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<\/a>The names of many ECCO 2018 participants<\/p><\/div>\n
\u201cHow do you do mathematics the Colombian way?\u201d\u00a0 This was the question posed by Federico Ardila<\/a> at the end of the first week of the 6th<\/sup>Encuentro Colombiano de Combinatoria (ECCO 2018)<\/a>.\u00a0 The question my master\u2019s thesis advisor asked motivated me to write a reflection of ECCO 2018 as a non-Colombian attempting to answer the question. I hope that this may also serve as an invitation\/motivation for anyone interested in combinatorics to participate in future ECCOs.<\/p>\n Two years ago, in 2016 I participated in the 5th<\/sup>Encuentro Colombiano de Combinatoria (ECCO 2016)<\/a>, an experience that changed my perspective and approach to doing mathematics and has motivated me to shape the inclusive mathematics community that I want to see. After her ECCO 2016 experience, Viviane Pons<\/a> (Universit\u00e9 Paris-Sud) wrote a wonderful blog post detailing and reflecting on many aspects of the conference. I encourage you to read the post here<\/a>.<\/p>\n What is ECCO?<\/u><\/strong><\/p>\n The Encuentro Colombiano de Combinatoria is a conference that runs every two years. More than a standard conference, it is a school and a gathering of mathematicians of all academic levels who bring their passion for learning and sharing combinatorics. In 2003, the first ECCO was organized by Federico Ardila as a resulting effort of his SFSU-Colombia Initiative. One goal was to build closer ties among students from Colombia, the USA, and other countries to provide a space for collaboration in person, especially for students who have limited access to such an experience. In 2016, Federico Ardila wrote an article for the Notices of the AMS, titled, \u201cTodos Cuentan: Cultivating Diversity in Combinatorics<\/a>,\u201d where he shares more on the creation of ECCO and his approach to creating spaces for students to grow in their mathematical learning, primarily in combinatorics.<\/p>\n ECCO 2018<\/u><\/strong><\/p>\n ECCO 2018 was hosted by the Universidad del Norte in Barranquilla, Colombia from June 5th<\/sup>to the 16th<\/sup>and also served as a CIMPA School.\u00a0 There were over 100 participants and about half were Colombian and the other half foreigners.\u00a0 This year\u2019s theme was \u201cCombinatorics meets Algebra, Geometry, and Optimization.\u201d\u00a0 The two\u00a0weeks consisted of four minicourses, which highlighted the theme.\u00a0 Two minicourses were delivered per week, one in the morning and one in the afternoon. \u00a0The first week\u2019s minicourses were led by G\u00fcnter Ziegler<\/a> (FU Berlin) and Vic Reiner<\/a> (Univ. of Minnesota).\u00a0 For those of you familiar with polytopes, you have probably encountered G\u00fcnter Ziegler\u2019s book, \u201cLectures on Polytopes.\u201d\u00a0\u00a0I\u00a0fanboyed as he signed my copy of the book. G\u00fcnter Ziegler\u2019s lectures presented us with extremal examples and combinatorial parameters of polytopes<\/em>.\u00a0 Vic Reiner delivered his lectures covering q-counting and representation theory<\/em>.\u00a0 The second week\u2019s minicourses were led by Lauren Williams<\/a> (Berkeley\/Harvard) and Rekha Thomas<\/a> (Univ. of Washington).\u00a0 Lauren Williams\u2019 lectures provided us with an introduction to total positivity and cluster algebras<\/em>.\u00a0Rekha Thomas\u2019 lectures took us into the world of polynomial optimization<\/em>.<\/p>\n The style and presentation of this ECCO was similar to the previous years, but one change was that this was the first year that Federico Ardila was not directly\u00a0involved in the organizing\u00a0committee.\u00a0 Now organized by a committee of former participants, this change highlights the sustainability\u00a0of the event and the strong foundations that Federico has laid for ECCO\u2019s success. Many joked that Federico was like the proud grandfather sitting around watching the fruition of his efforts.<\/p>\n After each lecture we took a coffee break where we had some great (and incredibly hot) Colombian coffee and pastries.\u00a0 Then we gathered again in the lecture hall where each day we had two graduate students or post-docs give a research talk. These students and post-docs were from institutions around the world (Chile, Colombia, Finland, Germany, Mexico, USA, etc.).\u00a0 After the talks, we then split into groups and participated in exercise sessions where we worked on problems related to the content of the minicourses that day. Each week also had a plenary talk and a session on open problems.\u00a0 The first week we had the pleasure of hearing from Mauricio Velasco<\/a> (Universdad de los Andes) and the second week we were honored to have Sara Billey<\/a> (Univ. of Washington). Viviane Pons and her team also led a SageMath tutorial per week. A new addition to ECCO was a poster session, where many undergraduate and graduate students (including myself), presented their work. The conference ended with a panel, which I had the pleasure of participating in, where motivations, struggles, and social issues within mathematics were discussed.<\/p>\n Math the Colombian Way<\/u><\/strong><\/p>\n Panel (Left to Right): Carolina Benedetti (moderator), Sebastian Sierra (undergraduate from Colombia), Gretter Dominguez (faculty from Cuba), Andr\u00e9s R. Vindas Mel\u00e9ndez and Federico Ardila<\/p><\/div>\n We often hear of the French, German, American, or Hungarian way of approaching mathematics, but how do you do mathematics the Colombian way?\u00a0 Home to Federico and many of the ECCO organizers, Colombia now has a strong combinatorics presence.\u00a0 The Colombian approach to doing mathematics (combinatorics), as I see it, places a strong emphasis in community building.\u00a0 To many mathematicians it is clear that mathematics is a collaborative effort, but there is more than just collaboration to building a community.\u00a0In building a community, there needs to be a sense of friendship and accountability.\u00a0 That sense of friendship and accountability allows everyone to actively participate in mathematics in a comfortable setting, without a fear of mistakes and also acknowledges that as a group there is no success if any person is left without understanding the mathematics occurring.<\/p>\n At the beginning of ECCO, participants were asked to read and share their thoughts of the Community Agreement.\u00a0 By laying down the expectations of respect, we assured one another that this would be a rewarding and welcoming experience for all.\u00a0 Many of the things on the Community Agreement seem like \u201ccommon sense,\u201d but as present times have shown us, common sense is not so common.\u00a0 Many participants shared that the Community Agreement set mental expectations and reduced any anxiety they may have had in realizing interactions with other participants.<\/p>\n Salsa Dancing! Rekha Thomas, Federico Ardila, Lauren Williams, Andr\u00e9s R. Vindas Mel\u00e9ndez<\/p><\/div>\n Part of the community building was also not in the classroom, rather it was centered around music and the dancefloor.\u00a0 The introduction of dance to a professional setting, such as a mathematics conference, may seem strange to many, but it is engrained in the Colombian way of mathematics.\u00a0 Dancing tears down the hierarchy and power dynamics that we often see in mathematics classrooms and conferences. At ECCO we had leading researchers seeing participants struggle with mathematical concepts, but we also had those participants see the leading mathematicians skirmish to learn some salsa moves on the dancefloor.\u00a0 Indeed, dancing with each other allowed for everyone to foster an inclusive and lively environment, as well as a cultural understanding of our host country and its people. The dancefloor was a space where many participants who were unfamiliar with the dances and music of Colombia soon were cheered on and supported by the local students to the point where there was a feeling of security. This spirit of support transferred to the conference, especially for the problem sessions.<\/p>\n At ECCO, the participants solidify their understanding of the concepts presented during the lectures by working on\u00a0exercises that were written by the minicourse instructors.\u00a0 During the problem sessions, the groups consisted of participants from all levels, normally a professor\/post-doc, a graduate student, and several undergraduates. Many of the problems were challenging yet rewarding once the groups worked together to reach a solution. \u00a0As with many approaches to learning mathematical concepts, by working on complex problems there is a building of perseverance and reflection.\u00a0 The exercises were mathematically meaningful, but what is noteworthy is that all group members played an active role in reaching a solution and understanding of the concepts.\u00a0 I observed that the more experienced mathematicians went directly to thinking about the abstraction of the problems, where the younger students emphasized a more concrete approach to exemplify the theory occurring in the problem, of course both ways of thinking are valuable.\u00a0 An overarching outcome from every problem session is that everyone can\u00a0engage, be excited about, and contribute to mathematics.\u00a0 After working on the problems for an hour or so, volunteers presented their group\u2019s solutions.\u00a0 Here we saw wonders of how working in a supportive environment can contribute to mathematical understanding beyond what we have been exposed to. For example, we had students who had never had Abstract Algebra presenting deep results from Representation Theory. Experiences like these are a result from the wonderful exposition of the minicourse instructors, but also the patience and guidance of the more mathematically experienced group members.<\/p>\n\n\t\t\t
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