Andrii Arman

Research interests

Combinatorics, extremal graph theory, random graphs, random algorithms, Ramsey theory, Euclidean Ramsey theory, convex and discrete geometry, complex and classical analysis.

Publications

Published

1. On Hadwiger’s covering problem in small dimensions, Canadian Mathematical Bulletin, Published online 2025:1-12, (2025) (with A.Bondarenko and A.Prymak)

2. On a Gallai-type problem and illumination of spiky balls and cap bodies, Mathematika, 71 (2), (2025) (with A. Bondarenko, A. Prymak, D. Radchenko)

3. Small Volume Bodies of Constant Width, Int. Math. Res. Not., Volume 2025, Issue 4, (2025) (with A. Bondarenko, F. Nazarov, A. Prymak, D. Radchenko).
   (featured in Scientific American, New Scientist, Quanta)

4. Minimal dispersion on the cube and the torus, J. Complex. 85, Article 101883 (2024) (with A. Litvak).

5. Convex bodies of constant width with exponential illumination number, Discrete. Comput. Geom. (2024) (with A.Bondarenko and A.Prymak).

6. Upper bounds on chromatic number of E^n in low dimensions, Electron. J. Combin. 31 (2) (2024) (with A.Bondarenko, A.Prymak, and D. Radchenko).

7. Linear-time uniform generation of random sparse contingency tables with specified marginals, Ann. Appl. Probab., 34, No. 2 (2024), 29 pages (with P. Gao and N. Wormald).

8. Colourful matchings, SIAM J. Discrete Math. 37 (2) (2023), 26 pages (with M. T. Sales and V. Rödl).

9. Every Steiner triple system contains almost spanning d-ary hypertree, Electron. J. Combin. 29 (2022), 16 pages (with M. T. Sales and V. Rödl).

10. Independent sets in subgraphs of a shift graph, Electron. J. Combin. 29 (2022), 10 pages (with M. T. Sales and V. Rödl).

11. Increasing paths in countable graphs,  J. Combin. Theory Ser. A 183 (2021), 18 pages (with B. Elliott and V. Rödl).

12. Fast uniform generation of random graphs with given degree sequences,  Random Structures and Algorithms 59 (2021), 24 pages (with P. Gao and N. Wormald).

13. The maximum number of cycles in a graph with a fixed number of edges, Electron. J. Combin 26 (2019), 16 pages (with S.Tsaturian).

14. A note on weak delta systems,  Discrete Mathematics 342 (11) (2019), 9 pages (with B. Kay and V. Rödl).

15. A result in asymmetric Euclidean Ramsey theory, Discrete Mathematics 341 (5) (2018), 7 pages (with S. Tsaturian).

16. Note on Ramsey theorem for posets with linear extensions, Electron. J. Combin 24 (2017), 6 pages (with V. Rödl).

17. An upper bound for the size of a k-uniform intersecting family with covering number k, J. Combin. Theory Ser. A 147 (2017), 9 pages (with T. Retter).

18. Triangle-free graphs with the maximum number of cycles, Discrete Mathematics 339 (2016), 13 pages (with D. Gunderson and S. Tsaturian).

Conference publications

1. Fast uniform generation of random graphs with given degree sequences, 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (with P. Gao and N. Wormald).

Other publications

1. Mathematical Competition of Ukrainian Students 2006–2007 (in Ukrainian, with A. Anikushyn et al.), published by Litera, Kiev, Ukraine (2008) 224 pages.

Submitted

1. Small volume bodies of constant width with tetrahedral symmetries (with A.Bondarenko, A.Prymak, and D. Radchenko), arxiv:2406.18428.

PhD Thesis

• Maximum number of cycles in graphs and multigraphs (written under supervision of Dr. D. Gunderson).

MSc Thesis

• Generalization of Ahlofrs Lemma and boundary behavior of analytic functions (written under supervision of Dr. N. Zorboska).

Teaching

University of Manitoba

• Math 4920 Undergraduate Research Projects (Estimation of volumes of bodies of constant width)

• Math 4910 Project course (Hadwiger's conjecture)

• Math 4300/7300 Combinatorial geometry

• Math 1240 Elementary Discrete mathematics

• Math 1700 Calculus 2

• Math 1710 Applied calculus 2

• Training University of Manitoba Mathletics teams 

Emory University

• Math 112 Calculus 2

• Math 221 Linear algebra

• Math  532 Graph theory II

Monash University

• Math 9004 Mathematical foundations for data science

International College of Manitoba

• Math 1210 Techniques of classical and linear algebra

• Math 1300 Vector geometry and linear algebra