Date/Time : 01 Dec 2020 16:00
Venue : via Zoom
Speaker : Filippo Bracci, Rome "Tor Vergata", Italy

Join Zoom Meeting https://nus-sg.zoom.us/j/84662919254?pwd=bXk4WWU2NTFPTEptNkZ3cjBLbGcrZz09 Meeting ID: 846 6291 9254 Password: 206241 Gromov hyperbolic spaces are well studied since their introduction. In 2000 Balogh and Bonk proved that bounded strongly pseudoconvex domains are Gromov hyperbolic with respect to the Kobayashi distance and the natural boundary is homeomorphic to the Gromov boundary. It was however only in the last five years that Gromov hyperbolicity was started to be used in depth in complex analysis. The most useful tool in Gromov hyperbolicity is the so-called “shadowing lemma”. In this talk I will present a general introduction to Gromov hyperbolicity in complex analysis and review some recent results and applications to one and several complex variables (such as the study of trajectory of semi-complete holomorphic vector fields in the unit disc and boundary extension results for biholomorphisms in scv without assuming boundary regularity of the domains).

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Date/Time : 17 Nov 2020 16:00
Venue : via Zoom
Speaker : Çağrı Sert , University of Zürich, Switzerland

Join Zoom Meeting https://nus-sg.zoom.us/j/86006972904?pwd=Wm9vWWFHMEUxc3l3aHIrZDMyRlN0Zz09 Meeting ID: 860 0697 2904 Password: 071999 Abstract: In a first part, we will provide a (biased) overview of the theory of random matrix products. In a second part, we will focus on large deviation principle type results in that theory and mention some recent results as well as open questions. In the last part, we will shift to random compositions of isometries of hyperbolic spaces where some of the questions/results mentioned in the first part can be answered/proved differently with geometric methods. Based on joint work with Boulanger, Mathieu, Sisto.

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Date/Time : 11 Nov 2020 14:00
Venue : via Zoom
Speaker : Zhu Chengbo, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/89815068389?pwd=UXpnNXFNczNvTzhza3BqTVRHTllBQT09 Meeting ID: 898 1506 8389 Password: 543629 Abstract:  The idea that the study of finite dimensional representations of compact Lie groups amounts to the study of rational representations of reductive algebraic groups can be traced back to Hermann Weyl in the 1930’s. It was I.M. Gelfand who advocated that infinite-dimensional representations of non-compact Lie groups should be investigated by methods of functional analysis, and more specifically theory of distributions, in his ICM Plenary Lecture in 1954 (Some aspects of functional analysis and algebra) and in the six-volume work by I.M. Gelfand et al. on “Generalized Functions” (1960’s). Through two angles, I will explain why one needs to and how one applies, the theory of distributions. 1. Models of representations of the group SL(2,R); 2. Basic invariants of smooth representations: matrix coefficients and characters

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Date/Time : 04 Nov 2020 09:00
Venue : via Zoom
Speaker : Luna Lomonaco, IMPA, Rio de Janeiro - Brazil

Join Zoom Meeting https://nus-sg.zoom.us/j/88295756539?pwd=RGVDZGNJUFJMdk1LbGJaQUFVVmY2dz09 Meeting ID: 882 9575 6539 Password: 608485 Abstract: Holomorphic correspondences are polynomial relations P(z,w)=0, which can be regarded as multi-valued self-maps of the Riemann sphere (implicit maps sending z to w). The iteration of such multi-valued map generates a dynamical system on the Riemann sphere (dynamical system which generalise rational maps and finitely generated Kleinian groups). We consider a specific 1-(complex)parameter family of (2:2) correspondences F_a (introduced by S. Bullett and C. Penrose in 1994), which we describe dynamically. In particular, we show that for every a in the connectedness locus M_{\Gamma}, this family is a mating between the modular group and rational maps in the family Per_1(1); we develop for this family a complete dynamical theory which parallels the Douady-Hubbard theory of quadratic polynomials; and we show that M_{\Gamma} is homeomorphic to the parabolic Mandelbrot set M_1. This is joint work with S. Bullett.

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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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