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Tropical Geometry, Amoebas and Polytopes

January 15 - April 30, 2018

Tropical geometry is a fast growing field at the interface between algebraic geometry and combinatorics with deep connections to many branches of pure mathematics, applied mathematics, and physics.

Algebraic varieties can be logarithmically degenerated to tropical varieties, which are polyhedral complexes satisfying certain combinatorial properties. At any intermediate stage before reaching its final limit, the degeneration process yields a structure known as an amoeba. Both tropical varieties and amoebas are dual to subdivisions of polytopes, and this leads to an infusion of combinatorial methods into algebraic, complex-analytic, and non-Archimedean geometry.

In our programme, we plan to focus on tropical algebra and applications; combinatorics, polytopes, and complexity; moduli spaces of curves and mirror symmetry; and tropical geometry and amoebas in higher dimension.

Scientific Advisory Board: Mark Gross (Cambridge), Ilia Itenberg (Paris), Michael Joswig (Berlin), Grigory Mikhalkin (Geneva), Bernd Sturmfels (Berkeley)

 

Workshop on Tropical algebra and applications, Jan 22-26

Workshop on Combinatorics, polytopes, and complexity, Feb 19-23

Workshop on Moduli spaces of curves and mirror symmetry, March 19-23

Workshop on Tropical varieties and amoebas in higher dimension, April 16-20 This conference is sponsored by the Simons Foundation.

Seminars Scroll to the next upcoming seminar

Recordings

Participants

Name University Country Arrival and Departure
Karim
Adiprasito
University: KTH Royal Institute of Technology Country: Sweden Arrival and Departure: Feb 6 - Feb 17
Marianne
Akian
University: Inria, Ecole Polytechnique, Paris Country: France Arrival and Departure: Jan 15 - Mar 2
Hulya
Arguz
University: Imperial College London Country: United Kingdom Arrival and Departure: Mar 25 - Mar 30
Farhad
Babaee
University: Université de Fribourg Country: Switzerland Arrival and Departure: Apr 15 - Apr 20
Spencer
Backman
University: University of Vermont Country: United States Arrival and Departure: Apr 15, Apr 8 - Apr 20, Apr 14
Elizabeth
Baldwin
University: University of Oxford Country: United Kingdom Arrival and Departure: Jan 20 - Feb 17
Benoit
Bertrand
University: I.U.T. de Tarbes Country: France Arrival and Departure: Apr 14 - Apr 29
Frederic
Bihan
University: Université de Savoi, Le Bourget-du Lac Country: France Arrival and Departure: Jan 15 - Feb 3
Guus
Bollen
University: Eindhoven University of Technology Country: The Netherlands Arrival and Departure: Feb 4 - Feb 10
Madeline
Brandt
University: University of California, Berkeley Country: United States Arrival and Departure: Jan 16 - Jan 27
Erwan
Brugallé
University: Université de Nantes Country: France Arrival and Departure: Mar 18, Apr 15 - Mar 23, Apr 28
Janko
Böhm
University: TU Kaiserslautern Country: Germany Arrival and Departure: Mar 26 - Apr 6
Dustin
Cartwright
University: University of Tennessee Country: United States Arrival and Departure: Mar 7 - Mar 16
Renzo
Cavalieri
University: Colorado State University Country: United States Arrival and Departure: Mar 4, Apr 15 - Mar 17, Apr 20
Melody
Chan
University: Brown University Country: United States Arrival and Departure: Apr 15 - Apr 20
Man-Wai
Cheung
University: Harvard University Country: United Kingdom Arrival and Departure: Mar 6 - Mar 10
Francisco
Criado Gallart
University: TU - Technische Universität Berlin Country: Germany Arrival and Departure: Feb 19 - Feb 21
Maria Angelica
Cueto
University: Ohio State University Country: United States Arrival and Departure: Mar 4 - Mar 16
Emanuele
Delucchi
University: Université de Fribourg Country: Switzerland Arrival and Departure: Jan 20 - Jan 31
Alicia
Dickenstein
University: Universidad de Buenos Aires Country: Sarghen Arrival and Departure: Feb 18 - Mar 24
Jan
Draisma
University: University of Bern Country: Argentina Arrival and Departure: Jan 15 - Apr 21
Antoine
Ducros
University: University Pierre et Marie Curie. Country: France Arrival and Departure: Apr 15 - Apr 20
Boulos
El Hilany
University: Universität Tübingen Country: Germany Arrival and Departure: Jan 15 - Jan 27
Alexander
Esterov
University: National Research University Higher School of Economics Country: Russia Arrival and Departure: Feb 22 - Mar 9
Lorenzo
Fantini
University: Institut Mathematiques de Jussieu Country: France Arrival and Departure: Apr 15 - Apr 20
Sara Angela
Filippini
University: Imperial College London Country: United Kingdom Arrival and Departure: Mar 18 - Mar 30
Alex
Fink
University: Queen Mary University of London Country: United Kingdom Arrival and Departure: Apr 1 - Apr 30
Jens
Forsgård
University: University of Geneva Country: Switzerland Arrival and Departure: Jan 15 - Apr 25
Tyler
Foster
University: Max Planck Institute for Mathematics Country: Germany Arrival and Departure: Mar 29 - Apr 14
Stephane
Gaubert
University: Inria, Ecole Polytechnique, Paris Country: France Arrival and Departure: Jan 14 - Mar 3
Jeffrey
Giansiracusa
University: Swansea University Country: United Kingdom Arrival and Departure: Feb 11 - Feb 17
Christoph
Goldner
University: Universität Tübingen Country: Germany Arrival and Departure: Mar 25 - Apr 4
Dima
Grigoriev
University: CNRS, Institut des Mathématiques de Lille Country: France Arrival and Departure: Feb 19 - Feb 23
Andreas
Gross
University: Imperial College London Country: United Kingdom Arrival and Departure: Feb 25 - Mar 19
Walter
Gubler
University: Universität Regensburg Country: Germany Arrival and Departure: Mar 18, Apr 15 - Mar 29, Apr 20
Alexander
Guterman
University: Lomonosov Moscow State University, MSU Country: Russia Arrival and Departure: Apr 15 - Apr 20
Paul
Görlach
University: Max Planck Institute for Mathematics in the Science Country: Germany Arrival and Departure: Apr 16 - Apr 30
Christian
Haase
University: Freie Universität Berlin Country: Germany Arrival and Departure: Feb 18 - Feb 24
Marvin
Hahn
University: Universität Tübingen Country: Germany Arrival and Departure: Apr 5, Feb 4 - Apr 13, Feb 24
Milena
Hering
University: University of Edinburgh Country: United Kingdom Arrival and Departure: Feb 18 - Mar 2
David
Holmes (Online)
University: Universiteit Leiden Country: The Netherlands Arrival and Departure: Apr 15 - Apr 20
June
Huh
University: Institute for Advanced Study, IAS Country: United States Arrival and Departure: Apr 15 - Apr 20
Ilia
Itenberg
University: Institut de Mathématiques de Jussieu - Paris Rive Gauche Country: France Arrival and Departure: Apr 4 - Apr 26
Zur
Izhakian
University: University of Aberdeen Country: United Kingdom Arrival and Departure: Apr 7 - Apr 30
Andres
Jaramillo Puentes
University: Tel Aviv University Country: Israel Arrival and Departure: Apr 1 - Apr 14
Philipp
Jell
University: Universität Regensburg Country: Germany Arrival and Departure: Jan 15 - Apr 26
Anders
Jensen
University: Aarhus University Country: Denmark Arrival and Departure: Jan 15, Apr 13 - Mar 27, Apr 30
Dave
Jensen
University: University of Kentucky Country: United States Arrival and Departure: Apr 15 - Apr 20
Marianne
Johnson
University: University of Manchester Country: United Kingdom Arrival and Departure: Jan 17 - Feb 24
Michael
Joswig
University: TU - Technische Universität Berlin Country: Germany Arrival and Departure: Jan 21, Feb 18 - Feb 2, Mar 1
Nikita
Kalinin
University: HSE St. Petersburg, Laboratory of game theory and decision making Country: Russia Arrival and Departure: Feb 12 - Feb 17
Mark
Kambites
University: University of Manchester Country: United Kingdom Arrival and Departure: Jan 21, Feb 17 - Jan 26, Feb 23
Kiran
Kedlaya
University: University of California, San Diego Country: United States Arrival and Departure: Apr 15 - Apr 19
Gary
Kennedy
University: Ohio State University Country: United States Arrival and Departure: Apr 15 - Apr 20
Ayush
Kumar Tewari
University: Universität Tübingen Country: Germany Arrival and Departure: Jan 14 - Jan 31
Max
Kutler
University: Yale University Country: United States Arrival and Departure: Mar 1 - Mar 10
Sara
Lamboglia
University: University of Warwick Country: United Kingdom Arrival and Departure: Feb 4 - Feb 10
Lionel
Lang
University: Stockholm University Country: Sweden Arrival and Departure: Jan 15 - Apr 28
Michal
Lason
University: University of Bern Country: Switzerland Arrival and Departure: Feb 23 - Mar 16
Yoav
Len
University: Fields Institute, University of Toronto Country: Canada Arrival and Departure: Jan 21 - Feb 2
Anton
Leykin
University: Georgia Institute of Technology Country: United States Arrival and Departure: Feb 11, Mar 18 - Feb 22, Mar 29
Bo
Lin
University: University of Texas at Austin Country: United States Arrival and Departure: Feb 12 - Apr 30
Georg
Loho
University: TU - Technische Universität Berlin Country: Germany Arrival and Departure: Jan 28 - Feb 17
Lucia
Lopez de Medrano
University: UNAM Country: Mexico Arrival and Departure: Mar 26 - Apr 14
Diane
Maclagan
University: University of Warwick Country: United Kingdom Arrival and Departure: Mar 18 - Apr 21
Gregorio
Malajovich
University: Universidade Federal do Rio de Janeiro Country: Brazil Arrival and Departure: Jan 15 - Feb 17
Hannah
Markwig
University: Universität Tübingen Country: Germany Arrival and Departure: Jan 14 - Apr 30
Thomas
Markwig
University: Universität Tübingen Country: Germany Arrival and Departure: Jan 14 - Apr 30
Margarida
Melo
University: Universita Roma Tre Country: Italy Arrival and Departure: Apr 2 - Apr 5
Grigory
Mikhalkin
University: University of Geneva Country: Switzerland Arrival and Departure: Mar 20 - Apr 28
Kalina
Mincheva
University: Yale University Country: United States Arrival and Departure: Jan 15 - Apr 30
Ralph
Morrison
University: Williams College Country: United States Arrival and Departure: Jan 14 - Feb 1
Johannes
Nicaise
University: Imperial College London Country: United Kingdom Arrival and Departure: Apr 15 - Apr 20
Benjamin
Nill
University: Otto von Guericke Universität Magdeburg Country: Germany Arrival and Departure:
Mounir
Nisse
University: KIAS, Korea Institute for Advanced Study Country: South Korea Arrival and Departure: Apr 8 - Apr 30
Jorge
Alberto Olarte
University: Freie Universität Berlin Country: Germany Arrival and Departure: Feb 19 - Feb 23
John Christian
Ottem
University: University of Oslo Country: Norway Arrival and Departure: Apr 18 - Apr 30
Marta
Panizzut
University: TU - Technische Universität Berlin Country: Germany Arrival and Departure: Feb 18 - Mar 5
Sam
Payne (Online)
University: University of Texas at Austin Country: United States Arrival and Departure: Mar 18, Apr 15 - Mar 24, Apr 20
Rudi
Pendavingh
University: Eindhoven University of Technology Country: The Netherlands Arrival and Departure: Feb 25 - Mar 10
Andrea
Petracci
University: University of Nottingham Country: United Kingdom Arrival and Departure: Mar 17 - Mar 24
Joe
Rabinoff
University: Georgia Institute of Technology Country: United States Arrival and Departure: Mar 11 - Mar 17
Dhruv
Ranganthan
University: Massachusetts Institute of Technology, MIT Country: United Kingdom Arrival and Departure: Jan 14 - Jan 19
Johannes
Rau
University: Universität Tübingen Country: Germany Arrival and Departure: Feb 25 - Mar 31
Yue
Ren
University: Max Planck Institute for Mathematics in the Science Country: The Netherlands Arrival and Departure: Jan 15 - Apr 30
Arthur
Renaudineau
University: Universität Tübingen Country: Germany Arrival and Departure: Feb 26 - Apr 30
Felipe
Rincon
University: University of Oslo Country: Norway Arrival and Departure: Jan 15 - Feb 24
Louis
Rowen
University: Bar-Ilan University Country: Israel Arrival and Departure: Apr 15 - Apr 20
Helge
Ruddat
University: Johannes Gutenberg-Universität Mainz Country: Germany Arrival and Departure: Feb 25 - Mar 17
Timur
Sadykov
University: Russian University of Economics Country: Russia Arrival and Departure: Feb 3 - Feb 10
Raman
Sanyal
University: Goethe University Frankfurt am Main Country: Germany Arrival and Departure: Feb 4 - Feb 24
Karin
Schaller
University: Freie Universität Berlin Country: Germany Arrival and Departure: Mar 11 - Mar 30
Benjamin
Schröter
University: TU - Technische Universität Berlin Country: Germany Arrival and Departure: Jan 15 - Apr 29
Kristin
Shaw
University: University of Oslo Country: Norway Arrival and Departure: Mar 18 - Apr 30
Eugenii
Shustin
University: Tel Aviv University Country: Israel Arrival and Departure: Mar 1 - Apr 30
Jeff
Sommars
University: University of Illinois at Chicago Country: United States Arrival and Departure: Jan 15 - Feb 16
Alejandro
Soto
University: Universität Tübingen Country: Germany Arrival and Departure: Mar 1 - Mar 24
Frank
Sottile
University: Texas A&M University Country: United States Arrival and Departure: Apr 1 - Apr 30
Bernd
Sturmfels
University: University of California, Berkeley Country: United States Arrival and Departure: Apr 15 - Apr 19
Luis
Felipe Tabera
University: Universidad de Cantabria Country: Spain Arrival and Departure: Apr 1 - Apr 14
Jenia
Tevelev
University: University of Massachusetts Amherst Country: United States Arrival and Departure: Mar 11 - Mar 17
Thorsten
Theobald
University: Goethe University Frankfurt am Main Country: Germany Arrival and Departure: Feb 18, Mar 25 - Mar 9, Apr 6
Bach
Tran
University: University of Edinburgh Country: United Kingdom Arrival and Departure: Feb 11 - Feb 17
Ngoc
Mai Tran
University: Hausdorff Center for Mathematics Country: Germany Arrival and Departure: Jan 15 - Feb 24
August
Tsikh
University: Siberian Federal University Country: Russia Arrival and Departure: Mar 18 - Apr 21
Ilya
Tyomkin
University: Ben Gurion University of the Negev Country: Israel Arrival and Departure: Mar 20 - Apr 30
Martin
Ulirsch
University: University of Michigan Country: United States Arrival and Departure: Mar 25, Apr 15 - Apr 1, Apr 20
Alejandro
Vargas
University: University of Bern Country: Switzerland Arrival and Departure: Jan 21, Apr 15 - Feb 24, Apr 20
Jan
Verschelde
University: University of Illinois at Chicago Country: United States Arrival and Departure: Jan 21 - Jan 27
Oleg
Viro
University: Stony Brook University Country: United States Arrival and Departure: Apr 15 - Apr 20
Annette
Werner
University: Goethe University Frankfurt am Main Country: Germany Arrival and Departure: Mar 19, Apr 15 - Mar 23, Apr 20
Jonathan
Wise (Online)
University: University of Colorado at Boulder Country: United States Arrival and Departure: Apr 15 - Apr 30
Josephine
Yu
University: Georgia Institute of Technology Country: United States Arrival and Departure: Mar 18 - Mar 29
Chi
Ho Yuen
University: Georgia Institute of Technology Country: United States Arrival and Departure: Jan 14 - Feb 10
Ilia
Zharkov
University: Kansas State University Country: United States Arrival and Departure: Mar 11 - Mar 17
Timo
de Wolff
University: TU - Technische Universität Berlin Country: Germany Arrival and Departure: Jan 22, Apr 15 - Mar 17, Apr 20

Preprints

  1. Tropicalized quartics and canonical embeddings for tropical curves of genus 3 - Marvin Anas Hahn Hannah Markwig Yue Ren Ilya Tyomkin
  2. Stillman's conjecture via generic initial ideals - Jan Draisma Michal Lason Anton Leykin
  3. Algorithms for Tight Spans and Tropical Linear Spaces - Simon Hampe Michael Joswig Benjamin Schröter
  4. Realization spaces of matroids over hyperfields - Emanuele Delucchi Linard Hoessly Elia Saini
  5. Describing Amoebas - Mounir Nisse Frank Sottile
  6. Polynomials and tensors of bounded strength - Arthur Bik Jan Draisma Rob H. Eggermont
  7. Real tropicalization and analytification of semialgebraic sets - Philipp Jell Claus Scheiderer Josephine Yu
  8. Counts of (tropical) curves in E×P^1 and Feynman integrals - Janko Böhm Christoph Goldner Hannah Markwig
  9. Tropical Mirror Symmetry in Dimension One - Janko Böhm Christoph Goldner Hannah Markwig
  10. Lefschetz (1,1)-theorem in tropical geometry - Philipp Jell Johannes Rau Kristin Shaw
  11. The algebraic boundary of the sonc cone - Jens Forsgård Timo de Wolff
  12. Higher Connectivity of Tropicalizations - Diane Maclagan Josephine Yu
  13. Tropical Carathéodory with Matroids - Georg Loho Raman Sanyal