Department of Mathematics and Statistics at the Faculty of Science
University of Calgary
Karoly Bezdek
- Canada Research Chair (Tier 1) - Computational & Discrete Geometry
- Professor
- Director - Centre for Computational & Discrete Geometry
- Pure Mathematics
Research Interests
Combinatorics, Geometry and Logic:
Computational Discrete Geometry:
Currently Teaching
| F2012 - MATH 213 - Honours Linear Algebra I | ||||||||||
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| W2013 - PMAT 319 - Transformation Geometry | ||||||||||
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Academic Positions
Canada Research Chair (Tier 1) in Computational and Discrete Geometry, Director of CCDG, Professor
Editor-in-Chief
Contributions to Discrete Mathematics
Graduate Supervision at U of C (2003 to present)
Ph.D. students: Marton Naszodi (2003-2007), Peter Papez (2003-2009), Zsolt Langi (2004-2008), Mate Salat (2009), Ryan Trelford (2009-)
M.Sc. students: Bouchra Sabbagh (2005-2007), Wes Maciejewski (2006-2007), Victoria Labute (2011-)
Publications
Book
- Bezdek, Karoly. Classical Topics in Discrete Geometry "CMS Books in Mathematics" Springer, 2010. 166.
Book Chapter
- Bezdek, Karoly. Sphere packings in 3-space Proceedings of the COE Workshop on Sphere Packings, Kyushu University Press, 2004. 32-49.
- Bezdek, Karoly, Naszodi, Marton and Visy, Balazs. On the {$m$}th {P}etty numbers of normed spaces 253. Dekker, 2003. 291-304.
- Bezdek, Karoly and Connelly, Robert . The minimum mean with translation cover for sets of diameter one Tech. Univ. Graz, 1999. 4-10.
- Bezdek, Karoly and Hausel, T. . On the number of lattice hyperplanes which are needed to cover the lattice points of a convex body 63. North-Holland, 1994. 27-31.
- Bezdek, Karoly and Zamfirescu, T. . A characterization of {$3$}-dimensional convex sets with an infinite {X}-ray number 63. North-Holland, 1994. 33-38.
- Beutelspacher, A. and Bezdek, Karoly. The {H}elly dimension relative to a lattice 63. North-Holland, 1994. 11-16.
- Bezdek, Karoly. Hadwiger-{L}evi's covering problem revisited 10. Springer, 1993. 199-233.
- Bezdek, Karoly. On planar tilings with finitely many sorts of tiles Physica, 1990. 79-85.
- Bezdek, Karoly, Connelly, R. and Kertesz, G.. On the average number of neighbors in a spherical packing of congruent circles 48. North-Holland, 1987. 37-52.
Conference Proceedings
Forthcoming
Journal Paper
- Bezdek, Karoly. Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width 47.2 2012. 275-287.
- Bezdek, Karoly. The illumination conjecture for spindle convex bodies 275.1 2011. 169–176.
- Bezdek, Karoly and Schneider, Rolf. Covering large balls with convex sets in spherical space 51.1 2010. 229-235.
- Bezdek, Karoly and Kiss, Gyorgy. On the X-ray number of almost smooth convex bodies and of convex bodies of constant width 52.3 2009. 342-348.
- Bezdek, Karoly and Litvak, Alexander. Covering convex bodies by cylinders and lattice points by flats 19.2 2009. 233-243.
- Bezdek, Karoly and Bezdek, Daniel. Shortest billiard trajectories 141.1 2009. 197-206.
- Bezdek, Karoly. From the Kneser-Poulsen conjecture to ball-polyhedra 29.8 2008. 1820-1830 .
- Bezdek, Karoly and Connelly, Robert. On the weighted Kneser-Poulsen conjecture 57.2 2008. 121-129.
- Bezdek, Karoly and Litvak, Alexander. On the vertex index of convex bodies 215.2 2007. 626-641.
- Bezdek, Karoly, Langi, Zsolt, Naszodi, Marton and Papez, Peter. Ball-polyhedra 38.2 2007. 201-230.
- Bezdek, Karoly, Connelly, Robert and Csikos, Balazs. On the perimeter of the intersection of congruent disks 47.1 2006. 53-62.
- Bezdek, Karoly and Naszodi, Marton. Rigidity of ball-polyhedra in Euclidean 3-space 27.2 2006. 255-268.
- Bezdek, Karoly. Sphere Packings Revisited 27.6 2006. 864-883.
- Bezdek, Karoly, Bisztriczky, Ted, Csikos, Balazs and Heppes, Aladar. On the transversal Helly numbers of disjoint and overlapping disks 87.1 2006. 86-96.
- Bezdek, Karoly. The illumination conjecture and its extensions 53.1-2 2006. 59-69.
- Bezdek, Karoly, Boroczky, Karoly and Kiss, Gyorgy. On the successive illumination parameters of convex bodies 53.1-2 2006. 71-82.
- Bezdek, Karoly, Naszodi, Marton and Oliveros-Braniff, Deborah. Antipodality in hyperbolic space 85. 2006. 22-31.
- Bezdek, Karoly, Bisztriczky, Ted and Boroczky, Karoly. Edge-antipodal 3-polytopes 52. 2005. 129-134.
- Bezdek, Karoly. Finding the best face on a Voronoi polyhedron - the strong dodecahedral conjecture revisited 145. 2005. 191-206.
- Bezdek, Karoly. On the monotonicity of the volume of hyperbolic convex polyhedra 46.2 2005. 609-614.
- Bezdek, Karoly and Connelly, Robert. The Kneser-Poulsen Conjecture for Spherical Polytopes 32.1 2004. 101-106.
- Bezdek, Karoly. On {$k\sp +$}-neighbour packings and one-sided {H}adwiger configurations 44.2 2003. 493-498.
- Bezdek, Karoly. The {R}adon number of the three-dimensional integer lattice 30.2 2003. 181-184.
- Bezdek, Karoly. On the maximum number of touching pairs in a finite packing of translates of a convex body 98.1 2002. 192-200.
- Bezdek, Karoly. Improving {R}ogers' upper bound for the density of unit ball packings via estimating the surface area of {V}oronoi cells from below in {E}uclidean {$d$}-space for all {$d\ge8$} 28.1 2002. 75-106.
- Bezdek, Karoly. Pushing disks apart-the {K}neser-{P}oulsen conjecture in the plane 553. 2002. 221-236.
- Bezdek, Karoly. The polyhedral {T}ammes problem 76.4 2001. 314-320.
- Bezdek, Karoly. On rhombic dodecahedra 41.2 2000. 411-416.
- Bezdek, Karoly. On a stronger form of {R}ogers's lemma and the minimum surface area of {V}oronoi cells in unit ball packings 518. 2000. 131-143.
- Bezdek, Karoly. A lower bound for the mean width of {V}oronoi polyhedra of unit ball packings in {$\bold E\sp 3$} 74.5 2000. 392-400.
- Bezdek, Karoly. Two-distance preserving functions from {E}uclidean space 39.1-3 1999. 185-200.
- Bezdek, Karoly and Langi, Zsolt. Almost equidistant points on {$S\sp {d-1}$} 39.1-3 1999. 139-144.
- Bezdek, Karoly. Voronoi polyhedra of unit ball packings with small surface area 39.1-3 1999. 107-118.
- Bezdek, Karoly. Danzer-{G}r\"unbaum's theorem revisited 39.1-3 1999. 7-15.
- Bezdek, Karoly. The minimum mean width translation cover for sets of diameter one 39.2 1998. 473-479.
- Bezdek, A. and Bezdek, Karoly. Finite and uniform stability of sphere packings 20.1 1998. 111-130.
- Bezdek, Karoly and Bisztriczky, Ted. A proof of {H}adwiger's covering conjecture for dual cyclic polytopes 68.1 1997. 29-41.
- Bezdek, Karoly. Isoperimetric inequalities and the dodecahedral conjecture 8.6 1997. 759-780.
- Bezdek, Karoly. Light-sources that illuminate the boundary points all but the vertices of a convex polyhedron 34.1-2 1997. 17-21.
- Bezdek, Karoly. Minimal translation covers for sets of diameter 1 34.1-2 1997. 23-27.
- Bezdek, A. and Bezdek, Karoly. Conway's fried potato problem revisited 66.6 1996. 522-528.
- Bezdek, Karoly. Kepler's conjecture and the dodecahedral conjecture 96.4 1996. 52-54.
- Bezdek, A. and Bezdek, Karoly. A solution of {C}onway's fried potato problem 27.5 1995. 492-496.
- Bezdek, A. and Bezdek, Karoly. Finite and uniform stability of sphere coverings 13.3-4 1995. 313-319.
- Bezdek, Karoly and Hausel, T. . Coating by cubes 35.1 1994. 119-123.
- Bezdek, Karoly, Brass, Peter and Harborth, Heiko . Maximum convex hulls of connected systems of segments and of polyominoes 35.1 1994. 37-43.
- Bezdek, Karoly. On affine subspaces that illuminate a convex set 35.1 1994. 131-139.
- Bezdek, Karoly. An illumination problem for zonoids 81.3 1993. 265-272.
- Bezdek, Karoly. A note on the illumination of convex bodies 45.1 1993. 89-91.
- Bezdek, Karoly and Bisztriczky, Ted. Hadwiger's covering conjecture and low-dimensional dual cyclic polytopes 46.3 1993. 279-286.
- Bezdek, Karoly, Ladvanszky, Janos and Zoller, Vilmos. The {E}uler line revisited 48.2 1993. 76-79.
- Bezdek, Karoly. On the illumination of unbounded closed convex sets 80.1-2 1992. 87-96.
- Bezdek, A. , Bezdek, Karoly and Bisztriczky, Ted. On illumination in the plane by line segments 41.1 1992. 39-50.
- Bezdek, Karoly. Hadwiger's covering conjecture and its relatives 99.10 1992. 954-956.
- Bezdek, Karoly. On the illumination of smooth convex bodies 58.6 1992. 611-614.
- Bezdek, Karoly. Research Problem 48 24.2 1992. 122-123.
- Bezdek, Karoly. Research Problem 47 24.2 1992. 121.
- Bezdek, Karoly. Research Problem 46 24.2 1992. 119-121.
- Bezdek, A. , Bezdek, Karoly and Bisztriczky, Ted. On the {$(n-2)$}-transversals of {$n$} convex subsets of the plane 40.3 1991. 263-268.
- Bezdek, Karoly. The problem of illumination of the boundary of a convex body by affine subspaces 38.2 1991. 362-375 (1992).
- Bezdek, Karoly. Lower bounds for packing densities 57.3-4 1991. 291-311.
- Bezdek, A. and Bezdek, Karoly. Interior points of the convex hull of few points in {${\bf E}\sp d$} 111.3 1991. 181-186.
- Bezdek, Karoly. On certain translation covers 10.2 1990. 279-286.
- Bezdek, Karoly and Bisztriczky, Ted. On hyperplanes and polytopes 109.1 1990. 39-48.
- Bezdek, A. and Bezdek, Karoly. Facets with fewest vertices 109.2 1990. 89-96.
- Bezdek, Karoly. On billiard arcs 30 1990. 155-166.
- Bezdek, Andras and Bezdek, Karoly. On the second smallest distance between finitely many points on the sphere 29.2 1989. 141-152.
- Bezdek, Karoly. Covering curves by translates of a convex set 96.9 1989. 789-806.
- Bezdek, Karoly and Schmitz, Michael . Zur {Z}erlegung von {E}inheitskugel\"uberdeckungen des {$E\sp d$} in {E}inheitskugelpackungen 28 1989. 65-82.
- Bezdek, Andras and Bezdek, Karoly. Polygonal cycles with a large number of components 32. 1989. 209-214 .
- Bezdek, A. and Bezdek, Karoly. On a discrete {D}ido-type question 44.4 1989. 92-100.
- Bezdek, A. and Bezdek, Karoly. A note on the ten-neighbour packings of equal balls 27 1988. 49-53.
- Bezdek, Karoly and Connelly, R. . Intersection points 31. 1988. 115-127 .
- Bezdek, Karoly. The thinnest holding-lattice of a set 103.3 1987. 177-185.
- Bezdek, Karoly. Compact packings in the {E}uclidean space 25 1987. 79-84.
- Bezdek, A. and Bezdek, Karoly. On the centroids of convex solids of revolution 30. 1987. 115-119.
- Bezdek, Karoly. Densest packing of small number of congruent spheres in polyhedra 30. 1987. 177-194.
- Bezdek, Karoly. Circle packings into convex domains of the {E}uclidean and hyperbolic plane and the sphere 21.3 1986. 249-255.
- Bezdek, Karoly. Ionpackings in the space 22 1986. 81-88.
- Bezdek, Karoly. A remark about the directed line-elements in the plane 22 1986. 89-94.
- Bezdek, Karoly. On a {D}ido-type question 29. 1986. 241-244 .
- Bezdek, A. , Bezdek, Karoly and Boroczky, K. . On compact packings 21.3-4 1986. 343-346.
- Bezdek, A. and Bezdek, Karoly. When is it possible to translate a convex polyhedron in an other one? 21.3-4 1986. 337-342.
- Bezdek, A. and Bezdek, Karoly. Enclosing a set by sets 21.3-4 1986. 409-413.
- Bezdek, A. and Bezdek, Karoly. \"{U}ber einige d\"unnste {K}reis\"uberdeckungen konvexer {B}ereiche durch endliche {A}nzahl von kongruenten {K}reisen 19 1985. 159-168.
- Bezdek, Karoly and Joo, Istvan. Stufenkonvexit\"at 19 1985. 169-175.
- Bezdek, Karoly. \"{U}ber einige optimale Konfigurationen von Kreisen 27. 1985. 143-151 .
- Bezdek, Karoly. Ausf\"ullungen in der hyperbolischen Ebene durch endliche Anzahl kongruenter Kreise 27. 1985. 113-124 .
- Bezdek, Karoly. Ein elementarer {B}eweis f\"ur die isoperimetrische Ungleichung in der euklidischen und hyperbolischen Ebene 27. 1985. 107-112 .
- Bezdek, Karoly and Pach, J . A point set everywhere dense in the plane 40.4 1985. 81-84.
- Bezdek, Andras and Bezdek, Karoly. Eine hinreichende {B}edingung f\"ur die \"{U}berdeckung des {E}inheitsw\"urfels durch homothetische {E}xemplare im {$n$}-dimensionalen euklidischen {R}aum 17 1984. 5-21.
- Bezdek, Karoly. \"{U}ber einige {K}reis\"uberdeckungen 14 1983. 7-13.
- Bezdek, Karoly. \"{U}ber {I}onenpackungen 18.2-4 1983. 277-285.
- Bezdek, Karoly. Ausf\"ullung eines {K}reises durch kongruente {K}reise in der hyperbolischen {E}bene 17.1-4 1982. 353-366.
- Bezdek, Karoly. Mosaics with each face having the same number of neighbors 28.4 1977/80. 297-303.
Other
- Bezdek, Karoly. Combinatorial Geometry by Janos Pach and Pankaj K. Agarwal 35.4 1998. 341-342.
Research Groups
Curricula Vitae
Degrees
- 1997 - Dr.Habil - Eotvos University, Budapest
- 1994 - D.Sc. - Hungarian Academy of Sciences
- 1985 - C.Sc. - Hungarian Academy of Sciences
- 1980 - Ph.D. - Eotvos University, Budapest
- 1978 - M.Sc. - Eotvos University, Budapest
Awards
- 2010 - Canada Research Chair - Tier 1 - NSERC
- 2003 - Canada Research Chair - Tier 1 - NSERC
Students
Masters Students:
Ph.D. Students:
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