Members

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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Dr Davoud Cheraghi

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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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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

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

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 Huxley Building
Phone: (+44) (0)20 7594 8559

Dr Soheyla Feyzbakhsh

Senior Lecturer

My research interests are in algebraic geometry, in particular, stability conditions on triangulated categories and applications of wall-crossing in classical algebraic geometry. 

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Dr Marco Guaraco

Dr Guaraco works in Geometric Analysis and Partial Differential Equations. He introduced the idea of using the physical theory of phase transitions as a theoretical framework for the study of minimal surfaces, in particular the Allen-Cahn equation. Combining this approach with min-max theory, he gave shorter proofs of the existence of a minimal hypersurface in any Riemannian manifold and, together with P. Gaspar, of the existence of infinitely many minimal hypersurfaces in generic manifolds. More recently, he has been interested in applications of the mean curvature flow and min-max theory to hyperbolic geometry, in particular to understanding the geometry of quasi-Fuchsian manifolds.

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Address: Huxley 
Phone: (+44) (0)20 7594 tba

Prof Gustav Holzegel

Professor 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

Dr Marie-Amelie Lawn

Senior 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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Prof Yankı  Lekili

Professor in Pure Mathematics

Lekili's main area of research is symplectic topology and its applications to low dimensional topology. He is also interested in connections between symplectic topology and algebraic geometry and geometric representation theory. Symplectic topology is concerned with the global topology of symplectic manifolds, a class of spaces that appeared first in classical mechanics. Over the past decades, symplectic geometry evolved from its roots in Hamiltonian mechanics into a branch of topology targeting global problems. Due to its relevance to string theory, the field has witnessed an explosion of activity in recent years, and many of the open questions currently under investigation by symplectic topologists have their origins in predictions made by theoretical physicists. Part of Lekili's research is motivated by a set of such predictions which goes by the name of the "mirror symmetry conjecture".

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Address: 625 Huxley Building
Phone: (+44) (0)20 TBA

Prof Travis Schedler

Professor in Pure Mathematics

Prof 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

Dr Steven Sivek

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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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Dr Martin Taylor

Royal Society Tata University Research Fellow (Senior Lecturer)

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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

Dr Pierre Descombes

Chapman Fellow

Pierre Descombes completed his PhD in Sorbonne université in Paris, under the supervision of the string theorist Boris Pioline, and the geometric representation theorist Olivier Schiffmann. He join this year the algebraic geometry group of Imperial, to work on enumerative geometry question with some inspiration from theoretical physics, in particular in Donaldson-Thomas theory and Gromov-Witten theory.

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Dr Mykola Matviichuk

Chapman Fellow

I study geometry of Poisson brackets on complex manifolds. Topics of my research include deformation theory, Higgs fields, Hilbert schemes and various moduli spaces related to elliptic curve. I am also broadly interested in geometric representation theory and mathematical physics.

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Dr Matt Booth- Research Associate

I am a noncommutative geometer, working in between algebraic geometry, homotopy theory, representation theory and algebraic topology.

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Peter Cameron

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Dr Samuel Johnston - Research Associate

Research interest: tropical geometry, log Gromov-Witten theory, mirror symmetry.

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Dr Riccardo Ontani- Research Associate

My area of interest is enumerative geometry.
I use localisation techniques to compute invariants, often in Donaldson-Thomas and quasimap theories.

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Dr Noah Porcelli - Research Associate

I'm interested in symplectic topology, and I think about Floer theory, Fukaya categories, and how one uses them to study the topology of Lagrangian submanifolds.

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Dr Yuhan Sun- Research Associate

I am interested in symplectic topology and its interaction with algebraic geometry and Hamiltonian dynamics.

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Dr Daniel Platt - Research Associate

Research interest: geometric analysis, machine learning.

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Dr Kevin Smith - Research Associate

Research interest: Kähler geometry.

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Dr Anne-Sophie Kaloghiros

Dr Ed Segal