What?
The purpose of this workshop is to bring together a number of young researchers and introduce them to a research topic through several introductory talks followed by specific lectures concerning the topic under study: the misterious field with one element and the different notions of algebraic geometry developed over it.
Who?
Everybody is welcome to attend, and young researchers, master students, phd students and postdocs are specially encouraged to do so. If you are interested on participating, send a message to one of the organizers to get further information.
When and where?
The workshop will take place at the Faculty of Sciences in the University of Granada, during November 23, 24 and 25.
How to get to the conference room
The lectures will take place on the "Seminario" (Seminar Room) of the "Centro de Instrumentación Científica" (Scientific Instruments Center) located in a different building. Here is how to arrive from the Math Department to the CIC building:
Speakers
Lectures will be given by the following people:
- Peter Arndt (Universität Göttingen, Germany)
- Javier López Peña (Queen Mary University of London, UK)
- Oliver Lorscheid (Universität Wuppertal, Germany)
- Snigdhayan Mahanta (Johns Hopkins University, USA)
- Florian Marty (MPIM Bonn, Germany)
- Jorge Plazas Vargas (Universiteit Utrecht, The Netherlands)
Program
The workshop will be divided in two parts. During the first day there will be three general introductory lectures dealing with some of the material that will be used in the next days. The will be three lectures of one hour and a haf each, on the following topics:
- Categories and homotopy theory (by Peter Arndt and Snigdhayan Mahanta),
- Algebraic Geometry (by Javier López Peña and Florian marty),
- Number theory and motives (by Oliver Lorscheid and Jorge Plazas Vargas)
- What is F_{1}? (by Peter Arndt),
- Geometry over Generalized Rings (by Peter Arndt),
- Geometry of monoids (by Javier López Peña),
- Algebraic groups over F_{1} (by Oliver Lorscheid),
- On some topological constructions in the context of F_{1}-geometry (by Snigdhayan Mahanta),
- A notion of smoothness for affine F_{1}-schemes (by Florian Marty),
- Zeta functions and motives over F_{1} (by Jorge Plazas Vargas),
- Open problems and research directions.
Timetable
Monday 23
- 9:00-10:00 Welcome and registration
- 10:00-10:30 Cofee break
- 10:30-12:00 Categories and homotopy theory (by Peter Arndt and Snigdhayan Mahanta)
- 12:00-13:30 Algebraic Geometry (by Javier López Peña and Florian Marty)
- 13:30-15:30 Lunch
- 15:30-17:00 Number theory and motives (by Oliver Lorscheid and Jorge Plazas Vargas)
Tuesday 24
- 9:00-10:00 What is F_1? (by Peter Arndt)
- 10:00-11:00 Zeta functions and motives over F1 (by Jorge Plazas Vargas)
- 11:00-11:30 Cofee break
- 11:30-12:30 Geometry of monoids (by Javier López Peña)
- 12:30-13:30 Algebraic groups over F1 (by Oliver Lorscheid)
Wednesday 25
- 9:00-10:00 Geometry over Generalized Rings (by Peter Arndt)
- 10:00-11:00 A notion of smoothness for affine F1-schemes (by Florian Marty)
- 11:00-11:30 Cofee Break
- 11:30-12:30 On some topological constructions in the context of F1-geometry (by Snigdhayan Mahanta)
- 12:30-14:00 Open problems and further research directions
Travel information
By plane
Granada's Airport is quite a small one, there are a few direct flights from Barcelona and Madrid in Spain, Bologna and Milan-Bergamo in Italy, or London Stansted, Liverpool, and Est Midlands in the UK. If you are coming by plane from a different city, the closest big airports are Malaga and Madrid. Below you can find some information on how to arrive to Granada from these cities.
By train or bus
In southern Spain buses are usually cheaper and faster than trains. If you prefer using the train you can check the schedules in the website of Renfe, the Spanish train company.
Malaga is fewer than 150 km away from Granada. From the Pablo Picasso Airport you can easily reach the bus an train stations of the city either takin a cab outside the airport (it takes about 20 minutes to reach the city center from the airport, depending on the traffic) or by taking the urban bus number 19, that stops both besides the train station and inside the bus station. This local bus ticket costs around 1 euro, and the trip takes around half an hour. The bus is the cheapest and fastest way to go from Malaga to Granada. Once in the bus station, find the "ALSA/Alsina Graells" selling point and buy your ticket there. Usually you can find buses between the two cities every hour. A one-way ticket costs around 10 euro.
Bus connections between Madrid and Granada are frequent and cheap. A one-way ticket costs around 15 euro. In order to travel to Granada by bus you must go to either "Avenida de America" or "Estación Sur (Mendez Alvaro)" bus stations, the bus company that sells the bus tickets is called "ALSA".
More information about buses prices and timetables can be found at the website of the bus company ALSA.
Participants
- Peter Arndt (Universität Göttingen, Germany)
- Sonia Azuaga (Universities of Málaga, and Rey Juan Carlos, Madrid)
- Hannes Bierwirth (University of Málaga)
- Anthony Blanc (University of Montpellier)
- José Ramón Brox López (University of Málaga)
- Francisco J. Castro (University of Sevilla)
- A. Daniel Cereto Ruiz (Universities of Málaga, and Rey Juan Carlos, Madrid)
- María Guadalupe Corrales García (University of Málaga)
- Óscar Cortadellas (University of Granada)
- Laiachi El Kaoutit (University of Granada)
- José Gómez-Torrecillas (University of Granada)
- Pedro A. Guil (University of Murcia)
- David Holmes (University of Warwick)
- Andreas Holmstrom (University of Cambridge)
- Pascual Jara (University of Granada)
- Jan Willem de Jong (University of Utrecht)
- F. Javier Lobillo (University of Granada)
- Javier López Peña (Queen Mary University of London, UK)
- Oliver Lorscheid (Universität Wuppertal, Germany)
- Snigdhayan Mahanta (Johns Hopkins University, USA)
- Antonio Martínez Cegarra (University of Granada)
- Florian Marty (MPIM Bonn, Germany)
- Stephen Meagher (University of Freiburg)
- Luis M. Merino González (University of Granada)
- Bram Mesland (University of Utrech)
- Fernando Muro (University of Sevilla)
- Gabriel Navarro (University of Granada)
- Sinem Odabasi (University of Murcia)
- Jorge Plazas Vargas (Universiteit Utrecht, The Netherlands)
- Antonio Rodríguez Garzón (University of Granada)
- Elena Rodríguez Jorge (University of Barcelona, UAB)
- Cristos A. Ruiz Toscano (University of Padova)
- Juana Sánchez Ortega (University of Málaga)
- José Félix Solanilla Hernández (University of Málaga)
- Alberto Venazzi (University of Leiden)
Further information
If you want to know more about the event, funding, accommodation or any related topic, contact one of the organizers:
- José Gómez Torrecillas - gomezj(at)ugr.es
- Pascual Jara Martínez - pjara(at)ugr.es
- Javier López Peña - j.lopez(at)qmul.ac.uk