Ruadhaí Dervan received his PhD from the University of Cambridge in 2016, and is currently a Research Fellow at Gonville & Caius College, Cambridge. His research focuses on complex geometry and algebraic geometry, especially canonical Kähler metrics, moduli theory and geometric analysis. Giulio Codogni obtained his PhD from the University of Cambridge in 2016, and is currently a Research Fellow at the Department of Mathematics and Physics, Roma Tre University. His research interests are in algebraic geometry, especially K-stability, moduli theory and modular forms.Filippo Viviani received his PhD from the University of Roma Tor Vergata in 2007, and is currently an Associate Professor at Roma Tre University. His research focuses on algebraic geometry, especially moduli theory and its connections with birational geometry and combinatorics.

• 1 F. Ambro and J. Kollár, Minimal Models of semi-log-canonical pairs.- 2 G. Codogni and J. Stoppa, Torus Equivariant K-stability.- 3 K. Fujita, Notes on K-semistability of topic polarized surfaces.- 4 E. Legendre, A note on extremal toric almost Kähler metrics.- 5 Y. Odaka, Tropical geometric compactification of moduli, I - M_g case.- 6 Z. Sjöström Dyrefelt, A partial comparison of stability notions in Kähler geometry.- 7 C. Spotti, Kähler-Einstein metrics via moduli continuity.- 8 X. Wang, GIT stability, K-stability and moduli space of Fano varieties.

Ruadhaí Dervan received his PhD from the University of Cambridge in 2016, and is currently a Research Fellow at Gonville & Caius College, Cambridge. His research focuses on complex geometry and algebraic geometry, especially canonical Kähler metrics, moduli theory and geometric analysis. Giulio Codogni obtained his PhD from the University of Cambridge in 2016, and is currently a Research Fellow at the Department of Mathematics and Physics, Roma Tre University. His research interests are in algebraic geometry, especially K-stability, moduli theory and modular forms.Filippo Viviani received his PhD from the University of Roma Tor Vergata in 2007, and is currently an Associate Professor at Roma Tre University. His research focuses on algebraic geometry, especially moduli theory and its connections with birational geometry and combinatorics.

• 1 F. Ambro and J. Kollár, Minimal Models of semi-log-canonical pairs.- 2 G. Codogni and J. Stoppa, Torus Equivariant K-stability.- 3 K. Fujita, Notes on K-semistability of topic polarized surfaces.- 4 E. Legendre, A note on extremal toric almost Kähler metrics.- 5 Y. Odaka, Tropical geometric compactification of moduli, I - M_g case.- 6 Z. Sjöström Dyrefelt, A partial comparison of stability notions in Kähler geometry.- 7 C. Spotti, Kähler-Einstein metrics via moduli continuity.- 8 X. Wang, GIT stability, K-stability and moduli space of Fano varieties.

Ruadhaí Dervan received his PhD from the University of Cambridge in 2016, and is currently a Research Fellow at Gonville & Caius College, Cambridge. His research focuses on complex geometry and algebraic geometry, especially canonical Kähler metrics, moduli theory and geometric analysis. Giulio Codogni obtained his PhD from the University of Cambridge in 2016, and is currently a Research Fellow at the Department of Mathematics and Physics, Roma Tre University. His research interests are in algebraic geometry, especially K-stability, moduli theory and modular forms.Filippo Viviani received his PhD from the University of Roma Tor Vergata in 2007, and is currently an Associate Professor at Roma Tre University. His research focuses on algebraic geometry, especially moduli theory and its connections with birational geometry and combinatorics.

• 1 F. Ambro and J. Kollár, Minimal Models of semi-log-canonical pairs.- 2 G. Codogni and J. Stoppa, Torus Equivariant K-stability.- 3 K. Fujita, Notes on K-semistability of topic polarized surfaces.- 4 E. Legendre, A note on extremal toric almost Kähler metrics.- 5 Y. Odaka, Tropical geometric compactification of moduli, I - M_g case.- 6 Z. Sjöström Dyrefelt, A partial comparison of stability notions in Kähler geometry.- 7 C. Spotti, Kähler-Einstein metrics via moduli continuity.- 8 X. Wang, GIT stability, K-stability and moduli space of Fano varieties.