Andrii Arman

Instructor I

Department of Mathematics, University of Manitoba

University Center, 339A

65 Chancellors Circle, Winnipeg, Manitoba

E-mail: Andrii.Arman@umanitoba.ca

andrew0arman@gmail.com

Research interests

ombinatorics, extremal graph theory, random graphs, randomised algorithms, Ramsey theory, Euclidean Ramsey theory,discrete and convex geometry, high dimensional geometry, complex and classical analysis.

Publications

Published

On asymptotic Lebesgue's universal covering problem, to appear in Bull. London Math. Soc., (with A. Bondarenko, D. Radchenko, A. Prymak)
Hadwiger's conjecture for cap bodies, to appear in Discrete, Convex, and Combinatorial Geometry Fest conference volume (Springer Proceedings in Mathematics & Statistics series) (with J.S. Kaire, and A. Prymak)
Illumination number of 3-dimensional cap bodies, Discrete Mathematics 349(7), (2026) (with J.S. Kaire, A. Prymak)
Small Volume Bodies of Constant Width with Tetrahedral Symmetries, SIGMA 21(109), (2025) (with A.Bondarenko, A.Prymak, and D. Radchenko)
On Hadwiger’s covering problem in small dimensions, Canadian Mathematical Bulletin, Published online 2025:1-12, (2025) (with A.Bondarenko and A.Prymak)
On a Gallai-type problem and illumination of spiky balls and cap bodies, Mathematika, 71 (2), (2025) (with A. Bondarenko, A. Prymak, D. Radchenko)
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)
Minimal dispersion on the cube and the torus, J. Complex. 85, Article 101883 (2024) (with A. Litvak).
Convex bodies of constant width with exponential illumination number, Discrete. Comput. Geom. (2024) (with A.Bondarenko and A.Prymak).
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).
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).
Colourful matchings, SIAM J. Discrete Math. 37 (2) (2023), 26 pages (with M. T. Sales and V. Rödl).
Every Steiner triple system contains almost spanning d-ary hypertree, Electron. J. Combin. 29 (2022), 16 pages (with M. T. Sales and V. Rödl).
Independent sets in subgraphs of a shift graph, Electron. J. Combin. 29 (2022), 10 pages (with M. T. Sales and V. Rödl).
Increasing paths in countable graphs, J. Combin. Theory Ser. A 183 (2021), 18 pages (with B. Elliott and V. Rödl).
Fast uniform generation of random graphs with given degree sequences, Random Structures and Algorithms 59 (2021), 24 pages (with P. Gao and N. Wormald).
The maximum number of cycles in a graph with a fixed number of edges, Electron. J. Combin 26 (2019), 16 pages (with S.Tsaturian).
A note on weak delta systems, Discrete Mathematics 342 (11) (2019), 9 pages (with B. Kay and V. Rödl).
A result in asymmetric Euclidean Ramsey theory, Discrete Mathematics 341 (5) (2018), 7 pages (with S. Tsaturian).
Note on Ramsey theorem for posets with linear extensions, Electron. J. Combin 24 (2017), 6 pages (with V. Rödl).
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).
Triangle-free graphs with the maximum number of cycles, Discrete Mathematics 339 (2016), 13 pages (with D. Gunderson and S. Tsaturian).

Conference publications

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

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

Submitted

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 2132 Engeneering Mathematical Analysis 2
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

Curriculum Vitae

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