Members

Senior Researchers

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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 DC

Dr Davoud Cheraghi

Senior Lecturer in Pure Mathematics

Dr Cheraghi works in complex analysis and geometry. He studies the moduli spaces of rational functions with prescribed covering structures, and the rigidity type conjectures. He has also made foundational contributions to the problem of local normal forms and maximal linearisation domains in complex dimension one (small-divisors). His work combines ideas from Teichmuller theory, nonlinear partial differential equations, and number theory, to study problems in holomorphic dynamics. Recently, he and his collaborator Mitsuhiro Shishikura made a breakthrough on the Renormalisation Conjecture, explaining universality phenomena in analytic dynamics. He currently holds a five-year EPSRC Fellowship.

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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

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

 Steven Sivek

Dr Steven Sivek

Lecturer

Dr Sivek works in low-dimensional topology.  His particular interests include gauge theory and Floer homology, contact and symplectic geometry, and relations between these subjects.  Among other things, this has recently included the development of contact invariants in monopole and instanton Floer homology, applications of these and other techniques from symplectic geometry to problems in knot theory and 3-manifolds, and the use of gauge theory to study symplectic fillings of contact manifolds.  He is also interested in holomorphic curve invariants in symplectic geometry.

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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

My research field lies at the intersection of Algebraic Geometry, Integrable Systems and High Energy Physics. I work on the Geometry of String Theory and its interface with other areas of Mathematics.
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 da Silva

Dr Genival G da Silva-Research Associate

My research interests are Hodge theory and Mirror symmetry.
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Dr Sara Filippini-Research Associate

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 Andreas Gross

Dr Andreas Gross-Research Associate

I am interested in tropical geometry, in particular in using it to describe the intersection theory of algebraic varieties by purely combinatorial means and the application thereof to enumerative problems.
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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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 Calum Spicer

Dr Calum Spicer-Research Associate

My research interests are in the intersection of foliation theory and algebraic geometry, with a particular focus on the birational geometry of foliations.
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 Welliaveetil, John

Dr John Welliaveetil- Research Associate

I am interested in the geometry of non-Archimedean spaces. In particular, I study the homotopy types of certain Berkovich spaces and the étale cohomology of a nicely behaved class of adic spaces.
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Dr Mattia Talpo - Research Associate

My main research interests are in algebraic geometry, more specifically in moduli theory, often involving algebraic stacks and/or logarithmic geometry.
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Visitors

Prof Mark Haskins

Dr Anne-Sophie Kaloghiros

Prof Vlad Markovic FRS

Dr Nikolai Nowaczyk

Dr Ed Segal

Research Students

Fabio Bernasconi (Paolo Cascini)
Alexander Eliad (Davoud Cheragi)
Giulia Gugiatti (Alessio Corti, Tom Coates)
Elana Kalashnikov (Tom Coates)
Dan Kaplan (Travis Schedler)
Yang Li (Simon Donaldson)
Kristina Kubiliūtė (Alessio Corti, Anne-Sophie Kaloghiros)
Luigi Lunardon (Johannes Nicaise)
Mirko Mauri (Paolo Cascini)
Enrica Mazzon (Johannes Nicaise)
Borislav Mladenov (Richard Thomas)
Daniel Platt (Simon Donaldson and Jason Lotay)
Mohammad Pedramfar (Davoud Cheragi)
Samuel Stark (Richard Thomas)
Andrea Tirelli (Travis Schedler)
Fredrik Vaeng Røtnes (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

View 2017 cohort.