Date/Time : 16 Mar 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Svetlana Makarova, Australian National University

When introducing the notion of moduli problems, perhaps the most trivial example one may consider is the “functor of points” of a variety X, whose “classifying space” (moduli space) is X itself. Its very close relative is the stack of ideal sheaves of length 1 subschemes: when X is normal and of dimension at least 2, this stack is the product of X with BG_m. Despite the apparent triviality, modifying this stack gives rise to interesting birational phenomena, about which I will speak. I will describe a certain enlargement U of the stack of ideal sheaves that yields, via taking the good moduli space, a birational contraction of X, and an open substack of U that yields a surgery diagram via non-GIT wall-crossing. If time permits, I will explain how the interpretation of the surgery as a fine moduli of sheaves helps prove instances Kawamata’s DK-hypothesis in this setting. This is joint work with Andres Fernandez Herrero (https://arxiv.org/abs/2508.13395).

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Date/Time : 11 Mar 2026 16:15
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Viet-Anh Nguyen, Universite de Lille

Let T be a positive dd^c-closed current of bidimension (1,1) on a projective manifold X. We show that for every c > 0 the set of points of X where the Lelong number of T is larger or equal to c is an analytic subset of dimension at most 1 of X. Moreover, the following Siu decomposition holds

T=\sum_{i\in I} λ_i[V_i] + T_0,

where {V_i}_{i\in I} is a (possibly empty) finite or countable family of compact analytic curves
in X, λ_i\in R^+, and T_0 is a positive dd^c-closed current of bidimension (1,1) on X whose Lelong number vanishes outside a finite or countable set. As a consequence, the cohomology class of every positive dd^c-closed current of bidimension (1,1) on X, which does not give mass to any proper analytic set, belongs to the movable cone M. This is a joint-work with Tien-Cuong Dinh.

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Date/Time : 06 Mar 2026 13:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ralf Spatzier, University of Michigan

I will discuss ideas in the proof of Margulis’ super rigidity theorem and Zimmer’s cocycle rigidity theorem.

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Date/Time : 04 Mar 2026 14:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ralf Spatzier, University of Michigan

I will introduce the main ingredients for classifying hyperbolic  higher rank habelian actions.

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Date/Time : 26 Feb 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Lingrui Ge, Peking University

We develop the dual based approach and introduce several new concepts and tools for the study of one-frequency quasiperiodic operators with analytic potentials. As applications we solve some long-standing arithmetic conjectures: the ten martini problem, sharp phase transition in frequency and absolute continuity of the integrated density of states, for the entire class of type I operators.

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Date/Time : 04 Feb 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Ngoc Cuong Nguyen, Kora Advanced Institute of Science & Technology

We study comprehensively local properties of functions in complex Sobolev spaces, introduced by Dinh and Sibony (2006), on a bounded open sub-set of C^n. The main tool is the corresponding functional capacity for the space which is inspired by the global one due to Vigny (2007). An inequality between this capacity and the Bedford-Taylor capacity for plurisubharmonic functions is proved, which is sharp as far as the exponents are concerned. Moreover, it is shown that the functional capacity is a Choquet capacity. The Alexander-Taylor type inequality for the capacity is also proved. This allows us to strengthen the results in the works of Dinh, Marinescu and Vu (2023), Vigny and Vu (2024).

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Date/Time : 04 Feb 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Dano Kim, Seoul National University

The theory of L2 extension theorems is a central topic in several complex variables with numerous applications to complex/algebraic geometry and complex analysis. They are analogous to vanishing theorems in algebraic geometry and often serve as a stronger counterpart of vanishing as exemplified in the proof of Siu’s invariance of plurigenera. In this talk, in the opposite direction, I will discuss how certain ideas from algebraic geometry are crucially used in answering a question raised by Demailly on understanding general L2 extension theorems, via the theory of log canonical pairs. This talk is partly based on joint work with Xu Wang (Trondheim).

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Date/Time : 04 Feb 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Asbjørn Nordentoft, University of Copenhagen

To any thin subgroup of a finite co-volume Fuchsian group one can associate a hyperbolic orbifold with geodesic boundary. The projection of the geodesic boundary gives a stratification (or partition) of the set of all thin subgroups. In this talk I will explain how in some cases one can understand the fibers of this stratification. This is related to the problem of lifting closed geodesics ‘simply and separating’. In the case of the modular group this gives a new and geometric perspective on a construction of Duke, Imamoglu and Toth using (minus) continued fractions.

This is joint work in progress with Ser Peow Tan

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Date/Time : 21 Jan 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Ming Hong Tee, Boston College

Given any Jordan domain U in the Riemann sphere equipped with the hyperbolic metric, one can construct the Epstein surface in hyperbolic 3 space corresponding to it. One important property of the Epstein surface is that its principal curvatures are related to the Schwazian derivative of the uniformization map of U. In this talk, we will exploit this property to relate the bending lamination of a pleated surface with the Schwazian derivative. Furthermore, if U is a domain for a Weil-Peterson curve, we will show that the hyperbolic metric and the quasi-hyperbolic metric are arbitrary closed and the two corresponding Epstein surfaces are arbitrary closed.

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