I am an algebraic geometer whose research interests focus on birational geometry, Kähler geometry, moduli spaces and special holonomy.
More specifically, I work on problems in the following areas:
- Existence of constant scalar curvature Kähler metrics (including Kähler-Einstein metrics) and its relation to K-stability.
- Classification of varieties of Fano type.
- Compactification of moduli spaces and geometric invariant theory.
- Computational algebraic geometry.
- Construction and characterisation of manifolds with special holonomy.
My research is supported by EPSRC grant EP/V055399/1. You can see a list of my publications. Below you can have a look at the talks I have given at workshops, conferences or seminars (some slides/videos available), places I went to on research visits and seminars and workshops I have (co-)organised.
I have signed the Statement of inclusiveness in research and I think you should sign it too.
Talks delivered
| 26 February 2021 | Asymptotically log del Pezzo surfaces. Fano varieties and birational geometry. University of Nottingham. Video |
| 29 September 2020 | Strong Calabi dream rational surfaces. Simons K-stability conference. Online. |
| 01 September 2020 | Asymptotically log del Pezzo surfaces. ZAG Marathon. Online. |
| 21 May 2020 | The moduli continuity method for log Fano pairs (delivered remotely due to CoVid-19 pandemic). Algebraic Geometry seminar. University of Nottingham, Nottingham, United Kingdom. |
| 06 November 2019 | The moduli continuity method for log Fano pairs Bayes Centre. EDGE Days 2019: Fano Varieties, Cone Singularities And Their Links. University of Edinburgh, Edinburgh, United Kingdom. |
| 13 June 2019 | K-stable polarised del Pezzo surfaces. Institute of Mathematical Sciences, ShanghaiTech University, Shanghai, China. |
| 02 May 2019 | Revisiting Hilbert’s work on invariants of polynomials to study cubic surfaces. Mathematical Sciences Departmental Seminar, University of Essex, Colchester, UK. |
| 10 April 2019 | The moduli continuity method for log Fano pairs. Birational Geometry, Kähler-Einstein Metrics And Degenerations, Laboratory of Mirror Symmetry, Higher School of Economics, Moscow, Russia. |
| 28 February 2019 | The moduli continuity method for log Fano pairs. GLEN Seminar, University of Manchester, UK. |
| 19 April 2018 | Asymptotically log del Pezzo surfaces. Algebra-Number Theory, University of Maryland, College Park, MD, USA. |
| 27 March 2018 | Strong Calabi dream surfaces and K-stability of polarised del Pezzo surfaces. Algebraic Geometry Seminar, Johns Hopkins University, Baltimore, MD, USA. |
| 8 February 2018 | K-Stability, Canonical Metrics, and Calabi Dream Rational Surfaces. COW seminar. City, University of London. London, UK. |
| 20 December 2017 | Compactification of the moduli space of certain K3 surfaces. The Shokurovs: workshop for birationalists. Center for Geometry and Physics. Institute for Basic Science. Postech. Pohang, Korea. Video |
| 6 September 2017 | Métricas de Kähler con curvatura escalar constante en superficies de del Pezzo. 4� Congreso de Jóvenes investigadores. Real Sociedad Matemática Española. Universidad de Valencia, Spain |
| 30 August 2017 | Stability and cscK metrics on polarised del Pezzo surfaces. Stability, Boundedness and Fano Varieties. Beijing International Centre for Research Mathematics, China. |
| 18 August 2017 | Moduli of Fano hypersurfaces and anti-canonical sections via computational algebraic geometry. Experimental Classification of Fano Varieties. University of Tübingen, Germany. |
| 29 June 2017 | Stability and cscK metrics on polarised del Pezzo surfaces. EDGE Days 2017. University of Edinburgh, UK. |
| 25 April 2017 | Positivity of the twisted CM line bundle for log pairs. Positivity in algebraic and complex geometry, International Centre for the Mathematical Sciences, Edinburgh, UK. |
| 4 April 2017 | Stability and cscK metrics on polarised del Pezzo surfaces. University of Bath, UK. |
| 14 March 2017 | Existence of constant scalar curvature Kaehler metrics on polarised del Pezzo surfaces. University of Versailles-St. Quentin, France. |
| 06 February 2017 | Geometric Invariant Theory and Moduli of log Pairs. University of Dusseldorf, Germany. |
| 01 February 2017 | On the moduli space of log K-polystable pairs formed by a hypersurface and a hyperplane section. University of Cambridge, UK. |
| 14 December 2016 | Moduli space of cubic surfaces and their anticanonical divisors. AaDAG seminar, Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Denmark. |
| 21 October 2016 | Moduli space of cubic surfaces and their anticanonical divisors. University of Basel, Switzerland. |
| 13 October 2016 | Moduli space of cubic surfaces and their anticanonical divisors. EDGE Seminar. University of Edinburgh, UK. |
| 07 September 2016 | Moduli space of cubic surfaces and their anticanonical divisors (poster). Cremona Conference 2016. University of Basel, Switzerland. |
| 03 June 2016 | K-stability of Polarized Del Pezzo Surfaces. Edge Days. University of Edinburgh, Scotland, UK. |
| 21 August 2015 | On the moduli space of cubic surfaces and their anticanonical divisors. Simons Center for Geometry and Physics. University of Stony Brook, NY. USA. Video. |
| 31 July 2015 | Singular Kahler-Einstein metrics of small angles. Centre for Geometry and Physics. Postech. Pohang, Korea. |
| 12 June 2015 | On the moduli space of cubic surfaces and their anticanonical divisors. University of California, San Diego. San Diego, CA. USA. |
| 24 March 2015 | On the moduli space of cubic surfaces and their anticanonical divisors. University of Harvard. Cambridge, MA. USA. |
| 26 February 2015 | On the moduli space of cubic surfaces and their anticanonical divisors. University of Notre Dame. Notre Dame, IN. USA. |
| 1 November 2014 | Kahler-Einstein metrics and birational geometry (poster). AGNES. University of Pennsylvania. Philadelphia, PA. USA. |
| 7 October 2014 | Singular Kahler-Einstein metrics of small angles. JHU-UMD Complex Geometry Seminar. University of Maryland. College Park, MD. USA. |
| 24 September 2014 | Asymptotically log del Pezzo surfaces. Algebraic Geometry Seminar. University of Georgia. Athens, GA. USA. |
| 5 April 2014 | Dynamic alpha-invariants of del Pezzo surfaces (poster). Texas Algebraic Geometry Symposium. Rice University. Houston, TX. USA. |
| 27 March 2014 | Kahler-Einstein edge metrics on log del Pezzo surfaces. Algebraic Geometry seminar. Johns Hopkins University. Baltimore, MD. USA. |
| 12 November 2013 | Kahler-Einstein edge metrics on Fano varieties via birational geometry. Algebraic Geometry Seminar. University of Missouri-Columbia, MI. USA. |
| 26 October 2013 | Kahler-Einstein metrics and birational geometry (poster). AGNES. Boston College, MA. USA. |
| 3 September 2013 | Log canonical thresholds, tigers and cats (poster). Foliation theory in Algebraic Geometry. Simons Center, NY. USA. |
| 01-03 July 2013 | Kähler-Einstein metrics and Algebraic Geometry. Computing Tians alpha-invariant (3 lectures). Graduate workshop on Kähler Geometry. Simons Center for Geometry and Physics, Stony Brook, NY. USA. Video 1, Video 2, Video 3. |
| 14 June 2013 | Kähler-Einstein metrics with cone singularities and Donaldson’s programme.LMS Invited Lectures (support talk). Edinburgh, UK. |
| 10 May 2013 | Kähler-Einstein metrics with cone singularities and birational geometry. NCTS/TPE Workshop. Taipei, Taiwan. |
| 25 April 2013 | Kähler-Einstein metrics with cone singularities and birational geometry. MAGIC Seminar. Imperial College London. London, UK. |
| 24 January 2013 | Kähler-Einstein metrics meet Birational Geometry on a del Pezzo surface. Junior Geometry Seminar. Imperial College London. London, UK. |
| 14 December 2013 | Donaldson’s program to solve the Yau-Tian-Donaldson conjecture from an algebraic viewpoint. Seminar on Geometry of Algebraic Varieties. Steklov Mathematical Institute. Moscow, Russia. |
| 30 November 2012 | Classification of algebraic surfaces and Minimal Model Programme. Geometry Club. Edinburgh, UK. (Abstract). Notes. |
| 16 November 2012 | Intersection Theory and classification of surfaces for the Layman. href=”http://www.maths.ed.ac.uk/geometryclub/” target=”_blank”>Geometry Club. Edinburgh, UK. (Abstract). Notes. |
| 04 October 2012 | The mathematical hitchhiker guide to travel funding. PG Colloquium Edinburgh, UK. (slides) |
| 16 February 2012 | Degenerations of del Pezzo surfaces after Hacking and Prokhorov. Geometry Seminar (EDGE). Edinburgh, UK. |
| 20 January 2012 | The Tale of the Minimal Model Program. 6th PG Edinburgh-Heriot-Watt Joint Colloquium. Edinburgh, UK. |
| 15 December 2011 | Log canonical thresholds on Del Pezzo surfaces: Computation and applications. Iskovskikh Seminar. Steklov Institute, Moscow, Russia. |
| 14 April 2011 | Log canonical thresholds of del Pezzo Surfaces in arbitrary characteristic. Warwick, UK. |
| 20 January 2011 | Travel funding for a young mathematician. PG Colloquium. Edinburgh, UK. (slides) |
| 15 April 2010 | Chords of Alexander Grothendieck’s Mathematics. PG Colloquium. Edinburgh, UK. (slides) |
| 19 February 2010 | What is a Toric Variety?. Geometry Club. Edinburgh, UK. (Abstract) |
| 2 February 2010 | Stiefel-Whitney classes and classification of Real Projective Spaces. SMSTC Seminar Series 2010. Scotland, UK. (slides) |
| March 2009 | Yau’s Solution to the Calabi Conjecture. Part III Seminar Series (Lent 2009). Cambridge, UK. |
| December 2008 | Parallelizable manifolds. Part III Seminar Series (Michaelmas 2008). Cambridge, UK. |
Research visits
| 18 June – 20 July 2016 | Hausdorff Institute for Mathematics. Bonn, Germany. |
| 11 January – 25 January 2016 | Differential Geometry Programme. MSRI. Berkeley, CA, USA. |
| 02 October – 11 October 2015 | Simon’s Centre for Geometry and Physics. Stony Brook, NY, USA. |
| 19 August- 30 August 2015 | Simon’s Centre for Geometry and Physics. Stony Brook, NY, USA. |
| 21 June – 05 July 2013 | Simon’s Centre for Geometry and Physics. Stony Brook, NY, USA. |
| 9-18 May 2013 | National Center for the Theoretical Sciences. Taipei, Taiwan. |
| 23-28 April 2013 | Imperial College London. London, UK. |
| 23-28 April 2013 | Imperial College London. London, UK. |
| 24-27 January 2013 | Imperial College London. London, UK. |
| 7-16 December 2012 | Higher School of Economics. Moscow, Russia. |
| 10-20 December 2011 | Higher School of Economics. Moscow, Russia. |
| 5-15 May 2011 | Moduli Spaces Programme. Newton Institute. Cambridge, UK. |
| 28 July – 8 August 2010 | Indian Association for the Cultivation of Science. Kolkata, India. |
Seminars and workshops organised
- Since 2020 – I am the organiser of MESS (Mathematics at Essex Seminar Series).
- Since 2020 – I am a co-organiser of ZAG (Zoom Algebraic Geometry) Seminar, the largest online weekly seminar in algebraic geometry in the world.
- 2022 – I am a co-organiser of AGGITatE Days 2022: Algebraic Groups and Geometric Invariant Theory at Essex.
- 2020-2021 – I was a co-organiser for the 2020 and 2021 editions of EDGE Days at the University of Edinburgh.
- 2020 – I was a local organiser for the CoDiMa Worskhop “Tools for Discrete Computational Mathematics” at Essex.
- 2014/2016 – I organised the Algebraic Geometry Seminar at Johns Hopkins University.
- 2013/2014 – (with Renjie Feng, Vamsi Pingali, Yanir Rubinstein and Bernie Shiffman) I organised “JHU-UMD Complex Geometry Seminar both at JHU (Baltimore) and UMD (College Park).
- June 2013 – (with Ivan Cheltsov) I hosted the “LMS Lecture Series in Edinburgh with main lecturer Prof Fedor Bogomolov. There is a recording of the lectures which we hope to make available soon.
- April 2013 – (with Paolo Cascini and Andrea Fanelli) Workshop Characteristic p methods in Algebraic Geometry at Imperial College London.
- 2010-2011 – (with Spiros Adams-Florou and Ciaran Meachan) the Geometry Club, which evolved into the current Hodge Club.
- February 2009 – SMSTC Seminar Series 2009/2010.