Research

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.

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

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