Károly Bezdek

Hungarian

Károly Bezdek (b. May 28, 1955, in Budapest, Hungary), is a mathematician and professor and a Canada Research Chair (Tier 1) at the University of Calgary. Bezdek is also a professor on leave from University of Pannonia and Eötvös Loránd University.

Early life and family

Károly Bezdek was born in Budapest, Hungary. His parents are Károly Bezdek, Sr. 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.^[1] Károly entered Eötvös Loránd University in Hungary, and completed his Diploma in Mathematics in 1978. Bezdek is married to Éva Bezdek, and has three sons: Dániel, Máté and Márk.

Professional accomplishments

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. 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 and 2006. During 1978–2003, while being on a number of special leaves from Eötvös Loránd University, he has held several visiting positions at research institutions in Canada, Germany, the Netherlands, and USA. This included a period of about 7 years at the Department of Mathematics of Cornell University in Ithaca, New York. 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. He is one of the three founding editors-in-chief of the free peer-reviewed electronic journal Contributions to Discrete Mathematics.^[2] He is also an associate editor for the Canadian Journal of Mathematics^[3] and the Canadian Mathematical Bulletin.^[4]

Research interests and notable results

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 100 research papers. His results include:

• A proof of tight bounds for the vertex index of spheres in Banach 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.^[5]

• 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.^[6]

• 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.^[7]

• 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^[8] 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.^[9]

• A discovery of a general principle for uniform stability of sphere packings (joint work with András Bezdek, Auburn University and Robert Connelly, Cornell University); published in A. Bezdek, K. Bezdek and R. Connelly, Finite and uniform stability of sphere packings, Discrete and Computational Geometry 20 (1998), 111–130.^[10]

• 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.^[11]

• A proof of the Boltyanski–Hadwiger Conjecture (1960) for convex polyhedra with symmetry; published in K. Bezdek, The problem of illumination of the boundary of a convex body by affine subspaces, Mathematika 38 (1991), 362–375.^[12]

• 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.^[13]

Books

His book on "Classical Topics in Discrete Geometry", published by Springer in 2010 is intended for a semester long graduate level course, giving a brief introduction to discrete geometry. It is also a research monograph that leads the reader to the frontiers of the most recent research developments in the classical core part of discrete geometry. Last but not least, the forty-some selected research problems offer a good chance to use the book as a short problem book aimed at advanced undergraduate and graduate students as well as researchers.^[14]

References

External links

• http://math.ucalgary.ca/profiles/karoly-bezdek
• http://math.ucalgary.ca/ccdg/
• http://cdm.math.ucalgary.ca/index.php/cdm
• http://www.chairs-chaires.gc.ca/chairholders-titulaires/profile-eng.aspx?profileId=267