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Directory of People » Karoly Bezdek

Karoly Bezdek

photograph of Karoly Bezdek

Job Title:

  • Professor
  • Canada Research Chair (Tier 1)
  • Director of Centre of Computational & Discrete Geometry

Phone:

  • +1 (403) 220-6919

Office:

  • MS 318

Email:

Web site:

Degrees:

Curriculum Vitae:

Member of:

  • CCDG

Research Interests:

  • Discrete Geometry (including the theory of Packing, Covering and Tiling)
  • Convex Geometry (including the Brunn-Minkowski theory of Convex Bodies, Convex Polytopes and Lattices/Geometry of Numbers)
  • Combinatorial Geometry
  • Geometric Analysis and Rigidity
  • Hyperbolic and Spherical Geometry

Ph. D. Students:

  • Ryan Trelford
  • Peter Papez (2009)
  • Mate Salat (2009)
  • Zsolt Langi (2008)
  • Marton Naszodi (2007)

Masters Students:

  • Wesley Maciejewski (2007)
  • Bouchra Mika Sabbagh (2007)

Teaching:

Past Courses:

  • MATH253 - Calculus II
  • PMAT319 - TRANSFORMATION GEOMETRY
  • PMAT423 - Differential Geometry
  • PMAT425 - Geometry
  • PMAT60347 - CONVEXITY
  • PMAT60352 - ANALYTIC CONVEXITY-HIGHER DIMENS
Representative Publications:
Forthcoming
Bezdek, Karoly and Schneider, Rolf. Covering large balls with convex sets in spherical space "Beitrage zur Alg. und Geom." (to appear)
Bezdek, Karoly. Tarski's plank problem revisited "Bolyai Soc. Math. Studies, Springer" (to appear)
Journal Paper
Bezdek, Daniel and Bezdek, Karoly. "Shortest billiard trajectories" Geometriae Dedicata 141 (2009): 197-206
Bezdek, Karoly and Litvak, Alexander. "Covering convex bodies by cylinders and lattice points by flats" Journal of Geometric Analysis 19.2 (2009): 233-243
Bezdek, Karoly and Kiss, Gyorgy. "On the X-ray number of almost smooth convex bodies and of convex bodies of constant width" Canadian Mathematical Bulletin. Bulletin Canadien de Mathematiques 52.3 (2009): 342-348
Bezdek, Karoly and Connelly, Robert. "On the weighted Kneser-Poulsen conjecture" Periodica Mathematica Hungarica. Journal of the J\\''anos Bolyai Mathematical Society 57.2 (2008): 121-129
Bezdek, Karoly. "From the Kneser-Poulsen conjecture to ball-polyhedra" European Journal of Combinatorics 29.8 (2008): 1820-1830
Bezdek, Karoly, Langi, Zsolt, Naszodi, Marton and Papez, Peter. "Ball-Polyhedra" Discrete Comput. Geom. 38.2 (2007): 201-230
Bezdek, Karoly and Litvak, Alexander. "On the vertex index of convex bodies" Advances in Mathematics 215.2 (2007): 626-641
Bezdek, Karoly, Naszodi, Marton and Oliveros-Braniff, Deborah. "Antipodality in hyperbolic space" Journal of Geometry 85 (2006): 22-31
Bezdek, Karoly. "Sphere Packings Revisited" European Journal of Combinatorics 27.6 (2006): 864-883
Bezdek, Karoly. "The illumination conjecture and its extensions" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 53.1-2 (2006): 59-69
Bezdek, Karoly and Naszodi, Marton. "Rigidity of ball-polyhedra in Euclidean 3-space" European Journal of Combinatorics 27.2 (2006): 255-268
Bezdek, Karoly, Boroczky, Karoly and Kiss, Gyorgy. "On the successive illumination parameters of convex bodies" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 53.1-2 (2006): 71-82
Bezdek, Karoly, Bisztriczky, Ted, Csikos, Balazs and Heppes, Aladar. "On the transversal Helly numbers of disjoint and overlapping disks" Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 87.1 (2006): 86-96
Bezdek, Karoly, Connelly, Robert and Csikos, Balazs. "On the perimeter of the intersection of congruent disks" Beitrage zur Algebra und Geometrie. Contributions to Algebra and Geometry 47.1 (2006): 53-62
Bezdek, Karoly. "Finding the best face on a Voronoi polyhedron - the strong dodecahedral conjecture revisited" Monatshefte fur Mathematik 145 (2005): 191-206
Bezdek, Karoly. "On the monotonicity of the volume of hyperbolic convex polyhedra" Beitrage zur Algebra und Geometrie. Contributions to Algebra and Geometry 46.2 (2005): 609-614
Bezdek, Karoly and Connelly, Robert. "The Kneser-Poulsen Conjecture for Spherical Polytopes" Discrete and Computational Geometry 32.1 ( 2004): 101-106
Bezdek, Karoly. "On {$k\sp +$}-neighbour packings and one-sided {H}adwiger configurations" Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 44.2 (2003): 493-498
Bezdek, Karoly. "The {R}adon number of the three-dimensional integer lattice" Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science 30.2 (2003): 181-184
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 {$d\ge8$}" Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science 28.1 (2002): 75-106
Bezdek, Karoly. "On the maximum number of touching pairs in a finite packing of translates of a convex body" Journal of Combinatorial Theory. Series A 98.1 (2002): 192-200
Bezdek, Karoly. "Pushing disks apart-the {K}neser-{P}oulsen conjecture in the plane" Journal f\"ur die Reine und Angewandte Mathematik 553 (2002): 221-236
Bezdek, Karoly. "The polyhedral {T}ammes problem" Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 76.4 (2001): 314-320
Bezdek, Karoly. "A lower bound for the mean width of {V}oronoi polyhedra of unit ball packings in {$\bold E\sp 3$}" Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 74.5 (2000): 392-400
Bezdek, Karoly. "On rhombic dodecahedra" Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 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" Journal f\"ur die Reine und Angewandte Mathematik 518 (2000): 131-143
Bezdek, Karoly. "Two-distance preserving functions from {E}uclidean space" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 39.1-3 (1999): 185-200
Bezdek, Karoly and Langi, Zsolt. "Almost equidistant points on {$S\sp {d-1}$}" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 39.1-3 (1999): 139-144
Bezdek, Karoly. "Voronoi polyhedra of unit ball packings with small surface area" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 39.1-3 (1999): 107-118
Bezdek, Karoly. "Danzer-{G}r\"unbaum's theorem revisited" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 39.1-3 (1999): 7-15
Bezdek, A. and Bezdek, Karoly. "Finite and uniform stability of sphere packings" Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science 20.1 (1998): 111-130
Bezdek, Karoly. "The minimum mean width translation cover for sets of diameter one" Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 39.2 (1998): 473-479
Bezdek, Karoly. "Isoperimetric inequalities and the dodecahedral conjecture" International Journal of Mathematics 8.6 (1997): 759-780
Bezdek, Karoly. "Light-sources that illuminate the boundary points all but the vertices of a convex polyhedron" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 34.1-2 (1997): 17-21
Bezdek, Karoly and Bisztriczky, Ted. "A proof of {H}adwiger's covering conjecture for dual cyclic polytopes" Geometriae Dedicata 68.1 (1997): 29-41
Bezdek, Karoly. "Minimal translation covers for sets of diameter 1" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 34.1-2 (1997): 23-27
Bezdek, A. and Bezdek, Karoly. "Conway's fried potato problem revisited" Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 66.6 (1996): 522-528
Bezdek, Karoly. "Kepler's conjecture and the dodecahedral conjecture" Mitteilungen der DMV, Bulletin of the German Mathematical Society 96.4 (1996): 52-54
Bezdek, A. and Bezdek, Karoly. "Finite and uniform stability of sphere coverings" Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science 13.3-4 (1995): 313-319
Bezdek, A. and Bezdek, Karoly. "A solution of {C}onway's fried potato problem" The Bulletin of the London Mathematical Society 27.5 (1995): 492-496
Bezdek, Karoly and Hausel, T. . "Coating by cubes" Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 35.1 (1994): 119-123
Bezdek, Karoly, Brass, Peter and Harborth, Heiko . "Maximum convex hulls of connected systems of segments and of polyominoes" Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 35.1 (1994): 37-43
Bezdek, Karoly. "On affine subspaces that illuminate a convex set" Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 35.1 (1994): 131-139
Bezdek, Karoly, Ladvanszky, Janos and Zoller, Vilmos. "The {E}uler line revisited" Elemente der Mathematik. Eine Zeitschrift der Schweizerischen Mathematischen Gesellschaft. Une Revue de la Soci\'et\'e Math\'ematique Suisse. Una Rivista della Societ\`a Matematica Svizzera 48.2 (1993): 76-79
Bezdek, Karoly. "An illumination problem for zonoids" Israel Journal of Mathematics 81.3 (1993): 265-272
Bezdek, Karoly and Bisztriczky, Ted. "Hadwiger's covering conjecture and low-dimensional dual cyclic polytopes" Geometriae Dedicata 46.3 (1993): 279-286
Bezdek, Karoly. "A note on the illumination of convex bodies" Geometriae Dedicata 45.1 (1993): 89-91
Bezdek, Karoly. "Research Problem 47" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 24.2 (1992): 121
Bezdek, Karoly. "Research Problem 46" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 24.2 (1992): 119-121
Bezdek, Karoly. "Research Problem 48" Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 24.2 (1992): 122-123
Bezdek, Karoly. "On the illumination of unbounded closed convex sets" Israel Journal of Mathematics 80.1-2 (1992): 87-96
Bezdek, Karoly. "On the illumination of smooth convex bodies" Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 58.6 (1992): 611-614
Bezdek, A. , Bezdek, Karoly and Bisztriczky, Ted. "On illumination in the plane by line segments" Geometriae Dedicata 41.1 (1992): 39-50
Bezdek, Karoly. "Hadwiger's covering conjecture and its relatives" The American Mathematical Monthly 99.10 (1992): 954-956
Bezdek, Karoly. "Lower bounds for packing densities" Acta Mathematica Hungarica 57.3-4 (1991): 291-311
Bezdek, A. , Bezdek, Karoly and Bisztriczky, Ted. "On the {$(n-2)$}-transversals of {$n$} convex subsets of the plane" Geometriae Dedicata 40.3 (1991): 263-268
Bezdek, A. and Bezdek, Karoly. "Interior points of the convex hull of few points in {${\bf E}\sp d$}" Monatshefte f\"ur Mathematik 111.3 (1991): 181-186
Bezdek, Karoly. "The problem of illumination of the boundary of a convex body by affine subspaces" Mathematika. A Journal of Pure and Applied Mathematics 38.2 (1991): 362-375 (1992)
Bezdek, A. and Bezdek, Karoly. "Facets with fewest vertices" Monatshefte f\"ur Mathematik 109.2 (1990): 89-96
Bezdek, Karoly and Bisztriczky, Ted. "On hyperplanes and polytopes" Monatshefte f\"ur Mathematik 109.1 (1990): 39-48
Bezdek, Karoly. "On certain translation covers" Note di Matematica 10.2 (1990): 279-286
Bezdek, Karoly. "On billiard arcs" Beitr\"age zur Algebra und Geometrie30 (1990): 155-166
Bezdek, Karoly and Schmitz, Michael . "Zur {Z}erlegung von {E}inheitskugel\"uberdeckungen des {$E\sp d$} in {E}inheitskugelpackungen" Beitr\"age zur Algebra und Geometrie28 (1989): 65-82
Bezdek, Andras and Bezdek, Karoly. "Polygonal cycles with a large number of components" Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 32 (1989): 209-214
Bezdek, Karoly. "Covering curves by translates of a convex set" The American Mathematical Monthly 96.9 (1989): 789-806
Bezdek, Andras and Bezdek, Karoly. "On the second smallest distance between finitely many points on the sphere" Geometriae Dedicata 29.2 (1989): 141-152
Bezdek, A. and Bezdek, Karoly. "On a discrete {D}ido-type question" Elemente der Mathematik. Revue de Math\'ematiques \'El\'ementaires. Rivista de Matematica Elementare 44.4 (1989): 92-100
Bezdek, A. and Bezdek, Karoly. "A note on the ten-neighbour packings of equal balls" Beitr\"age zur Algebra und Geometrie27 (1988): 49-53
Bezdek, Karoly and Connelly, R. . "Intersection points" Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 31 (1988): 115-127
Bezdek, Karoly. "The thinnest holding-lattice of a set" Monatshefte f\"ur Mathematik 103.3 (1987): 177-185
Bezdek, Karoly. "Densest packing of small number of congruent spheres in polyhedra" Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 30 (1987): 177-194
Bezdek, A. and Bezdek, Karoly. "On the centroids of convex solids of revolution" Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 30 (1987): 115-119
Bezdek, Karoly. "Compact packings in the {E}uclidean space" Beitr\"age zur Algebra und Geometrie25 (1987): 79-84
Bezdek, A. and Bezdek, Karoly. "Enclosing a set by sets" Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences 21.3-4 (1986): 409-413
Bezdek, Karoly. "Circle packings into convex domains of the {E}uclidean and hyperbolic plane and the sphere" Geometriae Dedicata 21.3 (1986): 249-255
Bezdek, A. and Bezdek, Karoly. "When is it possible to translate a convex polyhedron in an other one?" Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences 21.3-4 (1986): 337-342
Bezdek, Karoly. "On a {D}ido-type question" Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 29 (1986): 241-244
Bezdek, Karoly. "Ionpackings in the space" Beitr\"age zur Algebra und Geometrie22 (1986): 81-88
Bezdek, Karoly. "A remark about the directed line-elements in the plane" Beitr\"age zur Algebra und Geometrie22 (1986): 89-94
Bezdek, A. , Bezdek, Karoly and Boroczky, K. . "On compact packings" Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences 21.3-4 (1986): 343-346
Bezdek, Karoly. "Ausf\"ullungen in der hyperbolischen Ebene durch endliche Anzahl kongruenter Kreise" Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 27 (1985): 113-124
Bezdek, Karoly. "\"{U}ber einige optimale Konfigurationen von Kreisen" Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 27 (1985): 143-151
Bezdek, A. and Bezdek, Karoly. "\"{U}ber einige d\"unnste {K}reis\"uberdeckungen konvexer {B}ereiche durch endliche {A}nzahl von kongruenten {K}reisen" Beitr\"age zur Algebra und Geometrie19 (1985): 159-168
Bezdek, Karoly. "Ein elementarer {B}eweis f\"ur die isoperimetrische Ungleichung in der euklidischen und hyperbolischen Ebene" Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 27 (1985): 107-112
Bezdek, Karoly and Joo, Istvan. "Stufenkonvexit\"at" Beitr\"age zur Algebra und Geometrie19 (1985): 169-175
Bezdek, Karoly and Pach, J . "A point set everywhere dense in the plane" Elemente der Mathematik. Revue de Math\'ematiques \'El\'ementaires. Rivista de Matematica Elementare 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" Beitr\"age zur Algebra und Geometrie17 (1984): 5-21
Bezdek, Karoly. "\"{U}ber {I}onenpackungen" Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences 18.2-4 (1983): 277-285
Bezdek, Karoly. "\"{U}ber einige {K}reis\"uberdeckungen" Beitr\"age zur Algebra und Geometrie14 (1983): 7-13
Bezdek, Karoly. "Ausf\"ullung eines {K}reises durch kongruente {K}reise in der hyperbolischen {E}bene" Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences 17.1-4 (1982): 353-366
Bezdek, Karoly. "Mosaics with each face having the same number of neighbors" Mat. Lapok 28.4 (1977/80): 297-303
Conference Proceedings
Bezdek, Karoly. From the Kneser-Poulsen conjecture to ball-polyhedra via Voronoi diagrams IEEE Computer Society (CPS) (2007): 3-6
Book Chapter
Bezdek, Karoly, Bisztriczky, Ted and Boroczky, Karoly. Edge-antipodal 3-polytopes In . 52 (2005): 129-134
Bezdek, Karoly. Sphere packings in 3-space In . 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 In Discrete geometry. 253, Dekker (2003): 291-304
Bezdek, Karoly. Space Filling, Handbook of Discrete and Combinatorial Mathematics In . CRC Press (2000): 824-830
Bezdek, Karoly and Connelly, Robert . The minimum mean with translation cover for sets of diameter one In 107 Jahre Drehfluchtprinzip (Vorau, 1997). Tech. Univ. Graz (1999): 4-10
Bezdek, Karoly and Zamfirescu, T. . A characterization of {$3$}-dimensional convex sets with an infinite {X}-ray number In Intuitive geometry (Szeged, 1991). 63, North-Holland (1994): 33-38
Beutelspacher, A. and Bezdek, Karoly. The {H}elly dimension relative to a lattice In Intuitive geometry (Szeged, 1991). 63, North-Holland (1994): 11-16
Bezdek, Karoly and Hausel, T. . On the number of lattice hyperplanes which are needed to cover the lattice points of a convex body In Intuitive geometry (Szeged, 1991). 63, North-Holland (1994): 27-31
Bezdek, Karoly. Hadwiger-{L}evi's covering problem revisited In New trends in discrete and computational geometry. 10, Springer (1993): 199-233
Bezdek, Karoly. On planar tilings with finitely many sorts of tiles In Topics in combinatorics and graph theory (Oberwolfach, 1990). Physica (1990): 79-85
Bezdek, Karoly, Connelly, R. and Kertesz, G. On the average number of neighbors in a spherical packing of congruent circles In Intuitive geometry (Si\'ofok, 1985). 48, North-Holland (1987): 37-52
Other
Bezdek, Karoly. Combinatorial Geometry by Janos Pach and Pankaj K. Agarwal 35.4 (1998): 341-342

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