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Károly Bezdek

April 10, 2024

Károly Bezdek (born May 28, 1955, in Budapest, Hungary) is a Hungarian-Canadian mathematician. He is a professor as well as a Canada Research Chair of mathematics and the director of the Centre for Computational and Discrete Geometry at the University of Calgary in Calgary, Alberta, Canada. Also he is a professor (on leave) of mathematics at the University of Pannonia in Veszprém, Hungary. His main research interests are in geometry in particular, in combinatorial, computational, convex, and discrete geometry. He has authored 3 books and more than 130 research papers. He is a founding Editor-in-Chief of the e-journal Contributions to Discrete Mathematics (CDM).

Károly Bezdek
Born (1955-05-28) May 28, 1955 (age 68)
Budapest, Hungary
Nationality Hungarian Canadian
Known forbooks "Classical topics in discrete geometry", Springer, 2010 and "Lectures on sphere arrangements - the discrete geometric side", Springer, 2013
AwardsLászló Fejes Tóth Prize (2015), Research Excellence Award of the University of Calgary (2017), Immigrant of Distinction Award for Lifetime Achievement of the City of Calgary (2020)
Academic background
Alma materEötvös Loránd University (Ph.D., Math., 1980; Dr.habil., Math., 1997) and Hungarian Academy of Sciences (Candidate, 1985; Doctorate, 1995)
Doctoral advisorKároly Böröczky (Eötvös Loránd University)
Academic work
InstitutionsEötvös Loránd University, University of Calgary, and University of Pannonia
Main interestsConvex and discrete geometry
Notable ideasTheorems on extremal properties of packings, contact numbers, coverings, illumination numbers, Voronoi diagrams, ball-polyhedra, molecules, and billiards
Websitehttp://contacts.ucalgary.ca/info/math/profiles/101-152921

Early life and family edit

Károly Bezdek was born in Budapest, Hungary, but grew up in Dunaújváros, Hungary. His parents are Károly Bezdek Sr. (mechanical engineer) and Magdolna Cserey. His brother András Bezdek is also a mathematician. Károly and his brother have scored at the top level in several Mathematics and Physics competitions for high school and university students in Hungary. Károly's list of awards include winning the first prize in the traditional KöMal (Hungarian Math. Journal for Highschool Students) contest in the academic year 1972–1973, as well as winning the first prize for the research results presented at the National Science Conference for Hungarian Undergraduate Students (TDK) in 1978. Károly entered the Faculty of Science of the Eötvös Loránd University in Hungary, and completed his Diploma in Mathematics in 1978. Bezdek is married to Éva Bezdek, and has three sons: Dániel,[1] Máté [2] and Márk.[3][4]

Career edit

Károly Bezdek received his Ph.D. (1980) as well as his Habilitation degree (1997) in mathematics from Eötvös Loránd University, in Budapest, Hungary and his Candidate of Mathematical Sciences degree (1985) as well as his Doctor of Mathematical Sciences degree (1995) from the Hungarian Academy of Sciences.[5] He has been a faculty member of the Department of Geometry at Eötvös Loránd University in Budapest since 1978. In particular, he has been the chair of that department between 1999-2006 and a full professor between 1998 and 2012. During 1978–2003, while being on a number of special leaves from Eötvös Loránd University, he has held numerous visiting positions at research institutions in Canada, Germany, the Netherlands, and United States. This included a period of about 7 years at the Department of Mathematics of Cornell University in Ithaca, New York. Between 1998 and 2001 Bezdek was appointed a Széchenyi Professor of mathematics at Eötvös Loránd University, in Budapest, Hungary. From 2003 Károly Bezdek is the Canada Research Chair of computational and discrete geometry at the Department of Mathematics and Statistics of the University of Calgary and is the director of the Center for Computational and Discrete Geometry at the University of Calgary. Between 2006 and 2010 Bezdek was an associated member of the Alfréd Rényi Institute of Mathematics in Budapest, Hungary. From 2010 Bezdek is a full professor (on leave) at the Department of Mathematics of the University of Pannonia in Veszprém, Hungary. Between July–December, 2011 Bezdek was a program co-chair of the 6 month thematic program on discrete geometry and its applications at the Fields Institute in Toronto, Ontario, Canada. Also, he is one of the three founding editors-in-chief of the free peer-reviewed electronic journal Contributions to Discrete Mathematics.[6]

Research interests and notable results edit

His research interests are in combinatorial, computational, convex and discrete geometry including some aspects of geometric analysis, rigidity and optimization. He is the author of more than 130 research papers and has written three research monographs. In particular, he is known for the following works:

  • A new part of discrete geometry is studied in K. Bezdek and Zs. Lángi, Volumetric Discrete Geometry, Chapman and Hall - CRC Press, Boca Raton, FL, 2019, which is centered around several outstanding problems of discrete geometry where the volume plays a significant role. The results and proofs reflect and stimulate the fruitful interplay between linear algebra, geometry, geometric analysis, and combinatorics.[7]
  • A proof of the Goodman-Goodman Conjecture (1945) for centrally symmetric convex bodies in Euclidean d-space for d > 1 and a counterexample to it for convex bodies in general (joint work with Zsolt Lángi, Budapest University of Technology and Economics); published in K. Bezdek and Zs. Lángi, On non-separable families of positive homothetic convex bodies, Discrete and Computational Geometry 56/3 (2016), 802–813.[8]
  • A proof of the Boltyanski–Hadwiger Conjecture (1960) for wide intersections of congruent balls (also called fat spindle convex bodies) in Euclidean spaces of dimensions greater than or equal to 15; published in K. Bezdek, Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width, Discrete and Computational Geometry 47/2 (2012), 275–287.[9]
  • A variational characterization of shortest billiard trajectories in convex bodies of Euclidean d-space for d > 1 (joint work with Dániel Bezdek); published in D. Bezdek and K. Bezdek, Shortest billiard trajectories, Geometriae Dedicata 141/1 (2009), 197–206.[10]
  • A proof of tight bounds for the vertex index of (unit) balls in normed spaces supporting a quantitative approach to the Boltyanski–Hadwiger Conjecture (joint work with Alexander Litvak, University of Alberta); published in K. Bezdek and A. E. Litvak, On the vertex index of convex bodies, Advances in Mathematics 215/2 (2007), 626–641.[11]
  • A proof of the Kneser–Poulsen Conjecture (1955) for hemispheres in spherical d-space for all d > 1 (joint work with Robert Connelly, Cornell University); published in K. Bezdek and R. Connelly, The Kneser–Poulsen conjecture for spherical polytopes, Discrete and Computational Geometry 32 (2004), 101–106.[12]
  • A proof of the Kneser–Poulsen Conjecture (1955) in the Euclidean plane (joint work with Robert Connelly, Cornell University); published in K. Bezdek and R. Connelly, Pushing disks apart – the Kneser–Poulsen conjecture in the plane, Journal für die reine und angewandte Mathematik 553 (2002), 221–236.[13]
  • A stronger form of Rogers's lemma and its application to the problem of minimizing surface area of Voronoi cells in unit ball packings; published in K. Bezdek, Improving Rogers' upper bound for the density of unit ball packings via estimating the surface area of Voronoi cells from below in Euclidean d-space for all d > 7, Discrete and Computational Geometry 28 (2002), 75–106[14] and in K. Bezdek, On a stronger form of Rogers's lemma and the minimum surface area of Voronoi cells in unit ball packings, Journal für die reine und angewandte Mathematik 518 (2000), 131–143.[15]
  • A solution of John Horton Conway's "fried potato problem" (joint work with András Bezdek, Auburn University); published in A. Bezdek and K. Bezdek, A solution of Conway's fried potato problem, Bulletin of the London Mathematical Society 27 (1995), 492–496.[16]
  • A proof of the Boltyanski–Hadwiger Conjecture (1960) for convex polyhedra with symmetry in Euclidean 3-space; published in K. Bezdek, The problem of illumination of the boundary of a convex body by affine subspaces, Mathematika 38 (1991), 362–375.[17]
  • A proof of László Fejes Tóth's Hyperbolic Disk Packing Conjecture; published in K. Bezdek, Ausfüllung eines Kreises durch kongruente Kreise in der hyperbolischen Ebene, Studia Scientiarum Mathematicarum Hungarica 17 (1982), 353–366.[18]

Books edit

His three research monographs "Classical Topics in Discrete Geometry", CMS Books in Mathematics, Springer, New York, 2010, "Lectures on Sphere Arrangements - the Discrete Geometric Side", Fields Institute Monographs, Springer, New York, 2013, and "Volumetric Discrete Geometry", Discrete Mathematics and Its Applications, Chapman and Hall - CRC Press, Boca Raton, FL, 2019 (co-authored with Zs. Lángi), lead the reader to the frontiers of discrete geometry. The conference proceedings "Discrete Geometry and Optimization", Fields Institute Communications, Springer, New York, 2013, edited jointly by him, Antoine Deza (McMaster University) and Yinyu Ye (Stanford University) reflects and stimulates the fruitful interplay between discrete geometry and optimization.[19]

Awards edit

22 October 2020: 2020 Immigrant of Distinction Award for Lifetime Achievement of the City of Calgary[20]

15 May 2017: 2017 Research Excellence Award of the University of Calgary[21]

19 June 2015: 2015 László Fejes Tóth Prize (Hungarian: Fejes Tóth László-díj)[22]

References edit

  1. ^ "Dániel Bezdek".
  2. ^ "Máté Bezdek".
  3. ^ "Márk Bezdek".
  4. ^ Connelly, Robert (2006). "Dedication to Károly Bezdek". Periodica Mathematica Hungarica. 53 (1–2): 3. doi:10.1007/s10998-006-0016-1. S2CID 219320185.
  5. ^ "BIRS Scientific Advisory Board members short CV's".
  6. ^ "E-journal on Discrete Mathematics".
  7. ^ "Bezdek Booklist".
  8. ^ Bezdek, Károly; Lángi, Zsolt (2016). "On non-separable families of positive homothetic convex bodies". Discrete & Computational Geometry. 56 (3): 802–813. arXiv:1602.01020. doi:10.1007/s00454-016-9815-1. S2CID 13645322.
  9. ^ Bezdek, Károly (2012). "Illuminating Spindle Convex Bodies and Minimizing the Volume of Spherical Sets of Constant Width". Discrete & Computational Geometry. 47 (2): 275–287. arXiv:1102.1194. doi:10.1007/s00454-011-9369-1. S2CID 1106755.
  10. ^ "Shortest Billiard Trajectories".
  11. ^ Bezdek, K.; Litvak, A.E. (2007). "Tight Bounds for the Vertex Index of Convex Bodies". Advances in Mathematics. 215 (2): 626–641. arXiv:1110.4334. doi:10.1016/j.aim.2007.04.016. S2CID 14792826.
  12. ^ Connelly, Robert (2004). "The Kneser-Poulsen Conjecture in Spherical Spaces". Discrete & Computational Geometry. 32: 101–106. doi:10.1007/s00454-004-0831-1.
  13. ^ "The Kneser-Poulsen Conjecture in the Eucledian Plane".
  14. ^ Bezdek, Károly (2002). "Lower Bounds for the Surface Area of Voronoi Cells in Unit Sphere Packings (Part 2)". Discrete & Computational Geometry. 28: 75–106. doi:10.1007/s00454-001-0095-y.
  15. ^ "Lower Bounds for the Surface Area of Voronoi Cells in Unit Sphere Packings (Part 1)".
  16. ^ . Archived from the original on 2012-03-29.
  17. ^ "The Illumination Conjecture for Convex Polyhedra with Symmetry".
  18. ^ Bezdek, Károly (1986). "A Proof of the Hyperbolic Disk Packing Conjecture". Geometriae Dedicata. 21 (3): 249–255. doi:10.1007/BF00181530. S2CID 121942660.
  19. ^ "Bezdek Booklist".
  20. ^ Immigrant Services of Calgary (2020), Professor Károly Bezdek awarded the 2020 Immigrant of Distinction Award for Lifetime Achievement, City of Calgary, archived from the original on 2021-12-21, retrieved 2020-10-22
  21. ^ Centre for Computational and Discrete Geometry (2017), , University of Calgary, archived from the original on 2020-03-17, retrieved 2017-06-19
  22. ^ Centre for Computational and Discrete Geometry (2015), , University of Calgary, archived from the original on 2020-01-09, retrieved 2015-07-08

External links edit

April 10, 2024
károly, bezdek, born, 1955, budapest, hungary, hungarian, canadian, mathematician, professor, well, canada, research, chair, mathematics, director, centre, computational, discrete, geometry, university, calgary, calgary, alberta, canada, also, professor, leave. Karoly Bezdek born May 28 1955 in Budapest Hungary is a Hungarian Canadian mathematician He is a professor as well as a Canada Research Chair of mathematics and the director of the Centre for Computational and Discrete Geometry at the University of Calgary in Calgary Alberta Canada Also he is a professor on leave of mathematics at the University of Pannonia in Veszprem Hungary His main research interests are in geometry in particular in combinatorial computational convex and discrete geometry He has authored 3 books and more than 130 research papers He is a founding Editor in Chief of the e journal Contributions to Discrete Mathematics CDM Karoly BezdekBorn 1955 05 28 May 28 1955 age 68 Budapest HungaryNationalityHungarian CanadianKnown forbooks Classical topics in discrete geometry Springer 2010 and Lectures on sphere arrangements the discrete geometric side Springer 2013AwardsLaszlo Fejes Toth Prize 2015 Research Excellence Award of the University of Calgary 2017 Immigrant of Distinction Award for Lifetime Achievement of the City of Calgary 2020 Academic backgroundAlma materEotvos Lorand University Ph D Math 1980 Dr habil Math 1997 and Hungarian Academy of Sciences Candidate 1985 Doctorate 1995 Doctoral advisorKaroly Boroczky Eotvos Lorand University Academic workInstitutionsEotvos Lorand University University of Calgary and University of PannoniaMain interestsConvex and discrete geometryNotable ideasTheorems on extremal properties of packings contact numbers coverings illumination numbers Voronoi diagrams ball polyhedra molecules and billiardsWebsitehttp contacts ucalgary ca info math profiles 101 152921 Contents 1 Early life and family 2 Career 3 Research interests and notable results 4 Books 5 Awards 6 References 7 External linksEarly life and family editKaroly Bezdek was born in Budapest Hungary but grew up in Dunaujvaros Hungary His parents are Karoly Bezdek Sr mechanical engineer and Magdolna Cserey His brother Andras Bezdek is also a mathematician Karoly and his brother have scored at the top level in several Mathematics and Physics competitions for high school and university students in Hungary Karoly s list of awards include winning the first prize in the traditional KoMal Hungarian Math Journal for Highschool Students contest in the academic year 1972 1973 as well as winning the first prize for the research results presented at the National Science Conference for Hungarian Undergraduate Students TDK in 1978 Karoly entered the Faculty of Science of the Eotvos Lorand University in Hungary and completed his Diploma in Mathematics in 1978 Bezdek is married to Eva Bezdek and has three sons Daniel 1 Mate 2 and Mark 3 4 Career editKaroly Bezdek received his Ph D 1980 as well as his Habilitation degree 1997 in mathematics from Eotvos Lorand University in Budapest Hungary and his Candidate of Mathematical Sciences degree 1985 as well as his Doctor of Mathematical Sciences degree 1995 from the Hungarian Academy of Sciences 5 He has been a faculty member of the Department of Geometry at Eotvos Lorand University in Budapest since 1978 In particular he has been the chair of that department between 1999 2006 and a full professor between 1998 and 2012 During 1978 2003 while being on a number of special leaves from Eotvos Lorand University he has held numerous visiting positions at research institutions in Canada Germany the Netherlands and United States This included a period of about 7 years at the Department of Mathematics of Cornell University in Ithaca New York Between 1998 and 2001 Bezdek was appointed a Szechenyi Professor of mathematics at Eotvos Lorand University in Budapest Hungary From 2003 Karoly Bezdek is the Canada Research Chair of computational and discrete geometry at the Department of Mathematics and Statistics of the University of Calgary and is the director of the Center for Computational and Discrete Geometry at the University of Calgary Between 2006 and 2010 Bezdek was an associated member of the Alfred Renyi Institute of Mathematics in Budapest Hungary From 2010 Bezdek is a full professor on leave at the Department of Mathematics of the University of Pannonia in Veszprem Hungary Between July December 2011 Bezdek was a program co chair of the 6 month thematic program on discrete geometry and its applications at the Fields Institute in Toronto Ontario Canada Also he is one of the three founding editors in chief of the free peer reviewed electronic journal Contributions to Discrete Mathematics 6 Research interests and notable results editHis research interests are in combinatorial computational convex and discrete geometry including some aspects of geometric analysis rigidity and optimization He is the author of more than 130 research papers and has written three research monographs In particular he is known for the following works A new part of discrete geometry is studied in K Bezdek and Zs Langi Volumetric Discrete Geometry Chapman and Hall CRC Press Boca Raton FL 2019 which is centered around several outstanding problems of discrete geometry where the volume plays a significant role The results and proofs reflect and stimulate the fruitful interplay between linear algebra geometry geometric analysis and combinatorics 7 A proof of the Goodman Goodman Conjecture 1945 for centrally symmetric convex bodies in Euclidean d space for d gt 1 and a counterexample to it for convex bodies in general joint work with Zsolt Langi Budapest University of Technology and Economics published in K Bezdek and Zs Langi On non separable families of positive homothetic convex bodies Discrete and Computational Geometry 56 3 2016 802 813 8 A proof of the Boltyanski Hadwiger Conjecture 1960 for wide intersections of congruent balls also called fat spindle convex bodies in Euclidean spaces of dimensions greater than or equal to 15 published in K Bezdek Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width Discrete and Computational Geometry 47 2 2012 275 287 9 A variational characterization of shortest billiard trajectories in convex bodies of Euclidean d space for d gt 1 joint work with Daniel Bezdek published in D Bezdek and K Bezdek Shortest billiard trajectories Geometriae Dedicata 141 1 2009 197 206 10 A proof of tight bounds for the vertex index of unit balls in normed spaces supporting a quantitative approach to the Boltyanski Hadwiger Conjecture joint work with Alexander Litvak University of Alberta published in K Bezdek and A E Litvak On the vertex index of convex bodies Advances in Mathematics 215 2 2007 626 641 11 A proof of the Kneser Poulsen Conjecture 1955 for hemispheres in spherical d space for all d gt 1 joint work with Robert Connelly Cornell University published in K Bezdek and R Connelly The Kneser Poulsen conjecture for spherical polytopes Discrete and Computational Geometry 32 2004 101 106 12 A proof of the Kneser Poulsen Conjecture 1955 in the Euclidean plane joint work with Robert Connelly Cornell University published in K Bezdek and R Connelly Pushing disks apart the Kneser Poulsen conjecture in the plane Journal fur die reine und angewandte Mathematik 553 2002 221 236 13 A stronger form of Rogers s lemma and its application to the problem of minimizing surface area of Voronoi cells in unit ball packings published in K Bezdek Improving Rogers upper bound for the density of unit ball packings via estimating the surface area of Voronoi cells from below in Euclidean d space for all d gt 7 Discrete and Computational Geometry 28 2002 75 106 14 and in K Bezdek On a stronger form of Rogers s lemma and the minimum surface area of Voronoi cells in unit ball packings Journal fur die reine und angewandte Mathematik 518 2000 131 143 15 A solution of John Horton Conway s fried potato problem joint work with Andras Bezdek Auburn University published in A Bezdek and K Bezdek A solution of Conway s fried potato problem Bulletin of the London Mathematical Society 27 1995 492 496 16 A proof of the Boltyanski Hadwiger Conjecture 1960 for convex polyhedra with symmetry in Euclidean 3 space published in K Bezdek The problem of illumination of the boundary of a convex body by affine subspaces Mathematika 38 1991 362 375 17 A proof of Laszlo Fejes Toth s Hyperbolic Disk Packing Conjecture published in K Bezdek Ausfullung eines Kreises durch kongruente Kreise in der hyperbolischen Ebene Studia Scientiarum Mathematicarum Hungarica 17 1982 353 366 18 Books editHis three research monographs Classical Topics in Discrete Geometry CMS Books in Mathematics Springer New York 2010 Lectures on Sphere Arrangements the Discrete Geometric Side Fields Institute Monographs Springer New York 2013 and Volumetric Discrete Geometry Discrete Mathematics and Its Applications Chapman and Hall CRC Press Boca Raton FL 2019 co authored with Zs Langi lead the reader to the frontiers of discrete geometry The conference proceedings Discrete Geometry and Optimization Fields Institute Communications Springer New York 2013 edited jointly by him Antoine Deza McMaster University and Yinyu Ye Stanford University reflects and stimulates the fruitful interplay between discrete geometry and optimization 19 Awards edit22 October 2020 2020 Immigrant of Distinction Award for Lifetime Achievement of the City of Calgary 20 15 May 2017 2017 Research Excellence Award of the University of Calgary 21 19 June 2015 2015 Laszlo Fejes Toth Prize Hungarian Fejes Toth Laszlo dij 22 References edit Daniel Bezdek Mate Bezdek Mark Bezdek Connelly Robert 2006 Dedication to Karoly Bezdek Periodica Mathematica Hungarica 53 1 2 3 doi 10 1007 s10998 006 0016 1 S2CID 219320185 BIRS Scientific Advisory Board members short CV s E journal on Discrete Mathematics Bezdek Booklist Bezdek Karoly Langi Zsolt 2016 On non separable families of positive homothetic convex bodies Discrete amp Computational Geometry 56 3 802 813 arXiv 1602 01020 doi 10 1007 s00454 016 9815 1 S2CID 13645322 Bezdek Karoly 2012 Illuminating Spindle Convex Bodies and Minimizing the Volume of Spherical Sets of Constant Width Discrete amp Computational Geometry 47 2 275 287 arXiv 1102 1194 doi 10 1007 s00454 011 9369 1 S2CID 1106755 Shortest Billiard Trajectories Bezdek K Litvak A E 2007 Tight Bounds for the Vertex Index of Convex Bodies Advances in Mathematics 215 2 626 641 arXiv 1110 4334 doi 10 1016 j aim 2007 04 016 S2CID 14792826 Connelly Robert 2004 The Kneser Poulsen Conjecture in Spherical Spaces Discrete amp Computational Geometry 32 101 106 doi 10 1007 s00454 004 0831 1 The Kneser Poulsen Conjecture in the Eucledian Plane Bezdek Karoly 2002 Lower Bounds for the Surface Area of Voronoi Cells in Unit Sphere Packings Part 2 Discrete amp Computational Geometry 28 75 106 doi 10 1007 s00454 001 0095 y Lower Bounds for the Surface Area of Voronoi Cells in Unit Sphere Packings Part 1 Solution of Conway s Fried Potato Problem Archived from the original on 2012 03 29 The Illumination Conjecture for Convex Polyhedra with Symmetry Bezdek Karoly 1986 A Proof of the Hyperbolic Disk Packing Conjecture Geometriae Dedicata 21 3 249 255 doi 10 1007 BF00181530 S2CID 121942660 Bezdek Booklist Immigrant Services of Calgary 2020 Professor Karoly Bezdek awarded the 2020 Immigrant of Distinction Award for Lifetime Achievement City of Calgary archived from the original on 2021 12 21 retrieved 2020 10 22 Centre for Computational and Discrete Geometry 2017 Professor Karoly Bezdek awarded the 2017 Life time Achievement Research Excellence Award University of Calgary archived from the original on 2020 03 17 retrieved 2017 06 19 Centre for Computational and Discrete Geometry 2015 Professor Karoly Bezdek awarded the Laszlo Fejes Toth Prize University of Calgary archived from the original on 2020 01 09 retrieved 2015 07 08External links editK Bezdek University of Calgary website http contacts ucalgary ca info math profiles 101 152921 K Bezdek Canada Research Chair website http www chairs chaires gc ca chairholders titulaires profile eng aspx profileId 267 Center for Computational and Discrete Geometry website http math ucalgary ca ccdg Retrieved from https en wikipedia org w index php title Karoly Bezdek amp oldid 1192446892, wikipedia, wiki, book, books, library,

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