Date/Time : 13 Oct 2022 15:30
Venue : S17 #05-11 (SR5)
Speaker : Chen Junkai Alfred, National Taiwan University

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Meeting ID: 875 1147 6637
Passcode: 468399

Abstract: In minimal model program, divisorial contractions, flip and flops are considered to be the elementary maps. Divisorial contractions to points are well-understood and can be realized as weighted under certain embeddings. In this talk, we will present the recent developments toward the classification of divisorial contractions to curves. We will provide an outline of our proposed program and demonstrate some new examples. If time permits, we will talk about their factorizations as well. The talk is based on the joint work in progress with Hsin-Ku Chen and Jheng-Jie Chen.

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Date/Time : 01 Sep 2022 15:00
Venue : S17 #04-04 (SR3)
Speaker : Nhat Minh Doan, Vietnam Academy of Science and Technology

Abstract:  We investigate the terms arising in an identity for hyperbolic surfaces proved by Luo and Tan, namely showing that they vary monotonically in terms of lengths and that they verify certain convexity properties. Using these properties, we deduce two results. As a first application, we show how to deduce a theorem of Thurston which states, in particular for closed hyperbolic surfaces, that if a simple length spectrum “dominates” another, then in fact the two surfaces are isometric. As a second application, we show how to find upper bounds on the number of pairs of pants of bounded length that only depend on the boundary length and the topology of the surface. This is joint work with Hugo Parlier and Ser Peow Tan.

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Date/Time : 25 Aug 2022 15:00
Venue : S17 #04-04 (SR3)
Speaker : Timothée Bénard, University of Cambridge

Abstract:  A famous theorem due to Hopf-Tsuji-Sullivan-Kaimanovich asserts that the geodesic flow and the Brownian motion on a rank-one symmetric space of the non-compact type $\Lambda \backslash G/K$ are either both recurrent ergodic or both transient. In this talk, I will explain how this dichotomy can be extended to a much larger class of random walks, namely any right random walk on $\Lambda \backslash G$ induced by a Zariski-dense probability measure on $G$ with finite first moment.

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Date/Time : 18 Aug 2022 15:00
Venue : S17 #04-04 (SR3)
Speaker : Farhad Babaee, University of Bristol

Abstract: Tropical geometry is an effort to simplify algebraic subvarieties of the complex torus through the tropicalisation process to obtain tropical varieties. The upshot is that tropical varieties still retain a lot of information about the initial algebraic varieties. In this talk, I will explain basic notions in tropical geometry, and discuss how natural and useful it is to look at tropical geometry through the lens of complex geometry and holomorphic dynamics.

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Date/Time : 16 Aug 2022 15:00
Venue : S17 #04-04 (SR3)
Speaker : Wang Tianqi, National University of Singapore

Abstract: The notion of Anosov representations of a finitely generated group into a semisimple Lie group, introduced by Labourie, generalizes the notion of convex-cocompact representations to higher rank Lie groups. On the other hand, there are many non-discrete, and hence non-Anosov, representations that have good geometric properties, such as the primitive-stable representations introduced by Minsky. In this talk, we introduce a weakening of the notion of Anosov representations by requiring the Anosov condition to hold only on a chosen invariant closed geodesic subflows. This weakening allows for such non-discrete representations to arise as examples. We discuss several properties of this type of representations that are analogous to the properties of classical Anosov representations, such as stability and the limit maps being Hölder continuous in a weaker sense

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Date/Time : 11 Aug 2022 15:00
Venue : via Zoom
Speaker : Alexander Stoimenow, KAIST

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Meeting ID: 875 1147 6637
Passcode: 468399

Abstract: The braid groups $B_n$ were introduced in the 1930s in the work of Artin. An element in the braid group $B_n$ is called an $n$-braid. Alexander related braids to knots and links in 3-dimensional space, by means of a closure operation. In that realm, it became important to understand the braid representatives of a given link. Markov’s theorem relates these representatives by two moves, conjugacy in the braid group, and (de)stabilization, which passes between braid groups. Markov’s moves and braid group algebra have become fundamental in Jones’ pioneering work and its later continuation towards quantum invariants. Conjugacy is, starting with Garside’s, and later many others’ work, now relatively well group-theoretically understood. In contrast, the effect of (de)stabilization on conjugacy classes of braid representatives of a given link is in general difficult to control. Only in very special situations can these conjugacy classes be well described.

We are concerned with the question when infinitely many conjugacy classes of $n$-braid representatives of a given link occur. Birman and Menasco introduced a move called exchange move, and proved that it necessarily underlies the switch between many conjugacy classes of $n$-braid representatives of a given link.

After some very brief general introduction to knots and braids and their applications, we will discuss several results when the exchange move is also sufficient for generating infinitely many conjugacy classes of braid representatives.

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Date/Time : 27 Jul 2022 14:00
Venue : S17 #04-04 (SR3)
Speaker : Paolo Cascini, Imperial college

Abstract:  I will survey some recent results on the study of the birational geometry of foliations over complex projective varieties, focusing, in particular, on the case of algebraically integrable foliations.

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Date/Time : 04 Jul 2022 16:00
Venue : S17 #06-11 (SR6)
Speaker : Sang-hyun Kim, Korea Institute of Advanced Study

Abstract:  We prove that for each finite index subgroup H of the mapping class group of a closed hyperbolic surface, and for each real number r>1 there does not exist a faithful C^r-action (in Hölder’s sense) of H on a circle. For this, we partially determine the optimal regularity of faithful actions by right-angled Artin groups on a circle. (Joint with Thomas Koberda and Cristobal Rivas).

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Date/Time : 19 Apr 2022 16:00
Venue : via Zoom
Speaker : Nicholas Tholozan, École Normale Supérieure

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https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract: Let G/H be a reductive symmetric space. In 2016, Kobayashi and Kassel conjectured that the discrete subgroups of G acting properly discontinuously and cocompactly on G/H are « sharply » embedded in G. Here, I will present a proof of this conjecture, obtained jointly with Fanny Kassel, and discuss its many consequences (spectral theory of these compact quotients, stability under deformation and, in some cases, non-existence of such quotients).

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