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Personal profile

Research interests

My research focuses on manifolds with special holonomy, in particular hyperkähler, Calabi-Yau and G2-manifolds.

At the moment I am interested in studying sequences of metrics with special holonomy undergoing codimension one collapse, that is, sequences of n-dimensional special holonomy metrics converging to a space of one lower dimension. Some of this is motivated by theoretical physics, in particular the duality between M-theory and Type IIA String theory.

I have also been working on nearly Kähler manifolds, the cross-sections of G2-holonomy cones, and gauge theory, in particular monopoles with singularities.

 

 

Biography

I am currently a Royal Society University Research Fellow and Assistant Professor at Heriot-Watt University.

I have been a James H. Simons Instructor (postdoc) at Stony Brook University from the Fall 2013 to the Summer 2017. During the academic year 2015-2016 I have been on leave from Stony Brook: I spent the Fall semester 2015 at the Riemann Centre for Geometry and Physics at Leibniz Universität Hannover supported by a Riemann Fellowship and the Spring semester 2016 at the Mathematical Sciences Research Institute in Berkeley, California, supported by a Postdoctoral Fellowship in Differential Geometry.

I obtained my PhD at Imperial College London in 2013 under the supervision of Mark Haskins.

Fingerprint Dive into the research topics where Lorenzo Foscolo is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

Holonomy Mathematics
Monopole Mathematics
Kähler Manifold Mathematics
Deformation Theory Mathematics
Singularity Mathematics
Kähler Mathematics
Gluing Mathematics
Instantons Mathematics

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Research Output 2016 2019

ALF gravitational instantons and collapsing Ricci-flat metrics on the K3 surface

Foscolo, L., 8 May 2019, In : Journal of Differential Geometry. 112, 1, p. 79-120 42 p.

Research output: Contribution to journalArticle

Open Access
File
K3 Surfaces
Collapsing
Instantons
Metric
Torus

A gluing construction for periodic monopoles

Foscolo, L., 1 Dec 2017, In : International Mathematics Research Notices. 2017, 24, p. 7504-7550

Research output: Contribution to journalArticle

Open Access
File
Gluing
Monopole
Singularity
Moduli Space
Four-manifolds

Deformation theory of nearly Kähler manifolds

Foscolo, L., Apr 2017, In : Journal of the London Mathematical Society. 95, 2, p. 586–612 27 p.

Research output: Contribution to journalArticle

Open Access
File
Deformation Theory
Kähler Manifold
Flag Manifold
Spinors
Holonomy

Deformation Theory of Periodic Monopoles (With Singularities)

Foscolo, L., Jan 2016, In : Communications in Mathematical Physics. 341, 1, p. 351–390 40 p.

Research output: Contribution to journalArticle

Open Access
File
Deformation Theory
Monopole
Singularity
Moduli Space
Index Theorem

New G2-holonomy cones and exotic nearly Kähler structures on S6 and S3 x S3

Foscolo, L. & Haskins, M., 2 Dec 2016, In : Annals of Mathematics. 185, 1, p. 59-130

Research output: Contribution to journalArticle

Open Access
File
Holonomy
Kähler Manifold
Kähler
Cone
Cohomogeneity One