Geometría Tropical desde los tiempos de Hilbert (Yulieth Prieto)

Tropical Geometry Since Hilbert's Time (Yulieth Prieto) Talk given by Yulieth Prieto (Center for Research and Advanced Studies of the National Polytechnic Institute, CINVESTAV) at the Fellows' Seminar of the Institute of Mathematics of the National Autonomous University of Mexico (UNAM) on Tuesday, August 22, 2017, in the Graciela Salicrup Room of the Institute of Mathematics of UNAM. Abstract In 1900, during the international congress of mathematicians held in Paris, the great mathematician David Hilbert proposed a list of 23 unsolved problems. One of them was problem 16, in which Hilbert inquired about the topological type of maximal real algebraic curves. This problem can be described simply with the following question: How many forms can the zeros of a polynomial with real coefficients take? Specifically, the task was to describe all possible "configurations" of a curve of degree d. While the problem is very simple to solve for degrees less than or equal to 4, it presents serious difficulties in more general cases. In particular, the solution for the cases d=5 and d=6 given by Oleg Viro in the late 1970s introduced one of the most important tools in the study of real algebraic curves, now known as patchwork. Motivated by solving this problem, we will introduce the patchwork technique from a combinatorial perspective, using tools from tropical geometry. Once we are familiar with the terminology, we will mention some versions of Haas's theorem that partially solve Hilbert's Problem 16. This talk is aimed at mathematics students interested in the applications of algebra in other areas of pure mathematics, such as geometry and topology. Or simply, at any mathematician interested in learning what tropical geometry hides behind its rather exotic name. Video of the talk    • Geometría Tropical desde los tiempos de Hi...   Video thumbnail image https://goo.gl/photos/KBdXknf72oTAhrNq9 Yulieth Prieto at the Center for Research and Advanced Studies of the National Polytechnic Institute, CINVESTAV http://www.math.cinvestav.mx/en/stude... http://www.math.cinvestav.mx/en/gradu... Page of the Scholarship Recipients Seminar at the Institute of Mathematics of the National Autonomous University of Mexico (UNAM) http://www.matem.unam.mx/actividades/... Facebook page of Ciencias TV   / ciencias-tv-170487220017476   Academic videos on mathematics (talks) (Recorded)    • Matemáticas pláticas grabadas   Published Academic Videos    • Videos Académicos publicados   Academic Videos Published in 2017    • Videos Académicos publicados en 2017   Thumbnail Photo Album of Academic Videos Published in 2017 https://goo.gl/photos/7yKCos9N8T9SecGk9 Academic Videos Published in 2016    • Videos Académicos publicados en 2016   Thumbnail photo album of Academic Videos published in 2016 https://goo.gl/photos/Wk45yoGqPe5hKTw77 Academic Videos published in 2015    • Videos Académicos publicados en 2015   Academic Videos published in 2014    • Videos Académicos publicados en 2014   Academic Videos published in 2013    • Videos Académicos publicados en 2013   We appreciate the support of: universo.math http://universo.math.org.mx/   / universo.math   Department of Mathematics, CINVESTAV http://www.math.cinvestav.mx/ Faculty of Sciences, UNAM http://www.fciencias.unam.mx/ https://www.facebook.com/Facultad-de-...