{"id":3,"date":"2020-12-01T14:13:07","date_gmt":"2020-12-01T20:13:07","guid":{"rendered":"https:\/\/wpsites.ucalgary.ca\/site-template\/?page_id=2"},"modified":"2025-08-05T16:21:29","modified_gmt":"2025-08-05T22:21:29","slug":"sample-page","status":"publish","type":"page","link":"https:\/\/wpsites.ucalgary.ca\/tibor-bisztriczky\/","title":{"rendered":"RESEARCH INTERESTS AND CONFERENCE PHOTOS"},"content":{"rendered":"\n
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Tibor Bisztriczky<\/strong><\/p>\n\n\n\n

Professor Emeritus, <\/p>\n\n\n\n

Department Head (2000-2011), Faculty Professor (2014-2023) University of Calgary, tbisztri@ucalgary.ca<\/p>\n\n\n\n

B.Sc., 1970, McMaster University<\/em><\/strong>
M.Sc., 1971, McMaster University<\/em><\/strong>
Ph.D., 1974, University of Toronto<\/em><\/strong><\/p>\n\n\n\n

Associate Member, Renyi Institute, Hungarian Academy of Sciences, 2011<\/p>\n\n\n\n

Adjunct Professor of Mathematics & Statistics, York University,2012-2018<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n

RESEARCH INTERESTS<\/strong><\/h6>\n\n\n\n

Current research is in the fields of convex polytopes, and discrete geometry. Specific topics of interest include:<\/span><\/p>\n\n\n\n

– combinatorial constructions of classes of convex d-polytopes : self-duals , and those with facial structure determined by a total ordering of vertices.<\/p>\n\n\n\n

– a study of the geometric and combinatorial properties of convex 4-polytopes.The specific properties of interest are the following :<\/p>\n\n\n\n

Edge-antipodality <\/em>(A set V or, a polytope P with vertex set V, is antipodal<\/em><\/strong> if any two elements of V are antipodal. Antipodal d-polytopes have been studied extensively over the past fifty years, and it is known that any such P has at most 2d<\/sup> vertices. In the last decade I. Talata introduced the concept of an edge-antipodal<\/em><\/strong> P: any two vertices of P, that lie on an edge of P, are antipodal. It is known that edge-antipodal 3-polytopes are antipodal, and that for each d \u2265 4, there is an edge-antipodal P that is not antipodal. With K. Boroczky, we have began a program for the study (classification, and determining the maximum of the number of vertices) of edge-antipodal d-polytopes, d \u2265 4. Most progress has been achieved in the case that d = 4. There the focus is presently on strongly edge-antipodal<\/em><\/strong> P (any two vertices of P, that lie on the edge of P, are contained in distinct parallel facets of P).<\/span><\/p>\n\n\n\n

Separation<\/em> (One of the most famous conjectures in Discrete Geometry is attributed to H. Hadwiger, I.Z. Gohberg and A.S. Markus. It is that the smallest number h(K), of smaller homothetic<\/strong><\/em> copies of a compact convex set K in real d-space, d \u2265 2, with which it is possible to cover K, is at most 2d<\/sup> only if K is d-dimensional parallelotope<\/strong><\/em>. The G-M-H conjecture is confirmed for d = 2, open for d \u2265 3, and has a rich history with various equivalent formulations. The formulation of particular interest is due to K. Bezdek: if the origin is in the interior of K then h(K) is the smallest number of hyperplanes required to strictly separate the origin from any face of the polar K* of K. This formulation is particularly attractive in the case of polytopes and leads naturally to the following Separation Problem<\/em><\/strong>: Let P be a convex d-polytope. Determine the smallest number s(P) such that any facet of P is strictly separated from an arbitrary fixed interior point of P by one of s(P) hyperplanes. Again, most progress on the separation problem has been achieved in the case that d = 4 and the 4-polytope P is neighborly (any two vertices of P determine an edge of P). In particular, it is known that for certain classes of neighborly 4-polytopes P that s(P) \u2264 16. The big question now is if s(P) \u2264 16 for any neighborly 4-polytope?<\/span><\/p>\n\n\n\n

Topics in Combinatorial Geometry: Erdos-Szekeres type theorems, Transversal properties of families of ovals in the plane, Edge-antipodal 4-polytopes and Triangulations of simple convex polygons<\/span><\/p>\n\n\n\n

CONFERENCE PHOTOS 1988-2019<\/strong><\/h4>\n\n\n\n
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DISCRETE,CONVEX AND COMBINATORIAL GEOMETRY FEST, CALGARY JUNE 2025<\/strong><\/em><\/h2>\n\n\n\n
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AUBURN, AMS SPECIAL SESSION, DISCRETE AND CONVEX GEOMETRY, MARCH 2019<\/em><\/strong><\/p>\n\n\n\n

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BERLIN, CONVEX AND DISCRETE GEOMETRY, JOERGSHOP, JUNE 2017<\/em><\/strong><\/p>\n\n\n\n

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ATLANTA, AMS SPECIAL SESSION CONVEX & DISCRETE GEOMETRY, MARCH 2017<\/em><\/strong><\/span><\/p>\n\n\n\n

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OAXACA, CMO-BIRS, GEOMETRY, OCTOBER 2016<\/em><\/strong><\/p>\n\n\n\n

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BUDAPEST, DISCRETE GEOMETRY DAYS, JUNE 2016<\/em><\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

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BUDAPEST, DISCRETE GEOMETRY DAYS, JUNE 2016<\/em><\/strong><\/p>\n\n\n\n

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BANFF (BIRS), DISCRETE GEOMETRY & SYMMETRY, FEB. 2015<\/strong><\/p>\n\n\n\n

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BANFF(BIRS),COMBINATORIAL AND CONVEX GEOMETRY FEST,FEB. 2015<\/strong><\/p>\n\n\n\n

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HALIFAX, CMS, DISCRETE & COMBINATORIAL GEOMETRY SPECIAL SESSION, JUNE 2013<\/strong><\/p>\n\n\n\n

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BANFF (BIRS), TRANSVERSAL THEORY & HELLY TYPE THEOREMS, OCT. 2012<\/strong><\/p>\n\n\n\n

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SZEGED, DISCRETE & CONVEX GEOMETRY CONFERENCE, MAY 2012<\/strong><\/p>\n\n\n\n

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RICHMOND, AMS, CONVEXITY & COMBINATORICS SPECIAL SESSION, NOV. 2010<\/strong><\/p>\n\n\n\n

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KELOWNA, PRAIRIE DISCRETE MATH WORKSHOP, AUGUST 2009<\/strong><\/p>\n\n\n\n

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SEVILLA, PHENOMINA IN HIGH DIMENSIONS CONFERENCE, JUNE 2008<\/strong><\/p>\n\n\n\n

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BANFF (BIRS) & CALGARY, INTUITIVE GEOMETRY, SEPTEMBER 2007<\/strong><\/p>\n\n\n\n

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BUDAPEST, GEOMETRY FEST, JUNE 2007<\/strong><\/p>\n\n\n\n

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BANFF (BIRS), CONVEX GEOMETRY & APPLICATIONS, MARCH 2006<\/strong><\/p>\n\n\n\n

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SAN ANTONIO, AMS, CONVEX & DISCRETE GEOMETRY SPECIAL SESSION, JANUARY 2006<\/strong><\/p>\n\n\n\n

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BANFF (BIRS) & CALGARY, CONVEX AND ABSTRACT POLYTOPES, MAY 2005<\/strong><\/p>\n\n\n\n

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POLYTOPES DAY IN CALGARY, MAY 22,2005 <\/strong><\/h2>\n\n\n\n
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PITTSBURGH, AMS, CONVEXITY & COMBINATORICS SPECIAL SESSION, NOVEMBER 2004<\/strong><\/p>\n\n\n\n

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PITTSBURGH, AMS, CONVEXITY & COMBINATORICS SPECIAL SESSION, NOVEMBER 2004<\/strong><\/p>\n\n\n\n

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WORKSHOP ON GEOMETRIC TOMOGRAPHY, ALICANTE , SPAIN, OCTOBER 2004<\/strong><\/p>\n\n\n\n

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GAETA, COMBINATORICS CONFERENCE, MAY-JUNE 2000<\/strong><\/p>\n\n\n\n

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SEATTLE, MEETING IN HONOUR OF VIC KLEE’S 75’TH BIRTHDAY, AUGUST 2000<\/strong><\/p>\n\n\n\n

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HALIFAX, AFFFINE GEOMETRY CONFERENCE, MAY 1996<\/strong><\/p>\n\n\n\n

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MSRI, CONVEX GEOMETRY& GEOMETRIC FUNCTIONAL ANALYSIS, MAY 1996<\/strong><\/p>\n\n\n\n

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NATO-ASI, POLYTOPES: ABSTRACT, CONVEX AND COMPUTATIONAL, TORONTO,SEPT.1993<\/strong><\/p>\n\n\n\n

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CATANIA, COMBINATORICS CONFERENCE, SEPTEMBER 1991<\/strong><\/p>\n\n\n\n

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VIENNA, MATHEMATISCHE KOLLOQIUM, TECHNISCHE UNIVERSITAET, APRIL 1991<\/strong><\/p>\n\n\n\n

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RAVELLO, COMBINATORICS CONFERENCE, MAY 1988<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

RESEARCH INTERESTS Current research is in the fields of convex polytopes, and discrete geometry. Specific topics of interest include: – combinatorial constructions of classes of convex d-polytopes : self-duals , and those with facial structure determined by a total ordering of vertices. – a study of the geometric and combinatorial properties of convex 4-polytopes.The specific […]<\/p>\n","protected":false},"author":200,"featured_media":0,"parent":0,"menu_order":1,"comment_status":"closed","ping_status":"open","template":"","meta":{"site-sidebar-layout":"no-sidebar","site-content-layout":"default","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ngg_post_thumbnail":0,"footnotes":""},"class_list":["post-3","page","type-page","status-publish","hentry"],"featured_image_src":null,"featured_image_src_square":null,"_links":{"self":[{"href":"https:\/\/wpsites.ucalgary.ca\/tibor-bisztriczky\/wp-json\/wp\/v2\/pages\/3","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpsites.ucalgary.ca\/tibor-bisztriczky\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wpsites.ucalgary.ca\/tibor-bisztriczky\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wpsites.ucalgary.ca\/tibor-bisztriczky\/wp-json\/wp\/v2\/users\/200"}],"replies":[{"embeddable":true,"href":"https:\/\/wpsites.ucalgary.ca\/tibor-bisztriczky\/wp-json\/wp\/v2\/comments?post=3"}],"version-history":[{"count":40,"href":"https:\/\/wpsites.ucalgary.ca\/tibor-bisztriczky\/wp-json\/wp\/v2\/pages\/3\/revisions"}],"predecessor-version":[{"id":256,"href":"https:\/\/wpsites.ucalgary.ca\/tibor-bisztriczky\/wp-json\/wp\/v2\/pages\/3\/revisions\/256"}],"wp:attachment":[{"href":"https:\/\/wpsites.ucalgary.ca\/tibor-bisztriczky\/wp-json\/wp\/v2\/media?parent=3"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}