Date/Time : 03 Jul 2026 10:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Laura Schaposnik, University of Illinois Urbana-Champaign

The moduli space of Higgs bundles carries several natural geometric structures, making it a central example in the study of mirror symmetry and gauge theory. In this lecture we will explore special subspaces of Higgs bundle moduli spaces, often called branes, and explain how they arise from symmetries, real forms, and geometric constraints. We will discuss their interpretation through flat connections and surface group representations, and describe how different types of branes are related through natural correspondences, and how they can be seen through the Hitchin fibration. The goal is to illustrate how Higgs bundles connect algebraic geometry, representation theory, and ideas from mathematical physics.

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Date/Time : 29 Jun 2026 10:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Laura Schaposnik, University of Illinois Urbana-Champaign

Higgs bundles provide a rich meeting point between algebraic geometry, differential geometry, gauge theory, and mathematical physics. In this lecture we will introduce the basic objects: vector bundles on a Riemann surface equipped with Higgs fields, their stability condition, and the construction of the corresponding moduli spaces. We will then discuss the Hitchin fibration, one of the central structures in the theory, and explain how spectral curves encode much of the geometry of Higgs bundles. The lecture will emphasize the interplay between moduli spaces, integrable systems, and the geometric structures that make Higgs bundles such powerful objects.

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Date/Time : 10 Jun 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Wilderich Tuschmann, Karlsruher Institute of Technology

At its core, the Manifold Hypothesis asserts that real-world, high-dimensional data is not uniformly or randomly distributed throughout its high-dimensional “ambient” space, but concentrated on or near a low-dimensional manifold (or a collection of manifolds) embedded within that high-dimensional ambient space.

In my talk, I will discuss reasons and facts that speak for as well as against this hypothesis as well as address geometric alternatives.

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Date/Time : 20 May 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Doan Nhat Minh, Vietnam Academy of Science and Technology

Simple closed geodesics on a once-punctured torus are naturally organized by primitive homology classes, and their lengths can be studied through the McShane-Rivin norm ball. In this talk, I will explain how estimates on the normal turn of the boundary of this norm ball give a new polylogarithmic bound for length multiplicities: On every complete finite-area hyperbolic once-punctured torus X, the number of simple closed geodesics of any fixed length L is at most C_X(log L)^2. For the modular torus, this translates into a bound of order (log(log(3m)))^2 for Markoff fibers, improving previously known logarithmic estimates. If time permits, I will also discuss how the same normal-turn estimates give some new quantitative information about the local geometry of McShane-Rivin norm balls. This is joint work with Xiaobin Li and Van Nguyen.

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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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