Colombian Encounter of Tropical and Non-archimedean Geometry








Description

Tropical geometry is a piece-wise linear geometry which merges ideas from algebraic, symplectic and non-archimedean geometry with tools from combinatorics and convex geometry. Via the process of tropicalization, classical varieties and geometric problems can be connected to the tropical world and, in some cases, solved there. In non-archimedean geometry, the valuation on the underlying field makes the idea of tropicalization particularly natural and powerful. In recent years, this connection has received much attention and exhibited links to diverse topics such as Hodge theory, mirror symmetry and the study of zeta functions. The main goal of this event is to introduce students and young mathematicians to these exciting topics and to foster and strengthen the connections between local researchers and the international mathematical community.

The school will introduce the participants to tropical and non-archimedean geometry via two minicourses given by Ilia Itenberg (Sorbonne Université) and Marco Maculan (Sorbonne Université). Additionally, in the research talks we will explore the latest developments in the field.
We hope that this school can serve as the starting point for a local network of researchers and students and therefore can be continued in the coming years by follow-up events of a similar type.


Main objectives

  • Promote the cutting-edge research areas of tropical and non-archimedean geometry in Latin America.
  • Introduce students and young researchers to the field and connect them with internationally renowned senior researchers.
  • Foster collaborations in the region and establish a local network of collaborators and students in the field.
  • Strengthen the ties between Colombia and the international mathematical community.
  • Create accessible material for participants of this and future schools, derived from the minicourses and talks.


Organizers:

Pablo Cubides (Universidad de los Andes)
Johannes Rau (Universidad de los Andes)



Registration

Please register if you plan to attend regardless of whether you need financial support or not.
We are in the final stage of registrations and cannot provide travel support anymore. We still have limited funding for accomodation. Please indicate in the registration form if you need support. We will come back to you as soon as possible with an answer.

Registration form



Programme


Monday Tuesday Wednesday Thursday Friday
08:00-09:00 Registration
09:00-10:30 Minicourse 1
Itenberg 		Minicourse 1
 Itenberg 		Minicourse 1
 Itenberg 		Talk 1 Talk 5
10:30-11:00 Break Break Break Break Break
11:00-12:30 Problems 1 Problems 1 Minicourse 2
 Maculan 		Talk 2 Talk 6
12:30-14:00 Lunch Lunch Lunch Lunch Lunch
14:00-15:30 Minicourse 2
 Maculan 		Minicourse 2
 Maculan 		Excursion
Free afternoon 		Talk 3 Open problem session
15:30-16:00 Break Break Break Closing Toast
16:00-17:30 Problems 2 Problems 2 Talk 4





Minicourses

The conference will feature two minicourses aiming to introduce students and young researchers to the cutting-edge research areas of Tropical and Non-archimedean Geometry and their interactions. The courses are delivered by two leading experts in the two fields which are also renowned for the excellent exposition skills. Each course will be complemented by exercise sessions.


Minicourse 1

Tropical geometry
Ilia Itenberg (Sorbonne Université)


Tropical geometry can be seen as algebraic geometry over the tropical (max-plus) semifield. On tropical varieties, one can define different types of homology and intersection theories. These can be related to classical (complex and real) algebraic varieties in various ways.


Introductory texts

Minicourse 2

Non-archimedean geometry
Marco Maculan (Sorbonne Université)


Non-archimedean geometry is the geometry over valued fields. The existence of a valuation makes these varieties particularly prone to be tropicalized. Hence tropical methods have gotten much attention recently in the study of non-archimedean geometry. In particular, interesting applications towards mirror symmetry and zeta functions have been conjectured and partially found.




Talks

Ethan Cotterill, Universidade Estadual de Campinas, Brasil
Cristhian Garay, Centro de Investigación en Matemáticas AC (CIMAT), México
Ilia Zharkov, Kansas State University, USA
Andrés Jaramillo Puentes, University Duisburg Essen, Germany
Vlerë Mehmeti, Sorbonne Université, France




Practical Information

The summer school will be held in room SD-801 of los Los Andes University (this means building SD, room 801).





There is no registration fee but be aware that meals and accomodation are not covered. Registration is compulsory, as you will be registered in a list to be able to enter the campus.
We advice participants to get accomodation near the University campus.

At arrival:
We recommend participants to take a taxi from the airport to their accommodation (unless your hotel has a transport service, in which case this is also a good option). In order to do this you will need to either exchange or withdraw some money at the airport. The taxi will cost you around 20000 colombian pesos (say around 7-8 US dollars), maybe a bit less or a bit more (most of them only accept cash). You can see the exact amount in the taximeter + a charge of about 4500 pesos for airport ride (and if you arrive during the night there will be also an extra charge for that). You will find at the airport an official taxi cue from which you should get yours (they are all yellow btw).
If you are staying at Suites Tequendama make sure you give the address to the driver as Suites Tequendama is sometimes mistaken by Hotel Tequendama. Both are in the same area but you can avoid misunderstandings. See the map below for a suggested route.

About Bogotá:
Bogotá is 2650 meters above the sea, please keep in mind this is not yet the caribbean. Its neither very cold nor very warm, temperature oscillates between 15 to 25 C degrees during the day, and it drops a bit during the night, so do bring a jacket or sweater with you.
Electrical plugs are as in the US, so try to bring an adapter is you don't hace this type of plug. Here you can find more information about electrical plugs.

Things to do in one afternoon:

You can visit the historical center of Bogotá, around the neighborhood La Candelaria. Most of the Museums are concentrated in this neighborhood. We list some of the activities you could do around downtown Bogotá below:

Cerro de Monserrate
Museo Nacional
Museo de Arte Moderno
Biblioteca Nacional - Free exhibitions
Museo del Oro
Museo Botero
Graffitti Tour - There are several free and paid tours around La Candelaria, the historical center of Bogotá.

Some coffee shops:

Colo
Varietale
Arte y pasión

Other neighborhoods:

Zona G: located in Chapinero area, has most of the tastiest restaurants and coffee shops in Bogotá
Zona Rosa: in northern Bogotá, this area is popular for its bars and restaurants.

If you are staying over the weekend and want to go for a hike, Choachí is a town very close to Bogotá and you can visit there the Páramo el Verjón, a moorland with tons of frailejons. On Sundays Bogotá has the Ciclovía, from 7am to 2pm. During this time lots of avenues close for bycicles, pedestrians, etc.



Contact:

Pablo Cubides, email: p.cubideskovacsics[at]uniandes.edu.co
Johannes Rau, email: j.rau[at]uniandes.edu.co




Sponsors:


York Research Chair
Prof. Nantel Bergeron











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