Tropical Mathematics & its Applications

A joint research group in tropical mathematics has been formed by researchers in UK mathematics departments at universities including Manchester, Birmingham, Warwick, Queen Mary and Swansea, with financial support from the London Mathematical Society.

This page gives details of the next meeting, to be held in Birmingham. Funds are available to support the attendance of UK-based postgraduate students.

Venue

 Nuffield, G17

Speakers

• Stephane Gaubert (INRIA and Ecole Polytechnique, Paris, France)
• Adi Niv (Kibbutzim College, Tel-Aviv, Israel)
• Dhruv Ranganathan (DPMMS, Cambridge, UK)

Agenda

Please note: where academics have agreed to share their presentations, these are included as pdf format downloads.

• 12:00 Lunch
  Early participants meet in School of Mathematics (entrance hall) and go to lunch in Staff House (University of Birmingham).
• 13:00 Dhruv Ranganathan - How should we count one tropical curve?
  Abstract: Tropical geometry famously provides a way in which to count solutions to enumerative (or curve counting) problems in algebraic geometry. In order to achieve this, each tropical curve is counted with a certain multiplicity. Ideally, one would like this multiplicity to be localized over “smaller” problems attached to the vertices. I will give an introduction to these ideas, explain some subtleties that make it fun to think about, discuss what implications this has for older questions in the subject.

• 14:00 Adi Niv - Optimal assignments with supervisions (Presentation slides PDF)
  Abstract: In this talk I will provide a (graph theoretic) proof to the tropical Jacobi identity, alternative to the (matrix theoretic) proof recently obtained in my joint work with Marianne Akian and Stephane Gaubert. The latter proof was inspired by the classical Jacobi identity, which states that the (J^c,I^c)-minor of a matrix A corresponds, in some to be defined way, to the (I,J)-minor of A^{-1}. In other words, the compound of order k of A corresponds to the compound of order (n-k) of its inverse. We provide an application of the tropical Jacobi identity to optimal assignments with supervisions. More precisely, we consider the problem of assigning multiple tasks to one team, or daily tasks to multiple teams, where each team has a supervisor-task or a supervised task. 

  This is a joint work with Marie Maccaig and Sergey Sergeev.

• 15:00 - 16:00 Break - Tea/Coffee
• 16:00 Stephane Gaubert - Condition numbers in nonarchimedean semidefinite programming and what they say about stochastic mean payoff games (Presentation slides PDF)
  Abstract: Semidefinite programming consists in optimizing a linear form over a spectrahedron, the latter being across section of the cone of positive semidefinite matrices. This makes sense over any real closed field, and in particular, over fields of real Puiseux series, equipped with their non archimedean valuation. In this way, a tropical spectrahedron can be defined as the image by the valuation of a nonarchimedean spectrahedron. The nonarchimedean semidefinite feasibility problem, with generic valuations of the input matrices, turns out to be equivalent to stochastic mean payoff games with perfect information. We use this correspondence to define a condition number for stochastic mean payoff games, which controls the ``rotundity'' of the associated tropical spectrahedra. We bound the complexity of value iteration in terms of this condition number, and derive fixed parameter tractability results for stochastic mean payoff games with perfect information. This is a joint work with Xavier Allamigeon, Ricardo Katz and Mateusz Skomra.

• 18:00 Dinner
  

  A table has been booked in Wildwood restaurant (see wildwoodrestaurants.co.uk) in the City Centre Birmingham (66 New Street). After the last talk and some discussion we will start moving towards the University train station, where we will catch a train to Birmingham New Street.

Financial support

Financial support for UK-based postgraduate students is awarded on a first come first served basis; please give an estimate of your travel costs when confirming your attendance.

Directions from Central Birmingham Stations

(Birmingham New Street, Birmingham Moor Street)

The University of Birmingham (Edgbaston Campus) is located near University train station (to our knowledge, surprisingly, this is a unique station with this name in the UK).

If you arrive at Birmingham Moor Street then walk to Birmingham New Street station: there is no direct train from Birmingham Moor Street to University.

When you are at Birmingham New Street, it is safe to find platform 12 and take a train to Redditch or to Longbridge. Then leave the train at the second stop: University.  There are several other trains which stop at University: check the electronic screens.

From the train station, descend downhill towards the clock tower. Then, for the main venues of the workshop see the unmarked campus map [PDF] and the marked campus map [PDF]. Notice especially that the talks will take place *not* in School of Mathematics but in another building named Nuffield (this building is very close to School of Mathematics).

If you want to go for lunch then either find us at 11:45 - 12:00 at School of Mathematics entrance or go directly to Staff House and find us there on the 2^nd floor in Noble room.

Contacts