Tom Coates

ContactInformation

Department of Mathematics Phone: +44 (0)20 7594 3607Imperial College London Fax: +44 (0)20 7594 8517London SW7 2AZ E-mail: t.coates@imperial.ac.ukUnited Kingdom Web: http://coates.ma.ic.ac.uk

Education andEmployment

Reader in Pure MathematicsImperial College London, UK Dec 2009–present

Royal Society University Research FellowImperial College London, UK Jun 2005–Nov 2013

Clay Research Scholar and Postdoctoral FellowMathematical Sciences Research Institute, Berkeley, USA Jan 2005–May 2005

Benjamin Peirce Assistant ProfessorHarvard University, USA Aug 2003–Dec 2005

Clay Mathematics Institute Liftoff FellowImperial College London, UK Jun 2003–Aug 2003

University of California at Berkeley, USA 1998–2003

Ph.D. in Mathematics, awarded May 2003

• Thesis title: Riemann–Roch Theorems in Gromov–Witten Theory• Thesis advisor: Prof. Alexander Givental

Cambridge University, UK 1997–1998Part III of the Mathematical Tripos, with Distinction

Cambridge University, UK 1994–1997BA in Mathematics with First Class Honours

Grants andAwards

LMS Whitehead Prize Jul 2014

Philip Leverhulme Prize Nov 2010

European Union ERC Starting Independent Researcher Grant: Oct 2009–Sep 2015

This award pays for 4 post-docs, a visitor program, and my salary for 2013–15. These grants are extremely competitive, with roughly 12 awards per year inmathematics across Europe.

Royal Society University Research Fellowship: Jun 2005–Sep 2013

This provided salary and expenses for full-time research at Imperial College London.These fellowships are internationally competitive, across all sciences; on averageonly one or two are awarded in Mathematics each year.

Clay Research Scholarship: Spring 2005

The Clay Mathematics Institute is the leading source of private funding for mathsin the USA. This scholarship allowed me to take part in the semester-long researchprogram “New Topological Structures in Physics” at the Mathematical SciencesResearch Institute, Berkeley, USA in the spring of 2005.

Grant from the US National Science Foundation: Jul 2004–Jun 2007

This award (grant DMS-0401275) provided summer salary and expenses for a3-year research program titled Gromov–Witten Theory.

Herb Alexander Prize: May 2003

This prize is awarded annually for the best thesis in Mathematics at the Universityof California at Berkeley, USA.

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Other Grants EPSRC Pathways To Impact grant Oct 2011–Jun 2012

I co-wrote this with Dr Buck, Prof. Corti, and Dr Haskins. The grant (£29K)will pay for a residency by the artist Gemma Anderson at the Department ofMathematics, and associated exhibition and publication costs. Anderson willproduce artworks based on Coates–Corti’s Fanosearch research program, and onDr Buck’s research on DNA topology.

EPSRC Responsive Mode grant Oct 2010–Mar 2014

I co-wrote this with Prof. Corti. The grant (£380K), titled Extremal LaurentPolynomials, pays for a post-doc, a PhD student, high-performance computing,and several research workshops.

EPSRC Platform Grant Oct 2010–Sep 2015

I co-wrote this with Prof. Lamb, Dr Haskins, and others. The grant (£650K)provides five years of seed funding to improve the research environment in theDepartment of Mathematics.

EU Marie Curie Fellowship Oct 2011–Sep 2013

I co-wrote this with Dr Brini. The grant (£150K) provides salary and researchexpenses for Dr Brini to join my research group.

Leverhulme Artist in Residence grant Oct 2012–Jun 2013

I co-wrote this with Dr Buck. The grant (£15K) will pay for a residency bythe artist Gemma Anderson at the Department of Mathematics, and associatedexhibition costs.

Publications (1) Mutations of Fake Weighted Projective Spaces.T Coates, S Gonshaw, A Kasprzyk, N Nabijou.Electronic Journal of Combinatorics, 21 (2014), no. 4, paper #P4.14

(2) ? A Mirror Theorem for Toric Stacks.T Coates, A Corti, H Iritani, H-H Tseng. 2013.http://arxiv.org/abs/1310.4163To appear in Compositio Mathematica.

(3) Drawing and Mathematics: Geometry, Reasoning, and Form.G Anderson, D Buck, T Coates, A Corti. 2013To appear in TRACEY.

(4) Drawing in Mathematics: from Inverse Vision to the Liberation of Form.G Anderson, D Buck, T Coates, A Corti. 2013To appear in Leonardo.

(5) ? Mirror Symmetry and Fano Manifolds.T Coates, A Corti, S Galkin, V Golyshev, A Kasprzyk.In European Congress of Mathematics Krakow, 2-7 July, 2012, pp. 285–300. 2014.

(6) Minkowski Polynomials and Mutations.M Akhtar, T Coates, S Galkin, A Kasprzyk. SIGMA 8 (2012), Paper 094.

(7) The Quantum Lefschetz Hyperplane Principle can fail for orbifold hypersurfaces.T Coates, A Gholampour, H Iritani, Y Jiang, P Johnson, C Manolache.Mathematical Research Letters, 19 (2012), no. 5, 997–1005.

(8) Quantum Cohomology and Crepant Resolutions: A Conjecture.T Coates and Y Ruan. Annales de l’Institut Fourier, 63 (2013), no. 2, 431–478.

(9) ? Wall-Crossings in Toric Gromov–Witten Theory I: Crepant Examples.T Coates, H Iritani, H-H Tseng. Geometry and Topology, 13 (2009), 2675–2744.

(10) The Quantum Orbifold Cohomology of Weighted Projective Spaces.T Coates, A Corti, Y-P Lee, and H-H Tseng.Acta Mathematica, 202 (2009), 139–193.

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(11) Computing Genus-Zero Twisted Gromov–Witten Invariants.T Coates, A Corti, H Iritani, H-H Tseng.Duke Mathematical Journal, 147 (2009), no. 3, 377–438.

(12) On the Crepant Resolution Conjecture in the Local Case.T Coates. Communications in Mathematical Physics, 287 (2009), 1071–1108.

(13) Givental’s Lagrangian cone and S1-equivariant Gromov–Witten theory.T Coates. Mathematical Research Letters, 15 (2008), no. 1, 15–31.

(14) ? Quantum Riemann–Roch, Lefschetz and Serre.T Coates and A Givental. Annals of Mathematics, 165 (2007), no. 1, 15–53.

(15) Quantum cobordisms and formal group laws.T Coates and A Givental. In The Unity of Mathematics, Progr. Math., 244,pp. 155–171, Birkhauser Boston, 2006.

Preprints (16) ? A Fock Sheaf for Givental Quantization.T Coates, H Iritani. 2014.http://coates.ma.ic.ac.uk/preprints/Focksheaf.pdf

(17) ? The Crepant Transformation Conjecture for Toric Complete Intersections.T Coates, H Iritani, Y Jiang. 2014.http://arxiv.org/abs/1410.0024

(18) K-theoretic and Categorical Properties of Toric Deligne–Mumford Stacks.T Coates, H Iritani, Y Jiang, E Segal. 2014.http://arxiv.org/abs/1410.0027

(19) Four-dimensional Fano Toric Complete Intersections.T Coates, A Kasprzyk, T Prince. 2014.http://arxiv.org/abs/1409.5030

(20) Quantum Periods For Certain Four-Dimensional Fano Manifolds.T Coates, S Galkin, A Kasprzyk, A Strangeway. 2014.http://arxiv.org/abs/1406.4891

(21) The Quantum Lefschetz Principle for Vector Bundles as a Map Between GiventalCones.T Coates. 2014.http://arxiv.org/abs/1405.2893

(22) Some Applications of the Mirror Theorem for Toric Stacks.T Coates, A Corti, H Iritani, H-H Tseng. 2014.http://arxiv.org/abs/1401.2611

(23) ? Quantum Periods for 3-Dimensional Fano Manifolds.T Coates, A Corti, S Galkin, A Kasprzyk. 2013.http://arxiv.org/abs/1303.3288

(24) On the Convergence of Gromov–Witten Potentials and Givental’s Formula.T Coates, H Iritani. 2012.http://arxiv.org/abs/1203.4193

(25) Wall-Crossings in Toric Gromov–Witten Theory II: Local Examples.T Coates. 2008.http://arxiv.org/abs/0804.2592

(26) The Crepant Resolution Conjecture for Type A Surface Singularities.T Coates, A Corti, H Iritani, H-H Tseng. 2007.http://arxiv.org/abs/0704.2034

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FormerPostDocs

Dr Hiroshi Iritani

co-supervised with Prof. Cortinow Associate Professor (with tenure) at Kyoto University, Japan

Dr Paul Johnson

co-supervised with Prof. Cortinow Lecturer at the University of Sheffield

Dr Amin Gholampour

now Assistant Professor (tenure-track) at the University of Maryland, USA

Dr Sara Pasquetti

now Lecturer in Mathematics at the University of Surrey

Dr Andrea Brini

now CNRS Charge de Recherche, Universite Montpellier 2, France

Dr Yunfeng Jiang

now Assistant Professor (tenure-track) at the University of Kansas, USA

Dr Cristina Manolache

co-supervised with Prof. Cortinow Royal Society Dorothy Hodgkin Fellow at Imperial College London

CurrentPostDocs

Dr Al Kasprzyk

algebraic geometry, combinatoricsco-supervised with Prof. Corti

PhD students Andrew Strangeway

co-supervised with Prof. Corticompleted: Dec 2013

Mohammad Akhtar

expected completion: Jun 2015

Thomas Prince

EPSRC Prize Studentship 2012expected completion: Jun 2016

SelectedInvitedLectures andConferenceAddresses

Max Planck Institute for Mathematics, Bonn Sep 2014Workshop on “Motivic Structures on Quantum Cohomologyand Pencils of CY Motives”Invited talk: Fano Classification in Dimensions 3 and 4

University of Oxford May 2014Algebraic and Symplectic Geometry seminar, double-billThe Crepant Transformation Conjecture and Fourier–MukaiTransforms / Mirror Symmetry without Localization

University of Cambridge Apr 2014Differential Geometry and Topology seminarMirror Symmetry without Localization

University of Michigan, Ann Arbor, USA Apr 2014Workshop on “B-Model Aspects of Gromov–Witten Theory”Invited talk: Mirror Symmetry and Fano Manifolds

Universite Paris Diderot, Paris Jan 2014Conference on Quantum cohomology and quantum K-theoryInvited talk: Mirror Symmetry without Localization

University of Bath Oct 2013Algebraic Geometry SeminarMirror Symmetry and 3-Dimensional Fano Manifolds

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Maxwell Colloquium on Combinatorial Algebraic Geometry Oct 2013ICMS, University of EdinburghInvited talk: Mirror Symmetry and Fano Manifolds

Taida Institute for Mathematical Sciences Jun 2013National Taiwan University, TaipeiInvited lecture series: Orbifold Gromov–Witten Theory

UK–Japan Mathematical Forum Jan 2013Keio University, Japan. Invited lecture series:Gromov–Witten Theory, Mirror Symmetry, and Fano Manifolds

University of Warwick Nov 2012Algebraic Geometry SeminarMirror Symmetry and Fano Manifolds: an update

University of Leeds Feb 2012Algebra, Geometry and Integrable Systems ColloquiumGromov–Witten Invariants and Modular Forms

Banff International Research Station, Canada Oct 2011Workshop on “New Recursion Formulae and Integrablity”Invited talk: GW invariants of local P2 and quasi-modular forms

London Mathematical Society Course on “Symplectic Geometry” July 2011University of AberdeenInvited lecture series: Quantum cohomology

Freie Universitat Berlin. Algebraic Geometry Seminar Nov 2010Mirror Symmetry and Fano Varieties

Cambridge–Oxford–Warwick (COW) Algebraic Geometry seminar Mar 2010Gromov–Witten Invariants and Modular Forms

Institut Henri Poincare, Paris Jan 2010Workshop on Symplectic and Contact GeometryInvited talk: Gromov–Witten Invariants and Modular Forms

SISSA, Trieste. Algebraic Geometry Seminar Sep 2009Gromov–Witten Invariants and Modular Forms

Sichuan University, China. Geometry and Physics Workshop Aug 2009Invited lectures: The Crepant Resolution Conjecture at Higher Genus

MIT, USA. Workshop on Homological Mirror Symmetry Jun 2009Mini-course: Quantization, Gromov–Witten Theory, and Birational Geometry

University of Edinburgh. Department of Mathematics Colloquium Apr 2009From Mirror Symmetry to Modular Forms

Groupement de Recherche Geometrie Algebrique et Geometrie Jan 2009Complexe, Annual Conference, CIRM, LuminyMini-course: Quantum Cohomology and Birational Transformations

Oxford University. Algebraic and Symplectic Geometry Seminar Nov 2008Higher-Genus Gromov–Witten Invariants and Crepant Resolutions

ICMS, Edinburgh. Sep 2008Conference on “Higher Dimensional Algebraic Geometry”Invited talk: Higher Genus Gromov–Witten Invariants and Crepant Resolutions

Columbia University, USA. Invited lectures May 2008Quantum Cohomology and Birational Transformations

Universitat Zurich. Okonek Seminar Sep 2007Quantum Cohomology and Crepant Resolutions

Universite Libre de Bruxelles. Apr 2007Bruxelles-Koln Seminar on Symplectic GeometryThe Crepant Resolution Conjecture

Oxford University. Algebraic and Symplectic Geometry Seminar Mar 2007Mirror Symmetry and the Crepant Resolution Conjecture

Cambridge University. Geometry Seminar Mar 2007Mirror Symmetry and the Crepant Resolution Conjecture

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Institut Henri Poincare, Paris Feb 2007Conference on “Quantum Cohomology of Stacks and String Theory”Invited talk: Mirror Symmetry and the Crepant Resolution Conjecture

Harvard University, USA. Gauge Theory and Topology Seminar Nov 2006Lagrangian Cones and Mirror Symmetry

AMS Summer Institute on Algebraic Geometry, Seattle, USA Jul 2005Invited talk: The Gromov–Witten Theory of a Point and KdV

Northwestern University, USA May 2004Conference on “Geometry and Topology of String Theory”Invited talk: Quantum Extraordinary Cohomology

SUNY Stony Brook, USA. Department of Mathematics Colloquium Oct 2003Holomorphic Curves and Symplectic Geometry

MIT, USA. Differential Geometry seminar Oct 2003Symplectic Linear Algebra and Gromov–Witten Theory

Columbia University, USA. Algebraic Geometry seminar Sep 2003Quantization and Gromov–Witten Theory

Harvard University, USA. Harvard/MIT Algebraic Geometry seminar Sep 2003Quantization and Gromov–Witten Theory

University of California at Berkeley, USA. Symplectic Geometry seminar Apr 2003Quantization and Mirror Symmetry

Oxford University. Special seminar Nov 2001A new proof of the mirror theorem

Cambridge University, UK. Geometry seminar Nov 2001A new proof of the mirror theorem

PublicEngagementActivities

Invited talk at the workshop Beauty in Art and Mathematics at the Henry MooreInstitute, Leeds, in October 2014.

Keynote address at the conference Young Researchers in Mathematics, a conferencefor graduate students in all areas of mathematics, at the University of Warwickin July 2014.

Ongoing collaboration with the artist Gemma Anderson, based on my Fanosearchresearch project with Prof. Corti. This included a keynote address, joint withAnderson, Dr Buck, and Prof. Corti, at the interdisciplinary conference ThinkingThrough Drawing 2012: Drawing in STEAM, as well as exhibitions at EB&FlowGallery, London and Galerie Thore Krietemeyer, Berlin in 2013.

In March 2012 I took part in Voice of the Future, an event at the Houses of Parliamentwhere the Science and Technology Select Committee was replaced for the day by apanel of young scientists and engineers, who had the opportunity to ask questionsto David Willetts MP (Minister for Universities and Science), Chi Onwurah MP(Shadow Minister for Innovation and Science), and the members of the SelectCommittee.

Invited talk at Prospects in Mathematics 2011, a conference for prospective PhDstudents organized by the London Mathematical Society.

A successful public outreach campaign in early 2011, leading to:

– articles on the Fanosearch project in Science, New Scientist, Cosmos, PhysicsWorld, Le Temps (a Swiss daily newspaper), NWT Magazine (a Dutchpopular science magazine), and other publications.

– an interview by Corti on Norwegian radio

– an exhibit in a mathematical musem in Rome

– front-page billing on the Imperial College website

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In mid-2009 I took part in a documentary, The Truth Behind Crop Circles, forNational Geographic TV. I designed a mathematically-based crop circle pattern,based on a theorem by the Ancient Greek mathematician Apollonius of Perga, tohelp debunk the claim that crop circles are too mathematically and geometricallycomplicated to have been constructed by humans.

Sliceform, G Anderson and T Coates, Laser-cut Copper Etching, 2012.

327 and B4, G Anderson and T Coates, Copper Investment Casts of RP Forms, 2012.

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