Juan Camilo Torres PhD

Academic Information

• Doctor in Mathematics (April 2021)

Universidad de los Andes, Colombia

Thesis: The slack model in the study of polytopes (under the supervision of Professor Tristram Bogart and Professor João Gouveia)

• Master in Science - Mathematics (September 2013)

Universidad Nacional de Colombia

Dissertation: Relations Among Network Coding, Index Coding, and Guessing Games: The Linear Case (under the supervision of Professor Humberto Zarria)

• Mathematician (September 2019)

Pontificia Universidad Javeriana, Colombia

Dissertation: Funciones Aritméticas y Temas Selectos de Teoría de Números (under the supervision of Porfessor Iván Castro)

Honors and Distinctions

• Colciencias Fellowship, National Doctorates Call 2015

•  Order to the Xavierian Academic Merit

•  Honorable Mention to the Undergraduate Dissertation

•  Semestral Fellowship for Academic Excellence 2009-1

•  Semestral Fellowship for Academic Excellence 2008-3

•  Semestral Fellowship for Academic Excellence 2007-3

Teaching

• Graduate Assistant, Universidad de los Andes

Second semester 2020:

• Complementaria de Álgebra Lineal

• Complementaria de Álgebra Lineal

First semester 2020:

•  Complementaria de Álgebra Lineal

• Complementaria de Álgebra Lineal

• Lecturer, Universidad Sergio Arboleda

Second semester 2015:

• Variable Compleja (Matemáticas)

• Cálculo Diferencial

First semester 2015:

• Variable Compleja (Matemáticas)

• Cálculo Vectorial

Second semester 2014:

• Análisis Matemático I (Matemáticas)

• Cálculo Vectorial

• Teaching assistant, Universidad Nacional de Colombia 

Teaching assitant of the course Taller Tics y Educación Matemática from the Master in Enseñanza de las Ciencias Exactas y Naturales

March 2011 - June 2014

Participation in Events and Seminars as Exponent

• Talk (January 14, 2021): An algebraic approach to projective uniqueness with an application to order polytopes

Einstein Seminar on Discrete Geometry, Freie Universitat Berlin

• Talk (December 10 - 13, 2019): Graphic Polytopes and Projectively Unique Order Polytopes

Matemáticas por Estudiantes 2019, Universidad de los Andes

• Poster (June 17 - 21, 2019): Projectively Unique Order Polytopes

Effective Methods in Algebraic Geometry MEGA 2019, Universidad Complutense de Madrid

• Talk (April 12, 2019): Ideales Slack y Politopos de Orden 

Seminario Sabanero de Combinatoria SeSaCo, Universidad Sergio Arboleda 

Papers and Preprints

• Complex psd-minimal polytopes in dimensions two and three in collaboration with Tristram Bogart and João Gouveia

Code: ComplexPsdMinimality  AdditionalCalculations1 AdditionalCalculations2 AdditionalCalculations3 AdditionalCalculations4 AdditionalCalculations5 AdditionalCalculations6 All code in zip: Code 

Lists of doubly 3/4 polytopes: facets4 facets5 facets6 facets7 facets8 facets9 facets10 facets11 facets12 facets13  All data in zip: Data   

• An algebraic approach to projective uniqueness with an application to order polytopes (accepted in Discrete & Computational Geometry, Springer) in collaboration with Tristram Bogart and João Gouveia

arXiv:2005.00640v1, 2020 arxiv.org/pdf/2005.00640.pdf

Thesis and Dissertations

• Doctoral Thesis: The slack model in the study of polytopes under the supervision of Professor Tristram Bogart and Professor João Gouveia repositorio.uniandes.edu.co/bitstream/handle/1992/51154/23522.pdf?sequence=1 

• Master Dissertation: Relations Among Network Coding, Index Coding, and Guessing Games: The Linear Case under the supervision of Professor Humberto Zarria

• Undergraduate Dissertation: Funciones Aritméticas y Temas Selectos de Teoría de Números under the supervision of Porfessor Iván Castro

Hábitos de estudio: https://drive.google.com/file/d/1L1DVD8bWUWWkf1RMbCZ5pYhDQzw11OWN/view?usp=drive_link

Problema de las casas: https://docs.google.com/presentation/d/1G6mhKbSLjWZkaDG8pKco_5pU6RmaYmyo/edit?usp=sharing&ouid=116793034765971860066&rtpof=true&sd=true

Problema de las casas pdf: https://drive.google.com/file/d/1VvYuHYWqhHOR03xabGyaPzRIS-Wps5Cc/view?usp=sharing

Rectángulos: https://docs.google.com/presentation/d/1ynt9lgHrcrwipDthKMrqOPIN42Uky5xe/edit?usp=sharing&ouid=116793034765971860066&rtpof=true&sd=true

Beca: https://drive.google.com/file/d/1nLlzwTkyjxbqZaTBkc_guCXkjq2Cc4MX/view?usp=sharing 

Torneo: https://drive.google.com/file/d/15u5zNFD2R2Kxx47g430ukTp8OrRs2mpu/view?usp=sharing