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.
|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.|
|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
- 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.