Date/Time : 30 Sep 2021 10:00
Venue : via Zoom
Speaker : Brian Collier, University of California Riverside

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

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract:  In this talk, we will define a special class of nilpotent elements of complex semisimple Lie algebra and describe how a Slodowy slice construction defines connected components of moduli spaces of G-Higgs bundles on a compact Riemann surface for specific real groups G. Through the nonabelian Hodge correspondence, these components define connected components of the G-character variety with many nice features. We will then describe how these nice features, together with recent work of Guichard-Labourie-Wienhard on positive representations imply that such components are higher Teichmuller spaces, that is, they consist entirely of discrete and faithful representations. In the remaining time, we will describe what remains to be proven to finish the classification of higher Teichmuller spaces.

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Date/Time : 08 Sep 2021 16:00
Venue : via Zoom
Speaker : Duc-Manh Nguyen, University of Bordeaux

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

Meeting ID: 875 1147 6637
Passcode: 468399

Since the work of Eskin-Okounkov in 2001, it has been known that in any stratum of translation surfaces, the number of square-tiled surafces constructed from at most n squares grows like $c\pi^{2g}n^d$, where $d$ is the (complex) dimension of the stratum, $g$ is the genus of the surfaces, and $c$ is a rational number. Similar phenomena also occur in strata of quadratic differentials. Counting square-tiled surfaces in a given stratum is more or less the same as counting quadrangulations of a topological surface, with some constraints on the singularities and the holonomy of the associated flat metric. More recently, Engel showed that the asymptotics of the numbers of quadrangulations and triangulations with at most $n$ tiles are of the form $\alpha n^d$, where $\alpha$ is a constant in $Q[\pi]$ or $Q[\sqrt{3}\pi]$. In this talk, we will explain how the asymptotics above is related to the volume of some moduli spaces. Moreover, in some situations they can be computed from the self-intersection number of a divisor in some complex projective varieties. This implies in particular that the constant $\alpha$ belongs actually to either $Q\cdot\pi^d$, or  $Q\cdot(\sqrt{3}\pi)^d$ in those cases. This is joint work with Vincent Koziarz.

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Date/Time : 01 Sep 2021 16:00
Venue : via Zoom
Speaker : Elisha Falbel, Mathematics Institute of Jussieu–Paris Rive Gauche (IMJ-PRG)

Join Zoom Meeting https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09 Meeting ID: 875 1147 6637 Passcode: 468399 A path structure on a three-manifold is a contact structure (with fixed contact form) with a choice of two directions on each contact plane. It appears, for instance, in the theory of Anosov flows. I will explain how to classify such structures on a compact manifold with a large automorphism group extending a classification result of Ghys for Anosov flows. This is joint work with M. Mion-Mouton and J. M. Veloso.

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Date/Time : 17 Feb 2021 10:00
Venue : via Zoom
Speaker : Luo Yusheng, University of Michigan

Join Zoom Meeting https://nus-sg.zoom.us/j/83866564646?pwd=UnBpaEZqTjc1aXlZeGJZaEZCS2dqdz09 Meeting ID: 838 6656 4646 Password: 332346 Abstract:  The Sullivan dictionary provides a conceptual framework for understanding the connections between dynamics of rational maps and Kleinian groups. In this talk, we will explain how an explicit correspondence between kissing reflection groups and critically fixed anti-rational maps can be established. As an application, we show how this dynamical correspondence allows us to solve mating problems. We further establish a connection on the parameter/deformation space by proving an analogue of Thurston’s compactness theorem for acylindrical hyperbolic 3-manifolds in the rational map setting. If time permits, we will also talk about some open questions and further studies.

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Date/Time : 10 Feb 2021 17:00
Venue : via Zoom
Speaker : Thomas Peternell, University of Bayreuth

Join Zoom Meeting https://nus-sg.zoom.us/j/84061304664?pwd=NEkvd0V6djhFK3dtelBPbG41V3BTZz09 Meeting ID: 840 6130 4664 Password: 903906 Abstract:  I will discuss a Chern class criterion to when a semistable sheaf on a mildly singular variety is projectively flat and apply this to the uniformization of varieties with nef anticanonical bundles („ singular semipositive Ricci“).

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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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