Károly Bezdek
Encyclopedia
Károly Bezdek 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.
, 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. 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.
(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. He is also an associate editor for the Canadian Journal of Mathematics
and the Canadian Mathematical Bulletin
.
, 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:
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.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
and a Canada Research Chair (Tier 1) at the University of Calgary
University of Calgary
The University of Calgary is a public research university located in Calgary, Alberta, Canada. Founded in 1966 the U of C is composed of 14 faculties and more than 85 research institutes and centres.More than 25,000 undergraduate and 5,500 graduate students are currently...
. Bezdek is also a professor on leave from University of Pannonia and Eötvös Loránd University.
Early life and family
Károly Bezdek was born in BudapestBudapest
Budapest is the capital of Hungary. As the largest city of Hungary, it is the country's principal political, cultural, commercial, industrial, and transportation centre. In 2011, Budapest had 1,733,685 inhabitants, down from its 1989 peak of 2,113,645 due to suburbanization. The Budapest Commuter...
, Hungary
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
. 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
Középiskolai Matematikai és Fizikai Lapok
Középiskolai Matematikai és Fizikai Lapok is a Hungarian mathematics and physics journal for high school students...
(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 Eötvös Loránd University in Hungary, and completed his Diploma in Mathematics in 1978. Bezdek is married to Éva Bezdek, and has three sons: Dániel
23199 Bezdek
23199 Bezdek is a main belt asteroid with an orbital period of 1936.3988715 days . The asteroid was discovered by the Lincoln Near-Earth Asteroid Research project in Socorro, New Mexico on September 3, 2000. It is named after Daniel Karoly Bezdek, who won second place at the 2007 Intel...
, Máté
25038 Matebezdek
25038 Matebezdek is a Main Belt minor planet. It was discovered by the Lincoln Near-Earth Asteroid Research project in Socorro, New Mexico on August 17, 1998. It is named after Mate Jozsef Bezdek, who won second place at the 2008 Intel International Science and Engineering Fair...
and Márk.
Professional accomplishments
Károly Bezdek received his Ph.D.Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
(1980) as well as his Habilitation degree (1997) in mathematics from Eötvös Loránd University, in Budapest
Budapest
Budapest is the capital of Hungary. As the largest city of Hungary, it is the country's principal political, cultural, commercial, industrial, and transportation centre. In 2011, Budapest had 1,733,685 inhabitants, down from its 1989 peak of 2,113,645 due to suburbanization. The Budapest Commuter...
, Hungary
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
and his Candidate of Mathematical Sciences degree (1985) as well as his Doctor of
Mathematical Sciences degree (1995) from the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
. 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
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
in Ithaca
Ithaca
Ithaca or Ithaka is an island located in the Ionian Sea, in Greece, with an area of and a little more than three thousand inhabitants. It is also a separate regional unit of the Ionian Islands region, and the only municipality of the regional unit. It lies off the northeast coast of Kefalonia and...
, 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
University of Calgary
The University of Calgary is a public research university located in Calgary, Alberta, Canada. Founded in 1966 the U of C is composed of 14 faculties and more than 85 research institutes and centres.More than 25,000 undergraduate and 5,500 graduate students are currently...
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. He is also an associate editor for the Canadian Journal of Mathematics
Canadian Journal of Mathematics
The Canadian Journal of Mathematics is a bimonthly mathematics journal published by the Canadian Mathematical Society. It was established in 1949 by H.S.M. Coxeter and G. de B. Robinson. The current editors of the journal are Henry Kim and Robert McCann. The journal publishes articles in all...
and the Canadian Mathematical Bulletin
Canadian Mathematical Society
The Canadian Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and education in Canada.It was originally conceived in June 1945 as the Canadian Mathematical Congress...
.
Research interests and notable results
His research interests are in combinatorial, computationalComputational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational...
, convex
Convex geometry
Convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.Convex sets occur naturally in many areas of mathematics: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming,...
and discrete geometry
Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles,...
(including some aspects of geometric analysis
Geometric analysis
Geometric analysis is a mathematical discipline at the interface of differential geometry and differential equations. It includes both the use of geometrical methods in the study of partial differential equations , and the application of the theory of partial differential equations to geometry...
, rigidity
Rigidity
Rigid or rigidity may refer to:*Stiffness, the property of a solid body to resist deformation, which is sometimes referred to as rigidity*Structural rigidity, a mathematical theory of the stiffness of ensembles of rigid objects connected by hinges...
and optimization
Optimization
Optimization or optimality may refer to:* Mathematical optimization, the theory and computation of extrema or stationary points of functionsEconomics and business* Optimality, in economics; see utility and economic efficiency...
). 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 spaceBanach spaceIn mathematics, Banach spaces is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every Cauchy sequence in V has a limit in V In mathematics, Banach spaces is the...
s supporting a quantitative approach to the BoltyanskiVladimir BoltyanskyVladimir Grigorevich Boltyansky , also transliterated as Boltyanski, Boltyanskii, or Boltjansky, is a Soviet and Russian mathematician, educator and author of popular mathematical books and articles. He is best known for his books on topology, combinatorial geometry and Hilbert's third problem.-...
–HadwigerHugo HadwigerHugo Hadwiger was a Swiss mathematician, known for his work in geometry, combinatorics, and cryptography.-Biography:...
Conjecture (joint work with Alexander Litvak, University of AlbertaUniversity of AlbertaThe University of Alberta is a public research university located in Edmonton, Alberta, Canada. Founded in 1908 by Alexander Cameron Rutherford, the first premier of Alberta and Henry Marshall Tory, its first president, it is widely recognized as one of the best universities in Canada...
); published in K. Bezdek and A. E. Litvak, On the vertex index of convex bodies, Advances in Mathematics 215/2 (2007), 626–641.
- A proof of the KneserMartin KneserMartin Kneser was a German mathematician. His father Hellmuth Kneser and grandfather Adolf Kneser were also mathematicians....
–Poulsen Conjecture (1955) for hemispheres in spherical d-space for all d > 1 (joint work with Robert ConnellyRobert ConnellyRobert Connelly is a mathematician specializing in discrete geometry and rigidity theory. He is best known for discovering embedded flexible polyhedra. One such polyhedron is in the National Museum of American History....
, Cornell UniversityCornell UniversityCornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
); published in K. Bezdek and R. Connelly, The Kneser–Poulsen conjecture for spherical polytopes, Discrete and Computational GeometryDiscrete and Computational GeometryDiscrete & Computational Geometry is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986, the journal publishes articles on in discrete geometry and computational geometry....
32 (2004), 101–106.
- A proof of the KneserMartin KneserMartin Kneser was a German mathematician. His father Hellmuth Kneser and grandfather Adolf Kneser were also mathematicians....
–Poulsen Conjecture (1955) in the Euclidean plane (joint work with Robert ConnellyRobert ConnellyRobert Connelly is a mathematician specializing in discrete geometry and rigidity theory. He is best known for discovering embedded flexible polyhedra. One such polyhedron is in the National Museum of American History....
, Cornell UniversityCornell UniversityCornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
); 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.
- 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 GeometryDiscrete and Computational GeometryDiscrete & Computational Geometry is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986, the journal publishes articles on in discrete geometry and computational geometry....
28 (2002), 75–106 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.
- A discovery of a general principle for uniform stability of sphere packings (joint work with András Bezdek, Auburn UniversityAuburn UniversityAuburn University is a public university located in Auburn, Alabama, United States. With more than 25,000 students and 1,200 faculty members, it is one of the largest universities in the state. Auburn was chartered on February 7, 1856, as the East Alabama Male College, a private liberal arts...
and Robert ConnellyRobert ConnellyRobert Connelly is a mathematician specializing in discrete geometry and rigidity theory. He is best known for discovering embedded flexible polyhedra. One such polyhedron is in the National Museum of American History....
, Cornell UniversityCornell UniversityCornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
); published in A. Bezdek, K. Bezdek and R. Connelly, Finite and uniform stability of sphere packings, Discrete and Computational GeometryDiscrete and Computational GeometryDiscrete & Computational Geometry is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986, the journal publishes articles on in discrete geometry and computational geometry....
20 (1998), 111–130.
- A solution of John Horton ConwayJohn Horton ConwayJohn Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
's "fried potato problem" (joint work with András Bezdek, Auburn UniversityAuburn UniversityAuburn University is a public university located in Auburn, Alabama, United States. With more than 25,000 students and 1,200 faculty members, it is one of the largest universities in the state. Auburn was chartered on February 7, 1856, as the East Alabama Male College, a private liberal arts...
); 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.
- A proof of the BoltyanskiVladimir BoltyanskyVladimir Grigorevich Boltyansky , also transliterated as Boltyanski, Boltyanskii, or Boltjansky, is a Soviet and Russian mathematician, educator and author of popular mathematical books and articles. He is best known for his books on topology, combinatorial geometry and Hilbert's third problem.-...
–HadwigerHugo HadwigerHugo Hadwiger was a Swiss mathematician, known for his work in geometry, combinatorics, and cryptography.-Biography:...
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.
- A proof of László Fejes TóthLászló Fejes TóthLászló Fejes Tóth was a Hungarian mathematician who specialised in geometry. He proved that a honeycomb pattern is the most efficient way to pack centrally symmetric convex sets on the Euclidean plane . He also investigated packings on the sphere...
'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.
Books
His book on "Classical Topics in Discrete Geometry", published by SpringerSpringer Science+Business Media
- Selected publications :* Encyclopaedia of Mathematics* Ergebnisse der Mathematik und ihrer Grenzgebiete * Graduate Texts in Mathematics * Grothendieck's Séminaire de géométrie algébrique...
in 2010 is intended for a semester long graduate level course, giving a brief introduction to discrete geometry
Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles,...
. 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.
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