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.
Our budget is still in development, but we have some funding available covering
accomodation and partial support for transportation
destined to students and young researchers.
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.
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.
Bibliography
Coming soon!
