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].

My papers can all be found on arXiv.org here

**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.

*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

- 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

Email address: dairey@math.princeton.edu