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<![endif]--><!--[if gte mso 9]><xml> <o:shapedefaults v:ext="edit" spidmax="1026"/> </xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout v:ext="edit"> <o:idmap v:ext="edit" data="1"/> </o:shapelayout></xml><![endif]--> </head> <body style="tab-interval:36.0pt" vlink="purple" link="blue" lang="EN-US"> <div class="WordSection1"> <h1 style="text-align:center" align="center"><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">Notas biogrficas de </span><br> <span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">Olgierd Alf Biberstein</span></h1> <span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">&nbsp;<o:p></o:p></span> <p style="margin:0cm;margin-bottom:.0001pt;text-align:center" align="center"><strong><span style="font-family:Times;mso-ansi-language:EN" lang="EN">Guillermo Morales-Luna</span></strong><span style="mso-ansi-language:EN" lang="EN"><o:p></o:p></span></p> <p style="margin:0cm;margin-bottom:.0001pt;text-align:center" align="center"><i><span style="mso-ansi-language:EN" lang="EN">Departamento de Computacin<o:p></o:p></span></i></p> <p style="margin:0cm;margin-bottom:.0001pt;text-align:center" align="center"><span style="mso-ansi-language:EN" lang="EN">Centro de Investigacin y Estudios Avanzados del IPN, Cinvestav-IPN<o:p></o:p></span></p> <p style="text-align:center" align="center"><strong><span style="font-family:Times;mso-ansi-language:EN" lang="EN">23 de marzo de 2016</span></strong><span style="mso-ansi-language:EN" lang="EN"><o:p></o:p></span></p> <h3><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family: &quot;Times New Roman&quot;;mso-ansi-language:EN" lang="EN">Resumen:<o:p></o:p></span></h3> <p><span style="mso-ansi-language:EN" lang="EN">El profesor Olgierd Alf Biberstein ense en la Escuela Superior de Fsica y Matemticas del Instituto Politcnico Nacional (IPN), en la Ciudad de Mxico, desde 1970 hasta su muerte, ocurrida en 1997. Especialista en Anlisis Matemtico, Topologa y Geometra, form a un numeroso grupo de matemticos en el IPN. Sus cursos eran sumamente instructivos y universales en sus mtodos y el rigor de sus exposiciones. El profesor Biberstein fue sin duda alguna un ejemplar matemtico. <o:p></o:p></span></p> <h1><a name="SECTION00010000000000000000"></a><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">Introduccin <o:p></o:p></span></h1> <p><span style="mso-ansi-language:EN" lang="EN">El profesor Biberstein (V, 1921-VIII, 1997) influy de manera importante en la formacin de matemticos mexicanos en la Escuela Superior de Fsica y Matemticas del Instituto Politcnico Nacional en la Ciudad de Mxico, a lo largo de 27 aos, desde 1970. <o:p></o:p></span></p> <p><span style="mso-ansi-language:EN" lang="EN">Al gran talento matemtico del profesor Biberstein, se aadan rasgos diversos tales como el esmero y la claridad en la presentacin de sus cursos y conferencias, localizacin  natural de nuevos resultados y formulacin de nuevas demostraciones de resultados ya conocidos, amplia cultura general, conocimiento profundo de los clsicos de la literatura y de la msica, amistad sincera y desinteresada y un finsimo trato. Desde el punto de vista de los criterios actuales de valoracin del trabajo matemtico impuestos en nuestro medio, acaso el profesor Biberstein no obtendra las mximas calificaciones. Ciertamente, ocupado principalmente en la enseanza y en la supervisin de sus alumnos, podra pensarse que se dedicaba exclusivamente al trabajo docente. Mas no era as: sus textos contienen muchos resultados originales, frutos de su trabajo de investigacin. Sus cursos, pues, fueron su medio de comunicacin. <o:p></o:p></span></p> <p><span style="mso-ansi-language:EN" lang="EN">En el presente esbozo he de disculparme ante el lector, pues seguramente mi presentacin estar sesgada desde mi perspectiva de ex-alumno del profesor Biberstein, ms que de una perspectiva de colega suyo, para m un honrossimo trato que l tuvo a bien dispensarme. <o:p></o:p></span></p> <h1><a name="SECTION00020000000000000000"></a><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">Formacin <o:p></o:p></span></h1> <p><span style="mso-ansi-language:EN" lang="EN">Olgierd Alf Biberstein naci el 9 de mayo de 1921 en la ciudad polaca de Drohobycz<a name="tex2html1"></a><a href="#foot60"><span style="mso-bookmark:tex2html1"><sup>1</sup></span><span style="mso-bookmark:tex2html1"></span></a><span style="mso-bookmark:tex2html1"></span> localizada en el valle del ro Dniepr, cerca de la cordillera de los Crpatos, a 80 km al suroeste de Lepolis.<a name="tex2html2"></a><a href="#foot61"><span style="mso-bookmark:tex2html2"><sup>2</sup></span><span style="mso-bookmark: tex2html2"></span></a><span style="mso-bookmark:tex2html2"></span> . Su padre se llam Ernest Biberstein y su madre Eugenia Herschdoerfer. Acaso como una afortunada coincidencia puede remarcarse que en esta ltima ciudad, entre 1926 y 1939, floreci un grupo de grandes genios matemticos, en el cual se encontraban Stefan Banach, Stanis<img id="_x0000_i1025" src="file:////Users%5Cgml%5CDocuments%5CTeXDocuments%5COwnTexts%5C16Bios%5C:16OAB:Macintosh%20HD%5CUsers%5Cgml%5CDocuments%5CTeXDocuments%5COwnTexts%5C16Bios%5C16OAB%5Cimg1.png" width="5" border="0" height="16">aw Ulam, Hugo Steinhaus, Stanis</span><b style="mso-bidi-font-weight:normal"><span style="font-family:&quot;Lucida Grande&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;; color:black">B</span></b><span style="mso-ansi-language:EN" lang="EN">aw Mazur y W</span><b style="mso-bidi-font-weight:normal"><span style="font-family:&quot;Lucida Grande&quot;; mso-bidi-font-family:&quot;Times New Roman&quot;;color:black">B</span></b><span style="mso-ansi-language:EN" lang="EN">adys</span><b style="mso-bidi-font-weight:normal"><span style="font-family:&quot;Lucida Grande&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;; color:black">B</span></b><span style="mso-ansi-language:EN" lang="EN">aw Orlicz, entre muchos otros. Biberstein no tuvo oportunidad de conocerlos, mas l, al igual que ellos, fue un talentoso matemtico de origen polaco proveniente de esa regin, llamada Galicja<a name="tex2html3"></a><a href="#foot62"><span style="mso-bookmark:tex2html3"><sup>3</sup></span><span style="mso-bookmark: tex2html3"></span></a><span style="mso-bookmark:tex2html3"></span>. Biberstein recibi educacin bsica en su ciudad natal y ah acudi al Liceo Polaco. Como ilustrativo de lo refinado de su educacin elemental, baste decir que tom clases de dibujo con el pintor Bruno Schulz,<a name="tex2html4"></a><a href="#foot38"><span style="mso-bookmark:tex2html4"><sup>4</sup></span><span style="mso-bookmark:tex2html4"></span></a><span style="mso-bookmark:tex2html4"></span> quien fue adems un reconocido escritor en lengua polaca. Biberstein provena de una comunidad juda, pero estimo que su cultura materna fue polaca esencialmente. <o:p></o:p></span></p> <p><span style="mso-ansi-language:EN" lang="EN">En los aos de la guerra, Biberstein estudi en Francia. En 1939 y 1940 fue alumno del bachillerato de la Universidad de Estrasburgo (en 1940 sta se traslad a Clermont-Ferrand debido a la ocupacin alemana). En 1945 Biberstein obtuvo su ttulo de  <i style="mso-bidi-font-style:normal">Licence es Sciences (mention mathematique)</i> de la Universidad de Estrasburgo, y un ao despus el  <i style="mso-bidi-font-style: normal">Diplme d'Enseigment Superieure</i> en la misma universidad. Entonces estudi con profesores como J. Ehresmann, Andr Lichnerowicz, A. Roussel y Henri Cartan. En esta poca adquiri la nacionalidad francesa, la cual conserv por el resto de su vida. <o:p></o:p></span></p> <p><span style="mso-ansi-language:EN" lang="EN">En 1948 se traslad al continente americano. Estuvo dos aos en un programa de posgrado en la Universidad de Washington en San Luis, Missouri, y ah mismo tuvo un nombramiento de  <i style="mso-bidi-font-style:normal">graduate assistant</i> . En la Universidad de Washington estuvo trabajando con los profesores Z. Nohari, I. Hirschmann y W. Thron. <o:p></o:p></span></p> <p><span style="mso-ansi-language:EN" lang="EN">Prcticamente toda la dcada de los aos cincuenta Biberstein estuvo en Canad. Trabaj en las universidades de McGill, Ottawa, Montreal y Terra Nova. En 1957 obtuvo el Doctorado en Ciencias Matemticas de la Universidad de Montreal con la tesis  <i style="mso-bidi-font-style: normal">Elements de Geometrie Differentielle Minkowskienne</i> escrita bajo la supervisin del profesor Istvan Fary. Adems de su asesor, fungieron como sinodales en el examen los profesores G. Reeb, P. Dedecker, A. Avez y H. Busemann. Todos ellos tuvieron la mejor opinin sobre el trabajo de Biberstein. Doce aos ms tarde, el profesor Fary hace un reconocimiento a la manera independiente en la que sola trabajar Biberstein y un velado reproche a que Biberstein no hubiese publicado su tesis, urgindolo a que lo haga en lo inmediato, pues an en ese momento sus resultados habran sido muy novedosos. <o:p></o:p></span></p> <h1><a name="SECTION00030000000000000000"></a><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">Su vida en Amrica Latina <o:p></o:p></span></h1> <p><span style="mso-ansi-language:EN" lang="EN">Acaso debido a que el polaco fue su lengua materna, y ste posee una compleja estructura fontica y sintctica, Biberstein fue un polglota con profundos dominios de los idiomas que conoca. Tengo por seguro que conoca, adems del polaco, el yidish, el ruso, el alemn, el francs, el ingls y, por supuesto, el castellano. Lea autores clsicos (Horacio, Descartes, Newton y Euler) en latn. Acaso el griego, el sefard y algunos otros idiomas cercanos a los mencionados eran tambin conocidos por Biberstein. <o:p></o:p></span></p> <p><span style="mso-ansi-language:EN" lang="EN">Me atrevo a suponer que siempre se dispuso a aprender un nuevo idioma para leer a los autores clsicos de la literatura en esa lengua. Es pues el caso que Biberstein conoca el castellano an antes de conocer cualquier pas hispanoamericano y ya entonces lea en nuestro idioma a Cervantes, a otros autores del Siglo de Oro y a autores modernos como Borges, Cortzar, Neruda y Sbato. <o:p></o:p></span></p> <p><span style="mso-ansi-language:EN" lang="EN">A mediados de 1959, Biberstein inicia una estancia de tres aos en la Universidad de Costa Rica, con un nombramiento de  Profesor Extraordinario . Despus estuvo siete aos en Chile: uno en la Universidad de Concepcin y el resto en la Universidad de Chile en Santiago, con sendos nombramientos de profesor titular. Sus ltimos tres aos en la Universidad de Chile los utiliza para establecer ah la Facultad de Ciencias. Esto le vale un reconocimiento por la UNESCO. En 1969 realiza una estancia de medio ao en la Universidad de Los Andes en Mrida, Venezuela, y desde marzo de 1970 se incorpora a la planta docente de la Escuela Superior de Fsica y Matemticas del Instituto Politcnico Nacional (ESFM-IPN), en Mxico, en la cual se mantiene en actividad hasta su fallecimiento, ocurrido el 5 de agosto de 1997. <o:p></o:p></span></p> <p><span style="mso-ansi-language:EN" lang="EN">El profesor Biberstein queda pues como un ejemplo de educador y de cientfico. A quienes pudimos gozar de sus exposiciones y de la oportunidad de aprender de l nos queda, acaso como una mnima retribucin a su persona, mostrar a las nuevas generaciones el talento del profesor Olgierd Alf Biberstein. <o:p></o:p></span></p> <p><span style="mso-ansi-language:EN" lang="EN">En 2014 tuve el honor de recopilar un curso del prof. Biberstein sobre Variedades Diferenciables y que esta recopilacin fuera publicada por el Instituto Politcnico Nacional&nbsp;[</span><a href="16OAB.html#uno"><span style="mso-ansi-language:EN" lang="EN">1</span></a><span style="mso-ansi-language:EN" lang="EN">,</span><a href="16OAB.html#dos"><span style="mso-ansi-language:EN" lang="EN">2</span></a><span style="mso-ansi-language:EN" lang="EN">,</span><a href="16OAB.html#tres"><span style="mso-ansi-language:EN" lang="EN">3</span></a><span style="mso-ansi-language: EN" lang="EN">]. <o:p></o:p></span></p> <h2><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family: &quot;Times New Roman&quot;;mso-ansi-language:EN" lang="EN">Referencias <o:p></o:p></span></h2> <p class="MsoNormal" style="margin-left:14.2pt;text-indent:-14.2pt"><a name="uno"></a><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family: &quot;Times New Roman&quot;;mso-ansi-language:EN" lang="EN">1<span style="mso-tab-count:1">&nbsp;&nbsp; </span>Guillermo Morales-Luna. <em><span style="font-family:Times">Variedades Diferenciables: un enfoque debido a O. A. Biberstein, Vol. I, Elementos de lgebra exterior</span></em>.<span style="mso-spacerun:yes">&nbsp; </span>Publicaciones del Instituto Politcnico Nacional, 2014. <o:p></o:p></span></p> <p class="MsoNormal" style="margin-left:14.2pt;text-indent:-14.2pt"><a name="dos"></a><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family: &quot;Times New Roman&quot;;mso-ansi-language:EN" lang="EN">2 <span style="mso-tab-count:1">&nbsp; </span>Guillermo Morales-Luna. <span style="mso-spacerun:yes">&nbsp;</span><em><span style="font-family:Times">Variedades Diferenciables: un enfoque debido a O. A. Biberstein, Vol. II, Clculo diferencial en variedades</span></em>.<span style="mso-spacerun:yes">&nbsp; </span>Publicaciones del Instituto Politcnico Nacional, 2014. <o:p></o:p></span></p> <p class="MsoNormal" style="margin-left:14.2pt;text-indent:-14.2pt"><a name="tres"></a><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family: &quot;Times New Roman&quot;;mso-ansi-language:EN" lang="EN">3<span style="mso-tab-count:1">&nbsp;&nbsp; </span>Guillermo Morales-Luna. <span style="mso-spacerun:yes">&nbsp;</span><em><span style="font-family:Times">Variedades Diferenciables: un enfoque debido a O. A. Biberstein, Vol. III, Clculo integral en variedades</span></em>.<span style="mso-spacerun:yes">&nbsp; </span>Publicaciones del Instituto Politcnico Nacional, 2014. <o:p></o:p></span></p> <p><span style="mso-ansi-language:EN" lang="EN"><o:p>&nbsp;</o:p></span></p> <div class="MsoNormal" style="text-align:center" align="center"><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;; mso-ansi-language:EN" lang="EN"> <hr width="100%" size="2" align="center"> </span></div> <h4><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family: &quot;Times New Roman&quot;;mso-ansi-language:EN" lang="EN">Pies de pgina<o:p></o:p></span></h4> <p class="MsoNormal"><a name="foot60"></a><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">... Drohobycz</span><a href="16OAB.html#tex2html1"><sup><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;; mso-ansi-language:EN" lang="EN">1</span></sup></a><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN"> <o:p></o:p></span></p> <p class="MsoNormal" style="margin-left:36.0pt"><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">(Lase <em><span style="font-family:Times">drojbich</span></em>.) Utilizo aqu la grafa polaca que coincide con la ucraniana. En ruso es <em><span style="font-family:Times">Drogobycz</span></em> y en alemn <em><span style="font-family:Times">Drogobytsch</span></em>. <o:p></o:p></span></p> <p class="MsoNormal"><a name="foot61"></a><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">... Le\'opolis.</span><a href="16OAB.html#tex2html2"><sup><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;; mso-ansi-language:EN" lang="EN">2</span></sup></a><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN"> <o:p></o:p></span></p> <p class="MsoNormal" style="margin-left:36.0pt"><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">Supongo que la forma castellana para nombrar a esta ciudad ha de coincidir con la latina. La ciudad se llama <em><span style="font-family:Times">ww</span></em> en polaco, <em><span style="font-family:Times">Lvov</span></em> en ucraniano y <em><span style="font-family:Times">Lemberg</span></em> en alemn. <o:p></o:p></span></p> <p class="MsoNormal"><a name="foot62"></a><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">... Galicja</span><a href="16OAB.html#tex2html3"><sup><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;; mso-ansi-language:EN" lang="EN">3</span></sup></a><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN"> <o:p></o:p></span></p> <p class="MsoNormal" style="margin-left:36.0pt"><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">Pronnciase <em><span style="font-family:Times">galitcia</span></em>. <o:p></o:p></span></p> <p class="MsoNormal"><a name="foot38"></a><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">... Schulz,</span><a href="16OAB.html#tex2html4"><sup><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;; mso-ansi-language:EN" lang="EN">4</span></sup></a><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN"> <o:p></o:p></span></p> <p class="MsoNormal" style="margin-left:36.0pt"><span style="mso-fareast-font-family: &quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language: EN" lang="EN">(1892-1942) Schulz vivi siempre en Drohobycz y en 1942 fue asesinado por los ocupantes nazis. <o:p></o:p></span></p> <div class="MsoNormal" style="text-align:center" align="center"><span style="mso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;; mso-ansi-language:EN" lang="EN"> <hr width="100%" size="2" align="center"> </span></div> </div> </body> </html>