## Summary

Dr Mark Haskins is a Professor in Pure Mathematics at Imperial College London. His main research interests lie in differential geometry and geometric analysis, as well as evolution equations from theoretical physics. Dr. Haskins is a Leadership Fellow of the Engineering and Physical Sciences Research Council pursuing a research project on Geometric Analysis and Special Lagrangian geometry.

Currently his main interests include singular special Lagrangian n-folds, and the construction of new compact 7-manifolds with holonomy group G2. Recently Haskins and his collaborators at Imperial and Pisa have for the first time been able to determine the diffeomorphism type of many of the 7-manifolds underlying these G2 metrics. As a result he has shown that it is often possible to construct metrics with holonomy G2 on the same 7-dimensional space in many different ways. An exciting avenue for future research is to determine whether or not these G2 metrics can be smoothly deformed into each other through other G2 holonomy metrics.

Manifolds with G2 holonomy can have interesting three and four-dimensional submanifolds: associative and coassociative submanifolds. Associative submanifolds have been much harder to find because they can behave badly under small deformations. Haskins and his collaborators have proved the existence of many compact rigid associative 3-folds; the key is to relate the deformations of certain associative 3-folds to deformations of holomorphic curves in weak Fano 3-folds. The deformation theory for the latter is much better understood thanks to the powerful global tools of algebraic geometry.

Counting such associatives 3-folds may be useful to determine whether two G2 metrics can be smoothly deformed into each other.

Manifolds with holonomy G2 also appear naturally in Theoretical Physics in M-theory. The significance of these recent results on G2 metrics to M-theory is not yet clear.

We are organised a two day workshop G2 days on 11-12 June 2012 in London to bring together leading researchers working in G2 geometry and related areas. Speakers include: Bobby Acharaya, Sir Simon Donaldson, Nigel Hitchin, Dominc Joyce, Simon Salamon among others.

I recently co-organised a week-long summer school and a week-long research workshop Ricci curvature: limit spaces and Kaehler geometry at ICMS Edinburgh. Speakers included: Jeff Cheeger, Sir Simon Donaldson, John Lott, Aaron Naber, Gang Tian and Burkhard Wilking.

## Invited Lectures and Presentations

### Talks in 2012

*Cycles, calibrations and nonlinear PDE.*Conference on the occasion of H. Blaine Lawson’s 70th birthday, Stony Brook, Oct 2012*UK-Japan Mathematical Forum on Geometry, Probability and their Applications,*Keio University, Japan, July 2012.*G2 Days*, King''s College and UCL, 11-12 June 2012.*GAP (Geometry and Physics) 2012*, Perimeter Institute for Theoretical Physics, Canada, May 2012.- Lecture series on "Gluing methods in calibrated geometry"
*, 6th Winter School on Differential Geometry*, Korean Institute for Advanced Study, Korea, Feb 2012.

### Talks in 2011

*Workshop on Hyperkahler Geometry and related topics*, Hausdorff Research Institute for Mathematics, Bonn, Dec 2011.*King''s College Geometry Day 2*, King''s College London, Nov 2011.*Brussels-Cologne joint seminar on Symplectic and Contact Geometry*, Universite Libre de Bruxelles, Oct 2011.*Differential Geometry seminar*, University of California, Berkeley, Sept 2011.*Conference on special Lagrangian geometry*, National Taiwan University, Taipei, Taiwan, July 2011.*PDE/Analysis seminar*, Northwestern University, April 2011.*Extremal Kahler geometry Workshop*, Simons Center for Geometry and Physics, March 2011.*UK-Japan Winter School*, King''s College London, Jan 2011.

### Talks in 2010

*Mathematical Physics seminar*, Cardiff University, Nov 2010.*Colloquium*, SUNY Stony Brook, Sept 2010.*Geometry seminar*, SUNY Stony Brook, Sept 2010.*Differential Geometry seminar*, Harvard University, Sept 2010.*Differential Geometry seminar*, University of California, San Diego, Sept 2010.*British Mathematics Colloquium*, Edinburgh University, Apr 2010.*Second Killing-Weierstrass Colloquium*, Braniewo, Poland, Mar 2010.*Texas Geometry and Topology Conference*, TCU Fort Worth, Feb 2010.*Geometry-Analysis seminar*, Rice University, Feb 2010.

### Talks in 2009

*Geometry and Topology seminar*, Glasgow University, Dec 2009.*Algebraic Geometry seminar*, Cambridge University, Dec 2009.*Conference on Kahler and related geometries*, Laboratoire Jean Leray, Nantes University, France, Nov 2009.*Geometry seminar*, Mathematisches Institut, Westfalische Wilhelms-Universitat, Muenster, Oct 2009.*Geometry and Topology seminar*, Brown University, Sept 2009.*Geometry of Einstein metrics*, Nantes University, France, July 2009.*Geometry seminar*, University of Texas at Austin, April 2009.*Differential Geometry seminar*, MIT, Cambridge, April 2009.*Variational Problems in Differential Geometry*, University of Leeds, Mar 2009.

### Talks in 2008

*Riemann Surfaces, Harmonic Maps and Visualization*, Osaka City University International Academic Symposium, Dec 2008.*Ninth Pacific Rim Geometry Conference*, National Taiwan University, Taipei, Taiwan, Dec 2008.*Geometry seminar*, University of California San Diego, Dec 2008.*Differential Geometry seminar*, University of California Irvine, Dec 2008.*Geometry/PDE seminar*, University of British Columbia, Nov 2008.*Analysis in Singular Spaces*, Mathematical Sciences Research Institute, Berkeley, Nov 2008.*Geometry seminar*, Stanford University, Nov 2008.*Symplectic Geometry seminar*, Stanford University, Oct 2008.*Differential Geometry seminar*, University of California Santa Barbara, Oct 2008.*Geometrie*, Oberwolfach, Germany, July 2008.*Differential Geometry seminar*, Leeds University, Mar 2008.*Special structures in Riemannian geometry*, Banff International Research Station for Mathematical Innovation, Canada, Feb 2008.

## Other Significant Activities

### Recent meetings organised.

- 2-week summer school and workshop on Ricci curvature: limit spaces and Kahler geometry.
**July 2013**, ICMS Edinburgh. Coorganiser with Profs G Carron, M Singer, and Dr H Hein. - 2-day conference G_2 days.
**11-12 June 2012**. UCL/King''s College London. Coorganiser with Profs Sir S Donaldson, S Salamon, Drs B Acharya and J Lotay. - 3-day workshop Geometric PDE and Integrability. Jan 2012. Hausdorff Institute for Mathematics, Bonn. Coorganiser with Prof I Taimanov.
- Differential Geometry Workshop, British Mathematics Colloquium, Leiecster,
**April 2011.**Coorganiser with Dr K Leschke.

## Further Information

### London Mathematical Society Journals.

I am the editorial adviser responsible for Differential Geometry and Geometric Analysis for the three London Mathematical Society journals: Bulletin of the LMS, Journal of the LMS and Proceedings of the LMS.

The *Proceedings*, *Journal* and *Bulletin* of the London Mathematical Society are among the world''s leading mathematical research journals. Although they share a common Editorial Advisory Board, a paper should be submitted directly to one of the journals, determined by the length of the paper. Longer papers are considered by the *Proceedings*, and those of medium length by the *Journal*. The *Bulletin* publishes short research papers and has occasional surveys and research-expository papers, and obituaries. It also has a book reviews section providing a comprehensive coverage of research texts across the whole of mathematics and statistics.

The subject coverage of the LMS periodicals ranges across a broad spectrum of mathematics, covering the whole of pure mathematics together with some more applied areas of analysis, mathematical physics, theoretical computer science, probability and statistics. The current Editorial Board reflects predominantly pure interests, but the Society wishes to encourage a spread to more applicable areas and will consider papers submitted in areas of mathematics not covered by existing Board members.

How to submit a paper to one of these LMS journals

### Geometry-related seminars at Imperial.

Since 2005 I have organised the London Geometry and Topology seminar. About the seminar.

In 2011 Andre Neves and I started the Geometry and Analysis seminar with assistance of Reto Mueller (Imperial JRF).

## Publications

Haskins M, Hein H-J, Nordstroem J, 2015, ASYMPTOTICALLY CYLINDRICAL CALABI-YAU MANIFOLDS, *Journal of Differential Geometry*, Vol:101, ISSN:0022-040X, Pages:213-265

Corti A, Haskins M, Nordstroem J, et al. , 2015, G(2)-MANIFOLDS AND ASSOCIATIVE SUBMANIFOLDS VIA SEMI-FANO 3-FOLDS, *Duke Mathematical Journal*, Vol:164, ISSN:0012-7094, Pages:1971-2092

Degeratu A, Haskins M, Weiß H, 2015, Mini-Workshop: Singularities in $\mathrm G_2$-geometry, *Oberwolfach Reports*, Vol:12, ISSN:1660-8933, Pages:449-488

Corti A, Haskins M, Nordstroem J, et al. , 2013, Asymptotically cylindrical Calabi-Yau 3-folds from weak Fano 3-folds, *Geometry & Topology*, Vol:17, ISSN:1465-3060, Pages:1955-2059

Haskins M, Kapouleas N, 2012, Closed twisted products and SO(p) X SO(q)-invariant special Lagrangian cones, *Communications In Analysis and Geometry*, Vol:20, ISSN:1019-8385, Pages:95-162