Website of Oliver Leigh
Site d'Oliver Leigh
Oliver Leighs hemsida

ETH slides
Diapositives ETH
ETH diabilder
Welcome to my website.

I am a Postdoctoral Research Fellow in Algebraic Geometry at Stockholm University.

Previously, I completed a jointly awarded PhD at the University of Melbourne and the University of British Columbia.
Bienvenue sur mon site web.

Je suis chercheur postdoctoral en géométrie algébrique à l'Université de Stockholm.

Auparavant, j'ai completé un doctorat conjointement à l'Université de Melbourne et à l'Université de la Colombie-Britannique.
Välkommen till min hemsida.

Jag är postdoktor i algebraisk geometri vid Stockholms universitet.

Tidigare avslutade jag en gemensamt tilldelad doktorsexamen vid University of Melbourne och University of British Columbia.

Research Interests
Intérêts de recherche
Forskningsintressen

I am interested in enumerative problems in geometry that are motivated by physics. I primarily study these from an algebro-geometric viewpoint. This includes both Gromov-Witten and Donaldson-Thomas theory.

In Donaldson-Thomas theory we can count subschemes of Calabi-Yau threefolds by examining the local picture. Using this method we can count subscheme by considering 3D partitions and using the topological vertex. Below is a tool for visualising these.
Je m'intéresse aux problèmes énumératifs en géométrie motivés par la physique. J'étudie principalement ceux-ci en utilisant un point de vue géométrique algébrique. Cela inclut à la fois la théorie de Gromov-Witten et celle de Donaldson-Thomas.

Dans la théorie de Donaldson-Thomas, nous pouvons compter les sous-schémas d'une variété de Calabi-Yau de dimension trois. En utilisant cette méthode, nous pouvons compter le sous-schéma en considérant les partitions 3D et en utilisant le sommet topologique. Vous trouverez ci-dessous un outil permettant de les visualiser.
Jag är intresserad av enumerativa problem i geometri som motiveras av fysik. Jag studerar främst dessa från en algebra geometrisk synvinkel. Detta inkluderar både Gromov-Witten och Donaldson-Thomas teori.

I Donaldson-Thomas-teorin kan vi räkna delscheman av tredimensionella Calabi-Yau mångfalder genom att undersöka den lokala bilden. Med hjälp av denna metod kan vi räkna delscheman genom att betrakta 3D-partitioner och använda det topologiska hörnet. Nedan finns ett verktyg för att visualisera dessa.


Research Articles
Articles de recherche
Forskningsartiklar

Abstract
In this article we will provide a geometric proof of Zvonkine's
r
-ELSV using the methods of degenerated targets from [Li'02] and the Gromov-Witten/Hurwitz correspondence from [OP'06].
In preparation.
En préparation.
Pågående.
Abstract
The moduli space of stable maps with divisible ramification uses
r
-th roots of a canonical ramification section to parametrise stable maps whose ramification orders are divisible by a fixed integer
r
. In this article, a virtual fundamental class is constructed while letting domain curves have a positive genus; hence removing the restriction of the domain curves being genus zero. We apply the techniques of virtual localisation and obtain the
r
-ELSV formula as an intersection of the virtual class with a pullback via the branch morphism.
arXiv:2004.06739 [math.AG]
Abstract
We further the study of the Donaldson-Thomas theory of the banana threefolds which were recently discovered and studied by Bryan in [Bryan'19]. These are smooth proper Calabi-Yau threefolds which are fibred by Abelian surfaces such that the singular locus of a singular fibre is a non-normal toric curve known as a ``banana configuration''. In [Bryan'19] the Donaldson-Thomas partition function for the rank 3 sub-lattice generated by the banana configurations is calculated. In this article we provide calculations with a view towards the rank 4 sub-lattice generated by a section and the banana configurations. We relate the findings to the Pandharipande-Thomas theory for a rational elliptic surface and present new Gopakumar-Vafa invariants for the banana threefold.
arXiv:1907.01054 [math.AG]
Abstract
We develop a theory for stable maps to curves with divisible ramification. For a fixed integer
r>0
, we show that the condition of every ramification locus being divisible by
r
is equivalent to the existence of an
r
-th root of a canonical section. We consider this condition in regards to both absolute and relative stable maps and construct natural moduli spaces in these situations. We construct an analogue of the Fantechi-Pandharipande branch morphism and when the domain curves are genus zero we construct a virtual fundamental class. This theory is anticipated to have applications to r-spin Hurwitz theory. In particular it is expected to provide a proof of the
r
-spin ELSV formula [SSZ'15, Conj. 1.4] when used with virtual localisation.
arXiv:1812.06933 [math.AG]
Abstract
We prove that a generalisation of simple Hurwitz numbers due to Johnson, Pandharipande and Tseng satisfies the topological recursion of Eynard and Orantin. This generalises the Bouchard-Mariño conjecture and places Hurwitz-Hodge integrals, which arise in the Gromov-Witten theory of target curves with orbifold structure, in the context of the Eynard-Orantin topological recursion.
DOI: 10.4310/MRL.2016.v23.n5.a3 arXiv:1212.6850 [math.AG]

Contact Information
Informations de Contact
Kontaktinformation

Email:
Email:
E-post:


Visiting address:
Adresse de visite:
Beöksadress:
Room
Salle
Rum
109,
House
Bâtiment
Hus
6,
Roslagsv 101,
Kräftriket,
Sweden
Suède
Sverige


Postal address:
Adresse postale:
Postadress:
Oliver Leigh,
Matematik,
106 91 Stockholm,
Sweden