# Almuni of the Hodge Institute

Class of 2019
Sjoerd Beentjes JCMB 5401, sjoerd.beentjes at ed.ac.uk
My research is in algebraic geometry, in particular applications of the theory of stability conditions and derived categories to the enumerative geometry of curves on Calabi-Yau threefolds, such as Donaldson-Thomas, Pandharipande-Thomas, and BPS invariants. At the moment, I am interested in their underlying motivic and categorical refinements.
Natalia Iyudu
I am interested in noncommutative algebra and its interplay with (noncommutative) geometry, representation theory, operads, homological algebra, K-theory. The structures originated in physics, topology, geometry, such as Calabi-Yau algebras, Novikov algebras, operads of CFT, etc. are of particular interest. My papers are available at ArXiv.
Alexander Shapiro
My research revolves around integrable systems, geometric representation theory, character varieties, quantum groups, and cluster algebra.
Jenny August
I am a PhD student working with Michael Wemyss.
Juliet Cooke j.cooke848 at gmail.com
I am a PhD student of Andrew Ranicki, interested in the topology of manifolds.
Tim Weelinck
I'm a PhD student working with David Jordan. I'm interested in representation theory and geometry, and areas where the two collide e.g. quantum groups at roots of unity.

Class of 2018
Roberto Fringuelli
My research interests lie in algebraic geometry and representation theory. In particular, I am interested in moduli spaces of principal bundles on algebraic curves and their connections to physics.
Diletta Martinelli
My research interests are in algebraic geometry and in particular in higher dimensional birational geometry. My work aims to study effectivity questions on algebraic varieties related to their underlying topology as complex manifolds. I am also interested in positive characteristic methods, moduli spaces and Calabi-Yau manifolds.
Brent Pym
I work at the interface between differential, algebraic and noncommutative geometry. I am particularly interested in topics that have close ties with physics, including: the structure and classification of algebraic Poisson varieties; deformation quantization and noncommutative projective geometry; the Stokes phenomenon and resurgence; moduli spaces of bundles and connections; and links with derived symplectic and Poisson geometry.
Peter Samuelson
My research involves interactions between low dimensional topology (character varieties, skein algebras and modules, knot invariants) and representation theory (various versions of Hecke algebras, Hall algebras, quantum groups). I've recently been working with categorification (the Heisenberg category) and symplectic geometry (the Fukaya category of a surface).
Simon Crawford
I am a PhD student of Sue Sierra, interested in noncommutative algebraic geometry.
Soheyla Feyzbakhsh
I am a PhD student working with Arend Bayer.
Bach Tran
I am a PhD student working with Dr. Milena Hering. I am interested in toric varieties, mainly on $N_p$ property and normality of very ample bundles.

Class of 2017
Agnieszka Bodzenta
My research lies in the derived categories of coherent sheaves. I am mostly interested in relation between the derived category and birational geometry of the underlying variety."Agnieska is now at University of Warsaw."
Martin Kalck
I am interested in homological structures arising in representation theory, singularity theory and geometry.
Dimitra Kosta
My research originally lay in the area of birational geometry, yet recently I have also been interested in applications and the interplay between algebraic geometry and statistics.
Martina Lanini
My research addresses the interplay between representation theory (of Kac-Moody algebras, algebraic groups, quantum groups, Cherednik algebras), algebraic combinatorics (Kazhdan-Lusztig polynomials, moment graphs, Schubert calculus) and geometry (perverse sheaves, parity sheaves, degenerate flag varieties).
Chunyi Li
My research interested lies in algebraic geometry and noncommutative algebra. Specifically, I am interested in derived category, stability condition, quiver representation and birational geometry. I am currently working on the derived category of coherent sheaves on commutative/noncommutative smooth Fano surfaces.
Alice Rizzardo
I work in Algebraic Geometry, and specifically on derived categories of coherent sheaves on a projective variety. In particular, I have been studying functors between derived categories of coherent sheaves and how they can be expressed in a geometric way. In general, I am interested in investigating the behavior of the derived category of a scheme using techniques ranging from homological algebra to representation theory.
Spela Spenko
I have been working in noncommutative algebra, and I am interested in its interaction with algebraic geometry and free analysis. Recently I have been focusing on non-commutative resolutions of singularities.
Igor Krylov
I am PhD student of Ivan Cheltsov. My interests are: birational geometry and theory of singularities. I am currently working on birational geometry of del Pezzo fibration of degree one and existence of good models.

Class of 2016
Michael Wemyss
I am motivated mainly by problems in algebraic geometry and its interactions with noncommutative algebra, in particular resolutions of singularities and the minimal model program. As part of this, my research encompasses many of the related commutative and homological algebra structures and their representation theory, especially Cohen-Macaulay modules, triangulated and derived categories, cluster-tilting and higher AR theory. Michael is now Chair of Mathematics at University of Glasgow.
Julia Collins
I was formerly a researcher in the field of Knot Theory (topology); specifically, looking at slice knots and the structure of the knot concordance group. Occasionally I still publish papers, but my main job is to do outreach and teaching in the School of Mathematics.
Matthew Woolf
Matthew spent one year in Edinburgh, then returned to a post-doc at University of Illinois Chicago.
Wafa Alagal
I am a PhD student working with Antony Maciocia.

Class of 2015
I work on algebraic and geometric questions of a combinatorial flavor. At the moment, I'm interested in how the betti numbers of graded modules behave in families and upon degeneration.
I'm mostly interested in KZ equations, Drinfeld associators and related topics like quantum groups, knot theory, Cherednik algebras and operads.
Ciaran Meachan
My mathematical interests are centred around derived categories of coherent sheaves on smooth projective varieties; in particular, Calabi-Yau varieties. I am currently thinking about irreducible holomorphic symplectic manifolds and their derived autoequivalences.
Hendrik Suess
I am working in algebraic geometry. At the moment my special interest is focused on algebraic torus actions, Kähler-Einstein metrics and Cox rings of algebraic varieties.
Supreedee Dangskul
I am a PhD student working with Andrew Ranicki.
Aaron Greenspan
I am a PhD student working with Tom Leinster. I'm currently exploring concepts in and around the magnitude of enriched categories.
Joe Karmazyn
I'm a PhD student of Michael Wemyss and Iain Gordon, and have been in Edinburgh since September 2011. I began by studying PBW deformations of Calabi-Yau algebras defined by superpotentials, relating these to symplectic reflection algebras. I've moved on to consider the relation between the deformation theory of non-commutative and geometric resolutions of singularities.
Patrick Orson
I am a PhD student of Andrew Ranicki. I am interested in understanding an analytic invariant of smooth manifolds called the eta-invariant, in terms of algebraic topology and algebraic L-theory. This work has a strong relationship to (high- and low-dimensional) knot theory.
Chris Palmer
I am a PhD student of Andrew Ranicki. I am interested in combinatorial signature formulae for triangulated manifolds, trisections of symmetric Poincaré complexes and computational algebraic topology.
Carmen Rovi JCMB 5603, c.rovi@sms.ed.ac.uk, Tel. +44 0131 650 5067
I am a PhD student working with Andrew Ranicki. My research interests lie in the field of high-dimensional topology. I am specially interested in Surgery theory, and in the last months I have been working on the problem of multiplicativity of the signature of fibre bundles.
Rebecca Tramel
I am a PhD student of Arend Bayer, studying algebraic geometry, derived categories, and stability conditions.

Class of 2014
Will Donovan
I work on derived categories, in relation to birational geometry and non-commutative algebra, using ideas from mirror symmetry and geometric representation theory. Will moved on to start a post-doc at IPMU.
Evgeny Shinder
I am interested in Algebraic Geometry. Recently I have been studying derived categories of fake projective planes and fake quadrics. Currently I am working out a definition and properties of a zeta-function of a derived category which would generalize the generating series of Hilbert schemes of points in the surface case. Previously I have done some work in Algebraic K-theory (Voevodsky's motives and central simple algebras) and Number Theory (Mahler measure). Please see my webpage http://www.maths.ed.ac.uk/~eshinder for more details. Evgeny left Edinburgh to start a lecturer position in Sheffield.
Guillaume Pouchin
I am working on geometric representation theory, connecting the representation theory of objects such as quantum groups or affine Kac-Moody algebras to the geometry of spaces like quiver varieties or Higgs bundles on curves. Guillaume left to become "Professeur de classe préparatoire" at Lycée François Premier (Fontainebleu).
Rollo Jenkins
I'm a PhD student under Iain Gordon and Antony Maciocia. My thesis is on Koszul duality for the category O attached to rational Cherednik algebras and localisation, which takes Cherednik algebra modules and produces sheaves of W-algebra modules for some quiver variety. After completing his PhD in 2013, Rollo took on a post-doc at Campinas.
Francois Petit
I am interested in algebraic geometry and its interactions with deformation quantization. François moved to University of Luxembourg.
Dulip Piyaratne
I am a PhD student working under Antony Maciocia. My mathematical interests are in algebraic geometry. Currently, I am interested in derived categories, stability conditions and Fourier-Mukai theory. After finishing his PhD in Edinburgh, Dulip started a post-doc at IPMU.
Przemyslaw Pobrotyn
I am a PhD student of Prof. Agata Smotkunowicz interested in noncommutative ring theory.