Speaker: Andrei Vesnin (Tomsk State University)
Date and time: 24.02.2021, 17:00 (GMT +03:00)
Title: Hyperbolic polyhedra and hyperbolic knots: the right-angled case
Abstract: A polyhedron is said to be right-angled if all its dihedral angles are equal to pi/2. Three-dimensional hyperbolic manifolds constructed from bounded right-angled polyhedra have many interesting properties . Inoue [2,3] initiated enumerating bounded right-angled hyperbolic polyhedra by their volumes. Atkinson obtained low and upper bounds of volumes via vertex number . In  we enumerate ideal (with all vertices at infinity) right-angled hyperbolic polyhedra. The obtained results imply that the right-angled knot conjecture from  holds for knots with small crossing number. Atkinson’s upper bounds were improved in [7,8] for bounded and ideal cases both. Finally, we will discuss the relation of results from  with the maximum volume theorem from .
The talk is based on joint results with Andrey Egorov [5,7,8].
 A. Vesnin, Right-angled polyhedra and hyperbolic 3-manifolds, Russian Mathematical Surveys 72 (2017), 335-374.
 T. Inoue, Organizing volumes of right-angled hyperbolic polyhedra, Algebr. Geom. Topol. 8 (2008), 1523-1565.
 T. Inoue, Exploring the list the smallest right-angled hyperbolic polyhedra, Experimental Mathematics 2019, published online.
 C. Atkinson, Volume estimates for equiangular hyperbolic Coxeter polyhedra, Algebr. Geom. Topol. 9 (2009), 1225-1254.
 A. Vesnin, A. Egorov, Ideal right-angled polyhedra in Lobachevsky space, Chebyshevskii Sbornik 21 (2020), 65-83.
 A. Champanerkar, I. Kofman, J. Purcell, Right-angled polyhedra and alternating links, arXiv:1910.13131.
 A. Egorov, A. Vesnin, Volume estimates for right-angled hyperbolic polyhedra, Rendiconti dell’Instituto di Matematica dell’Universita di Trieste 52 (2020), 565-576.
 A. Egorov, A. Vesnin, On correlation of hyperbolic volumes of fullerenes with their properties, Comput. Math. Biophys. 8 (2020), 150-167.
 G. Belletti, The maximum volume of hyperbolic polyhedral, Trans. Amer. Math. Soc. 374 (2021), 1125-1153.
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