Title: Canonical representations of surface groups.Abstract: For $Sigma_{g,n}$ a genus $g$ surface with $n$ punctures, we study the character variety parameterizing representations of $pi_1(Sigma_{g,n})$. This character variety has a natural action of […]
Title: On the cone conjecture for log Calabi-Yau threefolds.Abstract: Let $Y$ be a smooth projective threefold admitting a $K3$ fibration $f: Y rightarrow mathbb{P}^{1}$ with $-K_{Y} = f^{ast} mathcal{O}(1)$. Then the extremal […]
Title: Symmetries of Fano varieties.Abstract: A landmark result of Birkar, Prokhorov, and Shramov shows that automorphism groups of Fano (or more generally rationally connected) varieties over C of a fixed dimension are […]
Title: On Fano and Calabi-Yau pairs of small coregularity.Abstract: The coregularity is an invariant that measures a specific type of combinatorial complexity of a pair. We will start this talk by defining […]
Title: Minimal model program for algebraically integrable foliations and generalized pairs.Abstract: In this talk, I will discuss my recent research that establishes the minimal model program for Q-factorial foliated dlt algebraically integrable […]
Title: A non-Archimedean characterization of local K-stability.Abstract: Log Fano cone singularities are generalizations of affine cones over Fano varieties. Motivated by the study of canonical metrics on Fano varieties, there is a […]
Title: On cohomology of BG.Abstract: Cohomology of classifying space/stack of a group G is the home which resides all characteristic classes of G-bundles/torsors. In this talk, we will try to explain some […]
Title: On the strong Sarkisov Program.Abstract: In this talk, I will explain some results about factorizing a birational map between Mori fibre spaces into Sarkisov links, such that the invariants of Sarkisov […]
Title: Unipotent homotopy theory of schemes.Abstract: In this talk, I will present a notion of unipotent homotopy theory for schemes, which is based on Toen's work on affine stacks. I will discuss […]
Title: Test ideals in mixed characteristic via the p-adic Riemann-Hilbert correspondence.Abstract: Multiplier ideals in characteristic zero and test ideals in positive characteristic are fundamental objects in the study of commutative algebra and […]
Title: Equivariant birational geometry.Abstract: I will discuss new invariants of actions of finite groups on algebraic varieties and their applications (joint with A. Kresch, I. Cheltsov and Zh. Zhang).
Title: A moduli-theoretic approach to heights on stacks.Abstract: A theory of heights of rational points on stacks was recently introduced by Ellenberg, Satriano and Zureick-Brown as a tool to unify and generalize […]