# Publications

## Papers

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### Abelian Sandpile

#### Stability of patterns in the Abelian sandpile (with Charles K. Smart)

Accepted to Annales Henri Poincaré. In the arXiv, updated January 2020

#### The Apollonian structure of integer superharmonic matrices (with Lionel Levine, Charles K. Smart)

Annals of Mathematics 186 (2017) 1-67. In the arXiv, updated July 17, 2017) Extra: Code to generate tiles. Workshop Video: ICERM workshop.

#### Apollonian structure in the Abelian Sandpile (with Lionel Levine, Charles K. Smart)

GAFA 26 (2016) 306-336 (preprint available. In the arXiv, updated May 22, 2014) Extra: images of Γ on various lattices.

#### Convergence of the Abelian Sandpile (with Charles K. Smart)

Duke Math J. 162 (2013) 627-642. (preprint available. In the arXiv, updated March 7, 2012)

### CS Theory

#### Semi-bandit Optimization in the Dispersed Setting (with Nina Balcan, Travis Dick)

Submitted. In the arXiv since July, 2019.

#### A partisan districting protocol with provably nonpartisan outcomes(with Ariel Procaccia, Dingli Yu)

Submitted. In the arXiv since October 24, 2017.

### Extremal problems

#### Extremal Collections of k-Uniform Vectors (with Joseph Briggs)

Submitted. In the arXiv since January 2018.

### COVID-19

#### Failure of montonicity in epidemic models (with Maria Chikina)

Manuscript. preprint available. In the arXiv since April 2020. Extra: Simulation code.

#### Modeling strict age-targeted mitigation strategies for COVID-19 (with Maria Chikina)

PLOS ONE 15 (2020). Extra: Simulation code, updated April 19. Seminar Video: PIMS/UBC Math-Bio Seminar.

### Geometry

#### Random volumes in d-dimensional polytopes (with Alan Frieze, Tomasz Tkocz.)

Discrete Analysis (2020). Also in the arXiv.

#### Sets resilient to erosion

Advances in Geometry 11 (2011) pp. 201-224. (preprint is available)

### Randomness

#### Comb inequalities for typical Euclidean TSP instances (with with Anish Sevekari)

(Submitted). In the arXiv since December 2020

#### Minimum-weight combinatorial structures under random cost-constraints (with Alan Frieze, Gregory Sorkin, Tomasz Tkocz)

(Submitted). In the arXiv, updated February 2020.

#### Separating effect from significance in Markov chain tests (with with Maria Chikina, Jonathan Mattingly, and Alan Frieze)

(Submitted). In the arXiv, submitted September 2019

#### Scalefree hardness of average-case Euclidean TSP approximation (with Alan Frieze)

Submitted. In the arXiv, updated August 2019.

#### On the cover time of the emerging giant (with Alan Frieze, Tomasz Tkocz)

(Submitted). In the arXiv, submitted August 2018

#### On random multi-dimensional assignment problems (with Alan Frieze, Tomasz Tkocz)

(Submitted). In the arXiv, submitted January 2019

#### On the rank of a random binary matrix (with Colin Cooper, Alan Frieze)

SODA 2019. Also in the arXiv.

#### Diffusion limited aggregation in the Boolean lattice (with Alan Frieze)

Annals of Applied Probability 28 (2018). In the arXiv, updated December 2017.

#### A note on dispersing particles on a line (with Alan Frieze)

Random Structures & Algorithms (2018). Also in the arXiv since November 2017.

#### A note on the localization number of random graphs: diameter two case (with Andrzej Dudek, Alan Frieze)

Discrete Applied Mathematics 254 (2019) 107-112. Also in the arXiv since December 2017.

#### Assessing significance in a Markov chain without mixing (with Maria Chikina, Alan Frieze)

PNAS 114 (2017) 2860-2864 (also: arXiv) Extra: Code for redistricting chain. Extra: Brief amici curiae in SCOTUS Gill v. Whitford gerrymandering case

#### Looking for vertex number one (with Alan Frieze)

Annals of Applied Probability 27 (2017) 582-630. Also in the arXiv, last updated May 2016.

#### Separating subadditive Euclidean functionals (with Alan Frieze)

STOC 2016. Journal version in Random Structures & Algorithms 51 (2017) 375-403. In the arXiv since January 8, 2015.

#### Traveling in randomly embedded random graphs (with Alan Frieze)

RANDOM 2017. Journal version in Random Structures & Algorithms (2018). Also in the arXiv. Extra: Code for Figure 1.

#### Between 2- and 3-colorability (with Alan Frieze)

Electronic Journal of Combinatorics 22 #P1.34. In the arXiv since April 19, 2014. Extra: bound.cpp.

#### An extension of the Moser-Tardos algorithmic local lemma

SIAM J. Discrete Math 28 911-917 (2014). (preprint available, last updated January 26, 2013)

#### The Lefthanded Local Lemma characterizes chordal dependency graphs

Random Structures 41 (2012) 546-556. In the arXiv since April 2012.

#### Highly nonrepetitive sequences: winning strategies from the Local Lemma

Random Structures & Algorithms 38 pp 140-161 (preprint also available, last updated October 24, 2010)

### Graph Theory

#### Distance Sequences in Locally Infinite Vertex-Transitive Digraphs

Combinatorica 26 (5) (2006) 577-585 (pdf is also available)

### Games

#### Maker-Breaker on Digraphs (with with Alan Frieze)

(Submitted). In the arXiv since March 2020

#### Walker-Breaker games (with Lisa Espig, Alan Frieze, Michael Krivelevich )

SIAM J. Discrete Math. 29 (2015). In the arXiv since January 22, 2014. (A preprint is also available.)

#### The topology of competitively constructed graphs (with Alan Frieze)

The Electronic Journal of Combinatorics 21 #P2.26, In the arXiv since December 3, 2013. (A preprint is also available.)

#### The Hales-Jewett number is exponential: game-theoretic consequences (with J. Beck and S. Vijay)

Analytic Number Theory: Essays in Honour of Klaus Roth
(Editors: William Chen, Tim Gowers, Heini Halberstam, Wolfgang Schmidt and Bob Vaughan) (A preprint is also available.)