The next meeting of the Joint Research Group will be at Queen Mary University of London on the afternoon of Wednesday, 13 March, 2019. Talks will be held in room Bancroft 1.13. The organisers are Felipe Rincón and Alex Fink.
|12:00||Meet in Queens' building foyer to walk to lunch
(at The Curve)
(University of Warwick /
Goethe University Frankfurt am Main)
|A tropical proof of the Prym-Brill-Noether Theorem|
|14:30||Zur Izhakian (University of Aberdeen)||Commutative ν-Algebra and Supertropical Algebraic Geometry|
|15:30||Tea and coffee, Bancroft building ground floor|
|16:15||Sara Lamboglia (Goethe University Frankfurt am Main)||A tropical version of Fano schemes|
|17:30||Meet at Bancroft ground floor to go to dinner|
If you are interested in attending the dinner, please register by 11 March so that adequate space can be reserved.
Some support for UK-based graduate students' travel expenses is available, and will be awarded on a first come, first served basis. Please apply with an estimate of your costs.
The nearest tube stations to Queen Mary are Stepney Green and Mile End. Both stations and the university lie on Mile End Road. The meeting venues are a six to eight minutes' walk from either.
The Queens' building is number 19 on this campus map. It is the palatial-looking building just behind the clock tower on Mile End Road, with a facade of whitish Portland stone. The Curve, where lunch is, is the main canteen, number 46. The Bancroft building is number 31; it's the one with Mucci's restaurant on its front left corner. Bancroft room 1.13 is on the first floor, straight ahead as you leave the main staircase.
Martin Ulirsch, A tropical proof of the Prym-Brill-Noether Theorem
In this talk I will explain how a careful understanding of the chip firing game on a folded chain of loops provides us with an upper bound on the dimension of Prym-Brill-Noether locus associated to a generic unramifed double cover. This gives a new tropical proof of the classical Prym-Brill-Noether Theorem due to Welters and Bertram as well as new upper bounds in the case of special unramified double covers. This is joint work with Yoav Len.
Zur Izhakian, Commutative ν-Algebra and Supertropical Algebraic Geometry
In this talk I will describe a framework for supertropical algebraic geometry, relying on commutative ν-semirings. It employs q-congruences, whose distinguished ghost and tangible clusters allow both quotienting and localization. Utilizing these clusters, g-prime, g-radical, and maximal q-congruences are naturally defined, satisfying the classical relations among analogous ideals. In this framework, the underlying spaces for a construction of schemes are provided by spectra of g-prime congruences, over which correspondences between q-congruences and varieties emerge directly.
Sara Lamboglia, A tropical version of Fano schemes
The classical Fano scheme Fd(X) of a variety X parametrises d-dimensional linear spaces contained in X. In this talk I am going to define a tropical analogue of the Fano scheme Fd(trop X) and I will show its relation with the tropicalization trop Fd(X) of the classical Fano scheme. In particular I will focus on the tropical version of Fano schemes of tropicalized linear spaces and tropicalized toric varieties.