Members

Senior Researchers

Buck, D.
 

Dr Dorothy Buck

Reader in Pure Mathematics

Dr Buck's fields of research are three-manifold topology and biomathematics. She and her group use topological techniques to illuminate structural and mechanical features of DNA-protein interactions. Buck has trained and works extensively in both pure mathematics and molecular biology. In addition to her PhD in Mathematics, with a second PhD advisor in Molecular Genetics and Microbiology, she worked in a wet lab for 6 years and was a postdoc at Johns Hopkins Medical Institute. Prior to joining Imperial, she was a tenure-track professor in Applied Mathematics at Brown University, and had been awarded a NSF postdoctoral Fellowship, a Burroughs Wellcome Fund Postdoctoral Fellowship, a Clay Liftoff Fellow and a NSF/BWF Doctoral Fellowship. She has been awarded over a million pounds in grants by the Engineering and Physical Sciences Research Council (EPSRC) for work in DNA Topology, as well as funding from Leverhulme and the LMS.

Photo from the EPSRC-funded Maths of Life Sandpit.

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Address: 623 Huxley Building
Phone: (+44) (0)20 7594 8570

Cascini, P.
 

Prof Paolo Cascini

Professor of Pure Mathematics

Prof Cascini's field of research is Algebraic Geometry, and, in particular, the birational geometry of projective varieties.

He is mostly interested in the study of positivity in complex geometry, using both algebraic and analytic methods. More specifically, he is interested in the Minimal Model Program, which aims to generalize the classification of complex projective surfaces known in the early 20th century, to higher dimensional varieties. He has held a prestigious Sloan fellowship, and is one of the authors of the famous BCHM paper, proving that all varieties have canonical models -- a huge step towards completing the Minimal Model Program and often described as the biggest breakthrough in algebraic geometry of the last 30 years.

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Coates, T
 

Prof Tom Coates

Professor of Pure Mathematics

Prof Coates studies the geometry and topology of symplectic manifolds and algebraic varieties using ideas from string theory. He is a Royal Society University Research Fellow and the winner of a Philip Leverhulme Prize for mathematics. He has striking foundational work on the quantum Riemann-Roch formula and the crepant resolution conjecture in Gromov-Witten theory. His current research interests include classification of Fano varieties, computation of Gromov-Witten invariants, and their relationship to mirror symmetry. 

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Address: 662 Huxley Building 
Phone: (+44) (0)207 594 3607

Corti, A.
 

Prof Alessio Corti

Professor of Pure Mathematics

Prof Corti's research focuses on the geometry of higher dimensional varieties. He has made seminal contributions to higher dimensional birational geometry, developing foundational techniques for the explicit study of the birational geometry of 3-folds. His work offered a conceptual understanding of birational maps between end products of the Minimal Model Program on a uniruled manifold, and insight on properties such as birational rigidity. In 2002 he was awarded the LMS Whitehead Prize.

His current work uses both birational geometry and techniques and ideas from mirror symmetry and Gromov-Witten theory to study the classification of Fano manifolds. 

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Address: 673 Huxley Building
Phone: (+44) (0)20 7594 1870

Donaldson, S.

Prof Sir Simon Donaldson FRS

Prof Donaldson uses global analysis to study problems in differential geometry, complex geometry and symplectic geometry. He is a Fields Medallist, a Fellow of the Royal Society, and a recipient of numerous other prizes; most recently the Nemmers, Shaw, and King Faisal prizes.

Donaldson's work combines the theory of nonlinear partial differential equations with geometry, topology and ideas from theoretical physics, particularly gauge theory. He has made seminal contributions to the study of 4-dimensional manifolds, including the introduction of the famous Donaldson invariants and the characterization of compact symplectic 4-manifolds using Lefschetz pencils. His current interests include the study of gauge theory on G2-manifolds and the problem of existence of extremal metrics, relating notions of algebro-geometric stability to the existence of constant scalar curvature and Kähler-Einstein metrics.

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Address: 674 Hu xl e y Building
Phone: (+44) (0)20 7594 8559

Haskins, M
 

Prof Mark Haskins

Professor of Pure Mathematics

Prof Haskins works in differential geometry and geometric analysis, often on equations arising in theoretical physics. He is an EPSRC Leadership Fellow, and one of the world’s leading experts on special Lagrangian geometry and exceptional holonomy. Together with Nicos Kapouleas, Dr Haskins has constructed large numbers of new examples of special Lagrangian cones, which is important for the study of moduli spaces of compact special Lagrangian submanifolds (the “A-branes” of string theory) and mirror symmetry. In other recent work he and his collaborators have found many new examples of compact manifolds with holonomy G_2 containing calibrated submanifo lds.

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Address: 668 Huxley Building
Phone: (+44) (0)20 7594 8550

Holzegal, G.

Dr Gustav Holzegel

Reader in Pure Mathematics

Dr Holzegel works in General Relativity, the theory of gravitation proposed by Einstein in 1915. His work combines techniques from geometry and non-linear hyperbolic partial differential equations. He holds an ERC starting grant.

Holzegel's main interest is the stability black holes, in particular the problem of proving the non-linear stability of the Kerr family of solutions of the vacuum Einstein equations. With Dafermos and Rodnianski he recently constructed the first nontrivial examples of spacetimes that dynamically converge to Kerr black holes.

He also studies the dynamics of asymptotically anti de Sitter (AdS) spacetimes. He and Smulevici surprised physicists with bounds on the decay rate of linear waves on Kerr-AdS spacetimes, which suggests that asymptotically AdS black holes may be non-linearly unstable.

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Address: 625 Huxley Building

 Prof Andre Neves

Prof Andre Arroja Neves

Professor of Pure Mathematics

Prof Neves studies nonlinear problems in geometric analysis, including geometric parabolic flows, scalar curvature rigidity, and min-max theory of minimal surfaces.  Recently he and his collborator Fernando Codá Marques completed a proof of the Willmore conjecture, a major problem which had been open since 1965. Among his other recent important results are a positive answer to Freedman-He-Wang's conjecture on the Möbius energy of non-trivial links, a counterexample to a weaker version of the Thomas-Yau conjecture, and a negative answer to the famous rigidity conjecture of Min-Oo (with Brendle and Marques). He recently won the  New Horizons in Mathematics Prize and the AMS Veblen Prize in Geometry. He holds  ERC and EPSRC programme grants, an LMS Whitehead Prize, a Philip Leverhulme Prize, and was an invited speaker at the International Congress of Mathematicians in 2014.

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Johannes Nicaise

Dr Johannes Nicaise

Reader in Pure Mathematics

Dr Nicaise’s field of research is algebraic geometry. A central problem in his research is Igusa’s monodromy conjecture, which predicts striking relations between arithmetic and geometric properties of integer polynomials. In 2013 he received a Starting Grant from the European Research Council to explore the connections between non-archimedean geometry, the monodromy conjecture, birational geometry and certain aspects of the theory of Mirror Symmetry. This project has already led to a proof of Veys’s 1999 conjecture on poles of maximal order of Igusa zeta functions.

Prior to joining Imperial College, Johannes Nicaise was Chargé de Recherche at the CNRS (France) and Associate Professor at the University of Leuven (Belgium).

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Address: 629 Huxley Building

Dr Travis Schedler

Dr Travis Schedler

Senior Lecturer in Pure Mathematics

Dr Schedler studies noncommutative and Poisson algebras from (symplectic) geometric, representation-theoretic, and cohomological points of view.  He received the American Institute of Mathematics five-year fellowship and NSF standard grants. With Etingof he defined Poisson-de Rham homology of Poisson varieties, conjecturally recovering the cohomology of their symplectic resolutions when they exist.  He classified with Bellamy most linear quotients and, recently, all quiver varieties admitting such resolutions. He studied with Ginzburg cyclic homology and its Gauss-Manin connection and noncommutative geometry via the representation functor following Kontsevich and Rosenberg. He computed Hochschild (co)homology of preprojective and Frobenius algebras and is investigating connections with topological field theories, Fukaya categories, and the b-function.

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Address: 622 Huxley Building

Thomas, R.
 

Prof Richard Thomas FRS

Professor of Pure Mathematics

Prof Thomas studies mirror symmetry and moduli problems in algebraic geometry.  He has been awarded the LMS Whitehead Prize, the Philip Leverhulme Prize, the Royal Society Wolfson Research Merit Award, and was an invited speaker at the International Congress of Mathematicians in 2010.  Together with Prof Donaldson he defined the Donaldson-Thomas invariants of Calabi-Yau 3-folds, now a major topic in geometry and the mathematics of string theory. For the special case of curve-counting, the more recent Pandharipande-Thomas invariants further refine the DT invariants. He has applied ideas from symplectic geometry to group actions on derived categories and to knot theory.  Recently he has been using derived category techniques to shed light on a classical algebro-geometric problem dating back more than a century.

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Address: 659 Huxley Building
Phone: (+44) (0)20 7594 8515

Research Fellows

Cristina Manolache

Dr Cristina Manolache

Dorothy Hodgkin Fellow

Algebraic geometry.

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Research Associates

Hulya Arguz

Dr Hülya Argüz 

Research Associate

I am interested in algebraic geometry with applications to mirror symmetry. I am currently working on an approach to the classification problem of Fano varieties using the Gross-Siebert program in mirror symmetry.

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Dr Andrea Brini

Dr Andrea Brini

Research Associate

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 Dan Pomerleano

Dr Genival G da Silva

Research Associate

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Eleonora Di Nezza

Dr Eleonora Di Nezza

Research Associate

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 Dan Pomerleano

Mr Andreas Gross

Research Associate

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Liana Heuberger

Dr Liana Heuberger 

Research Associate

 I am interested in birational and toric geometry, in particular constructing Fano fourfolds and investigating their canonical rings.

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 Marie-Amelie Lawn

Dr Marie-Amelie Lawn

Teaching Fellow

My main research interests are in Differential Geometry, and more precisely pseudo-Riemannian Geometry and problems of Lorentzian geometry related to General Relativity. I am especially interested in submanifold theory (minimal/maximal surfaces, CMC surfaces, mean curvature flow.)

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Yevgeny Liokumovich

Dr Yevgeny Liokumovich

Research Associate

I am interested in quantitative aspects of Min-Max Theory, systolic geometry, quantitative topology

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 Dan Pomerleano

Dr Rafael Montezuma 

Research Associate

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Dan Pomerleano

Dr Dan Pomerleano

Research Associate

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Dan Pomerleano

Dr Ivaldo Paz Nunes

Research Associate

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Ed Segal 

Dr Edward Segal

Teaching Fellow

I'm interested in the interactions between geometry, algebra and theoretical physics. More specifically, I work on topological field theories, derived categories, and related things.

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Hiromu Tanaka

Dr Hiromu Tanaka

Research Associate

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 Dr Paul Wedrich

Dr Paul Wedrich

Research Associate

 I am interested in low-dimensional topology and my research focuses on knot- and link homology theories.

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 Dan Pomerleano

Dr John Welliaveetil

Research Associate

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Visitors

 Placeholder

Professor Spyros Alexakis

Academic Visitor

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 Nikolai Nowaczyk

Dr Nikolai Nowaczyk

Academic Visitor

Differential Geometry, Spin Geometry

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Research Students

Senja Barthel (Dorothy Buck)
Luca Battistella (Alessio Corti, Cristina Manolache)
Pierrick Bousseau (Richard Thomas)
Francesca Carocci (Richard Thomas; Cristina Manolache)
Fjodor Gainullin (Dorothy Buck)
Thomas Hockenhull (Dorothy Buck)
Elana Kalashnikov (Tom Coates)
Dan Kaplan (Travis Schedler)
Marco Marengon (Dorothy Buck)
Navid Nabijou (Tom Coates)
Charles Nurser (André Neves)
Otto Overkamp (Alexei Skorobogatov; Johannes Nicaise)
Andrea Petracci (Alessio Corti)
Nicolau Sarquis (André Neves)
Zak Turcinovic (Richard Thomas; Ed Segal)
Celso Viana (André Neves)
Jakub Witaszek (Paolo Cascini)

Joint Imperial-King's-UCL London School of Geometry & Number Theory Research Students

Joint Imperial-King’s-UCL London School of Geometry & Number Theory Research Students

 Tibor Backhausz
 Gregiorio Baldi
 Stephanie Chan
 Dougal Davis
 Andrea Dotto
 Stevan Gajovic
 Michele Giacomini
 Giada Grossi
 Giulia Gugiatti
 Ben Heuer
 Nikoleta Kalaydzhieva
 Tim King
 Fabian Lehmann
 Yin Li
 Luigi Lunardon
 Joseph MacColl
 Samuel Porritt
 Andrea Sartori
 Raffael Singer
 Misja Steinmetz
 Jose Swinson
 Galen Voysey
 Albert Wood