, TX, Summer 2014
• Texas Undergraduate Topology and Geometry Conference, Austin, TX, Spring 2014
• Logic, Dynamics and Their Interactions, with a Celebration of the Work of Dan Mauldin, Denton, TX, Summer 2012

Contact Information

Email address: dairey@math.princeton.edu