Research Output per year

## 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 Fingerprint is based on mining the text of the person's scientific documents to create an index of weighted terms, which defines the key subjects of each individual researcher.

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## Research Output 2016 2019

- 5 Article

## 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 journal › Article

## A gluing construction for periodic monopoles

Foscolo, L., 1 Dec 2017, In : International Mathematics Research Notices. 2017, 24, p. 7504-7550Research output: Contribution to journal › Article

## 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 journal › Article

## 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 journal › Article

## New G_{2}-holonomy cones and exotic nearly Kähler structures on S^{6} and S^{3} x S^{3}

Foscolo, L. & Haskins, M., 2 Dec 2016, In : Annals of Mathematics. 185, 1, p. 59-130Research output: Contribution to journal › Article