Date/Time : 27 Oct 2020 17:00
Venue : via Zoom
Speaker : Andreas Höring, Université de Nice - Sophia Antipolis, France

Join Zoom Meeting https://nus-sg.zoom.us/j/87501413614?pwd=MXBqd1ZxVS9jRlBUcmVLOTdIMklTQT09 Meeting ID: 875 0141 3614 Password: 804632 Abstract: While the canonical bundle is the central object of the minimal model program and has been studied by many authors, the positivity of the cotangent bundle is much more elusive. In this talk I will show how foliation theory leads to renewed interest in the cotangent bundle and give some recent results for varieties with trivial canonical class and elliptic surfaces.

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Date/Time : 21 Oct 2020 14:00
Venue : via Zoom
Speaker : Jia Jia, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/83889134319?pwd=SVA4YURXYlZtSUVQSUFzWFB3Mlg2Zz09 Meeting ID: 838 8913 4319 Password: 067273 Abstract:  In this talk, we will give a structure theorem of endomorphisms of normal projective surfaces via the equivariant minimal model program. Combining with some local dynamics and known results, we will give an application of the main theorem to Zariski dense orbit property in dimension two. This is joint work with Doctor Junyi Xie and Professor De-Qi Zhang.

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Date/Time : 14 Oct 2020 10:00
Venue : via Zoom
Speaker : Junliang Shen, MIT

Join Zoom Meeting https://nus-sg.zoom.us/j/82961016557?pwd=SC85byszaFlHNDMzMmRBR1p6clNvdz09 Meeting ID: 829 6101 6557 Password: 706382 Abstract:  The moduli space of Higgs bundles and Hitchin‘s integrable system lie at the crossroads of mathematical physics, representaton theory, and geometry. In this talk, we focus on the structure of cohomology for the moduli of Higgs bundle from the viewpoints of the non-abelian Hodge theory, hyper-Kähler geometry, and mirror symmetry. In particular, we will discuss recent progress on the P=W conjecture and Hausel-Thaddeus’ topological mirror symmetry conjecture. Based on joint work with Mark de Cataldo and Davesh Maulik.

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Date/Time : 07 Oct 2020 09:00
Venue : via Zoom
Speaker : Sara Maloni, University of Virginia

Join Zoom Meeting https://nus-sg.zoom.us/j/86085470675?pwd=VFVkOVJoMGcrWmZpenZBenRScVozdz09 Meeting ID: 860 8547 0675 Password: 058406 Abstract:  Thurston conjectured that quasi-Fuchsian manifolds are determined by the induced hyperbolic metrics on the boundary of their convex core and Mess generalized those conjectures to the context of globally hyperbolic AdS spacetimes. In this talk I will discuss a universal version of these conjectures (and prove the existence part) by considering convex sets spanning quasicircles in the boundary at infinity of hyperbolic and anti-de Sitter space. This work generalizes Alexandrov and Pogorelov’s results about the characterization metrics induced on the boundary of a compact convex subset of hyperbolic space. In addition, in anti-de Sitter space quasicircles can be characterize by the width of their convex hulls, as Bonsante and Schlenker showed. Time permitting, we will discuss why this is not true in hyperbolic space, except when the hulls have small width. (This is joint work with Bonsante, Danciger and Schlenker.)

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Date/Time : 30 Sep 2020 10:00
Venue : via Zoom
Speaker : Yu-Wei Fan, UC Berkeley

Join Zoom Meeting https://nus-sg.zoom.us/j/98579645138?pwd=cFZlc1QzZktFOFF1UEJjamlIUEFJUT09 Meeting ID: 985 7964 5138 Password: 872111 Abstract: We will start with a gentle introduction to the notions of categorical dynamical systems and their entropy, in which the latter is motivated from connections between Teichmuller theory and Bridgeland stability conditions. Then we will compare categorical entropy with the topological entropy of holomorphic dynamics. Finally, we will introduce a new canonical invariant that is complementary to the categorical entropy, and see how it is a generalization of the Poincare rotation number. Partly based on joint work with Simion Filip.

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Date/Time : 22 Sep 2020 16:00
Venue : via Zoom
Speaker : Jérémy Toulisse, Université de Nice - Sophia Antipolis, France

Join Zoom Meeting https://nus-sg.zoom.us/j/94773388232?pwd=WWpGK1dHaEZLcEx6TWpVVU9jNUdhZz09 Meeting ID: 947 7338 8232 Password: 861264 Abstract: The pseudo-hyperbolic space H^{2,n} is the pseudo-Riemannian analogue of the classical hyperbolic space. In this talk, I will explain how to solve an asymptotic Plateau problem in this space: given a topological circle in the boundary at infinity of H^{2,n}, we construct a unique complete maximal surface bounded by this circle. This construction relies on Gromov’s theory of pseudo-holomorphic curves. This is a joint work with François Labourie and Mike Wolf.

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Date/Time : 16 Sep 2020 14:00
Venue : via Zoom
Speaker : Jialun Li , University of Zürich, Switzerland

Join Zoom Meeting https://nus-sg.zoom.us/j/96068904418?pwd=YkY1YmhEaHlvMk9TbERJSEllMFJ5UT09 Meeting ID: 960 6890 4418 Password: 788160 Abstract: Let mu be a Borel probability measure on SL2(R) with a finite exponential moment, such that the support of mu generates a Zariski dense subgroup in SL2(R). We can define a unique probability measure on the circle, which is called the mu stationary measure or Furstenberg measure. We will prove, using Bourgain’s discretized sum-product estimate, that the Fourier coefficients of this measure go to zero with a polynomial speed. Starting from this result, we can obtain a spectral gap of the transfer operator, whose properties enable us to get an exponential error term in the renewal theorem in the context of random products of matrices.

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Date/Time : 09 Sep 2020 11:00
Venue : via Zoom
Speaker : Hsueh-Yung Lin, Kavli-IPMU, Japan

Join Zoom Meeting https://nus-sg.zoom.us/j/95748660096?pwd=M2Y1eVJvb01iTzQrZ29CNGZuREM4UT09 Meeting ID: 957 4866 0096 Password: 871058 Abstract: Let X be a compact Kähler manifold. The celebrated Kodaira embedding theorem asserts that if the Kähler cone of X contains a rational cohomology class, then X is projective. Instead of considering Kähler classes, we will study the algebraicity of X when X carries a 1-dimensional positive rational Hodge class. We will first discuss and formulate some precise problems (depending on the notion of positivity) then focus on the following results: 1) If the interior of the dual Kähler cone of X contains a rational class, then the Picard variety of X is projective. 2) If the interior of the dual pseudoeffective cone of a compact Kähler threefold X contains a rational class, then X is projective.

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Date/Time : 02 Sep 2020 10:00
Venue : via Zoom
Speaker : Hongtaek Jung , Institute for Basic Science - South Korea

Join Zoom Meeting https://nus-sg.zoom.us/j/94193089627?pwd=SGZ6cUtXNnp6ejFpZUpGWHFkalM5dz09 Meeting ID: 941 9308 9627 Password: 788615 Abstract: It is known that the PSL(n,R)- Hitchin components of closed surfaces of negative Euler characteristic admit global Darboux coordinates with respect to the Goldman symplectic form. I will discuss an analogous result for the “PSL(3,R)-Hitchin components”  or the deformation spaces C(O) of convex projective structures of closed orbifolds O of negative Euler characteristic.  For this, I will present how to construct the Goldman type symplectic form on C(O).  Then I will introduce two ingredients to construct the global Darboux coordinates: a decomposition theorem that splits C(O) into simpler symplectic manifolds and an action-angle principle. This is joint work with Suhyoung Choi.

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