Date/Time : 03 Feb 2021 10:00
Venue : via Zoom
Speaker : Andrew Zimmer, University of Winsconsin-Madison

Join Zoom Meeting https://nus-sg.zoom.us/j/87303863968?pwd=VFhyUkU5V05jM3FxVnhFQTk0UXZkQT09 Meeting ID: 873 0386 3968 Password: 687478 Abstract: A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. When the group is word hyperbolic, these representations are Anosov representations (which have been extensively studied over the past 15 years). The non-word hyperbolic is less understood and in this talk I will describe some recent results about the general structure of the groups that can admit convex co-compact representations. Most of what I will discuss is joint work with Mitul Islam.

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Date/Time : 27 Jan 2021 17:00
Venue : via Zoom
Speaker : Simone Diverio, Roma Sapienza

Join Zoom Meeting https://nus-sg.zoom.us/j/82968914141?pwd=ckgvWDNRZE5nblJKNS9KUGZidkw1UT09 Meeting ID: 829 6891 4141 Password: 841138 Abstract: In the last few years there has been a renewed interest around an old conjecture by Griffiths characterizing which should be the positive characteristic forms for any given Griffiths positive holomorphic Hermitian vector bundle. According to this conjecture, they should be precisely the characteristic forms belonging to the positive cone spanned by the Schur forms. After recalling the various notions of positivity for holomorphic Hermitian vector bundles, and how they are (or should be) related, we shall explain a recent result obtained in collaboration with my PhD student F. Fagioli, which gives a partial confirmation of the above conjecture. Such a result is obtained as a consequence of a pointwise, differential-geometric Gysin formula for the push-forward of the curvature of the tautological line bundles over flag bundles.

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Date/Time : 20 Jan 2021 16:00
Venue : via Zoom
Speaker : Frédéric Naud, Institut de Mathématiques de Jussieu - Paris 6

Join Zoom Meeting https://nus-sg.zoom.us/j/85799518051?pwd=N0JDU2pGbXAwcThKZVE3UEh5MmJXZz09 Meeting ID: 857 9951 8051 Password: 336911 We will define a notion of random covers of hyperbolic surfaces (compact or non- compact) through random representations of their fundamental groups. We will then show how some tools from group combinatorics can be used to study, in a probabilistic sense, the “low spectrum” of these surfaces in the large euler characteristic limit. Joint work with Michael Magee and Doron Puder.

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Date/Time : 06 Jan 2021 10:00
Venue : via Zoom
Speaker : Jingjun Han, Johns Hopkins University

Join Zoom Meeting https://nus-sg.zoom.us/j/83092658434?pwd=dDlHclhrMmNvQjZkUFFVeEpOdEhDUT09 Meeting ID: 830 9265 8434 Password: 664940 Abstract: Kawamata log terminal (klt) singularities form an important class of singularities due to its fundamental roles in MMP, Kähler-Einstein geometry, and K-stability. Recently, Chi Li introduced a new invariant called the local volume of a klt singularity which encodes lots of interesting geometric and topological information. A folklore conjecture predicts that local volumes satisfy the ascending chain condition (ACC) when the coefficients of the boundary divisors belong to a DCC set. In this talk, we will show the ACC conjecture for local volumes holds when the ambient variety is fixed. We will also explore the relation between log canonical thresholds, local volumes, and delta-plt blow-ups. This is based on ongoing joint work with Yuchen Liu and Lu Qi.

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Date/Time : 09 Dec 2020 15:00
Venue : via Zoom
Speaker : Tsviqa Lakrec , The Hebrew University of Jerusalem, Israel

Join Zoom Meeting https://nus-sg.zoom.us/j/81609880468?pwd=Wk5Dak1QK0ZpL1lkWVo5S0VOVVB5dz09 Meeting ID: 816 0988 0468 Password: 692705 Abstract: I will discuss a quantitative equidistribution result for the random walk on a torus arising from the action of the group of affine transformations. This is a joint work with Weikun He and Elon Lindenstrauss. Under the assumption that the Zariski closure of the group generated by the linear part acts strongly irreducibly on R^d, we give quantitative estimates (depending only on the linear part of the random walk) for how fast this random walk equidistributes, unless the initial point and the translation part of the affine transformations can be perturbed so that the random walk is trapped in a finite orbit of small cardinality. In particular, we prove that the random walk equidistributes in law to the Haar measure if and only if the random walk is not trapped in a finite orbit. This extends the results of Bourgain-Furman-Lindenstrauss-Mozes and He-de Saxcé on quantitative equidistribution of the random walk arising from the action of the automorphism group of the torus. I will also mention a new joint work with He and Lindenstrauss that extends these results to nilmanifolds.

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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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