Junior Algebraic geometry Warwick Seminar (JAWS)
Seminar Organisers: Tommaso Faustini, Mayo Mayo García and Marc Truter
Rooms and Times
Term 1: D1.07 3 - 4 pm Thursdays
Term 2: D1.07 3 - 4 pm Thursdays
Term 3: MS.04 3 - 4 pm Thursdays
Term 2
Week 2 Jan 22
Sae Koyama (Cambridge)
Enumerating elliptic curves in toric threefolds using tropical geometry
Tropical methods have been a powerful tool in enumerative geometry. The main idea is that we can define “tropical” objects, which are combinatorial in nature, and use those to define tropical invariants which will coincide with algebraic invariants. For instance, Mikhalkin showed that genus 0 curve counts coincide with weighted counts of genus 0 tropical curves. The difficulty with extending this to higher genus is the existence of tropical objects that don’t come from algebraic ones. We discuss how logarithmic techniques can be used to deal with these contributions and derive enumerative consequences in the case of elliptic curves in toric threefolds.
Week 5 Feb 12
Sean Fitzgerald (Trinity)
Week 6 Feb 19
Siao Chi Mok (Cambridge)
Week 7 Feb 26
Tianchen Zhao (Exeter)
Week 8 Mar 5
Yijue Hu (Nottingham)
Week 9 Mar 12
Week 10 Mar 19
Filippo Papallo (Genova)
Term 3
Week 1 Apr 30
Week 2 May 7
Week 3 May 14
Week 4 May 21
Matthias Ferreira (Sorbonne)
Week 5 May 28
Week 6 Jun 4
Week 7 Jun 11
Brais Gerpe Vilas (Sheffield)
Week 8 Jun 18
Week 9 Jun 25
Week 10 Jul 2
Term 1
Week 3 Oct 23
Daniel Green Tripp (Bristol)
An equidistribution theorem on toric varieties
A version of Weyl’s equidistribution theorem states that, for almost all points in the n-dimensional compact torus, the average of the Dirac measures on the powers of the point converges to the normalised Haar measure. We will explore how to generalise this statement to the n-dimensional complex algebraic torus; at this moment, toric varieties will emerge as our saviours, giving us the convergence. Time permitting, I will also discuss possible future directions on finding even more interesting convergences. Based on an ongoing joint work with Farhad Babaee.
Week 5 Nov 6
Parth Shimpi (Glasgow)
It’s supported on P1, how complicated could it be?
"Not complicated at all", at least that is the case I will make. In the deep dark forest prowled by serpentine complexes and monstrous sheaves that are challenging to identify (let alone analyse), rational curves provide a warm and cozy retreat --- the calm of knowing where everything sits and nothing can go wrong. Be it a surface, a threefold, or simply a single curve: if all you care about is what sits near a P1, I will sketch how a little representation theory goes a long way in providing a complete map of the derived category.
Week 7 Nov 20
Ines Chung-Halpern (LSGNT)
Cluster varieties, integral linear manifolds and mirror symmetry
Cluster varieties are a class of algebraic varieties carrying deep combinatorial structure, which allows us to adapt methods from toric geometry to a more general setting. In this talk, I will introduce cluster varieties in dimension 2 and their tropicalisations, which combinatorially encodes much of their geometric data in its integral linear structure. We will see how the analogue of polytopes on these linear manifolds gives rich examples of compactifications of cluster varieties, and allows us to compute examples of mirror symmetry for Fano varieties.
Week 8 Nov 27
Dan Simms (LSGNT) [Time and Room Change: 1 - 2 pm B3.01]
Localisation in Enumerative Geometry
This talk will introduce the modern approach to studying enumerative geometry via the intersection theory of moduli spaces. When the moduli spaces are poorly behaved, one must jump through several hoops to find a ‘virtual fundamental class’ in order to do this properly. Rather than going down this road, we will see how things can be simplified in the presence of a torus action. This will take us on a journey through equivariant cohomology, and will hopefully end with a couple of nice applications.
COW Seminar (Warwick) 2 - 5pm
Week 8 Nov 28
CALF Seminar (Warwick, IAS seminar room) 1 - 5pm