Date/Time : 08 Apr 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Fabrizio Bianchi , University of Pisa, Italy

Around 1980, Ruelle gave an explicit second-order expansion at c=0 of the Hausdorff dimension of the Julia set of the quadratic family f_c(z)=z^2+c. McMullen later extended this result to polynomial perturbations of z^d for arbitrary degree d. I will discuss an analogue of this problem and formula for skew-product maps of C^2. This is a joint work with Yan Mary He.

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Date/Time : 06 Apr 2026 10:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Siyuan Tang, Xiamen University

We study the dynamics of $SL_{2}(\mathbb{R})$ on the stratum of translation surfaces. In particular, we obtain an effective closing lemma on $\mathcal{H}(2)$. More precisely, we show that unless a small discriminant Teichmüller curve near $x\in\mathcal{H}(2)$, the geodesic push-forward of horocycle orbit $a_{t}u_{[0,1]}x$ has the discretized fractal dimension near 1 in a direction transverse to the $SL_{2}(\mathbb{R})$-orbit. The proofs make use of spectral gaps, of the Margulis function technique, and of the classification of Teichmüller curves in $\mathcal{H}(2)$.

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Date/Time : 25 Mar 2026 14:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Farhad Babaee, University of Bristol

I will discuss several basic concepts in tropical geometry and explain how certain results in tropical geometry can be understood within the framework of the continuity of slices of tropical currents. This talk is based on joint work with Tien Cuong Dinh.

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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 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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