Date/Time : 20 Aug 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Yongnam Lee, Institute for Basic Science

Motivated by DeVleming’s work on moduli of surfaces in P^3 and Chen-Hu-Jiang’s work on moduli of threefolds with volume 2 and geometric genus 4, we study the deformation of pairs of P^3 and hypersurfaces using the classification of Q-Gorenstein degenerations of P^3 with canonical singularities. We prove that if a degenerating threefold has canonical singularities, then the moduli space is smooth at the corresponding pair. Consequently, we find some boundary divisors of the moduli of smooth hypersurfaces. Finally, using the double cover method, we derive some information on the moduli space of threefolds X with canonical singularities with the same volume and geometric genus as a double cover of P^3 branched over a hypersurface. This is joint work with Jungkai Chen and Phin-Sing Soo.

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Date/Time : 20 Aug 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Minsung Kim, Pohang University of Science and Technology

In chaotic systems, the mixing property is known for the fast decay of correlation. It is called rapid mixing if the correlation function decays super-polynomially. The mixing mechanism for hyperbolic systems and their compact group extensions was studied by Dolgopyat in a series of his papers in the late 90s’.

In this talk, we prove rapid mixing for almost all random walks generated by m larger equal than 2 translations on an arbitrary nilmanifold. For several classical classes of nilmanifolds, we show m=2 suffices. This provides a partial answer to the question raised in the work of Dolgopyat (’02) about the prevalence of rapid mixing for random walks on homogeneous spaces.

This is joint work with Dmitry Dolgopyat and Spencer Durham.

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Date/Time : 12 Aug 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Wenfei Liu, Xiamen University

The set V of volumes of stable surfaces, as a subset of positive rational numbers, satisfies the descending chain condition. Equivalently, any nonempty subset of V attains the minimum.

In this talk, I will report a joint work with Jihao Liu, showing that the minimal volume of a stable surface with Picard rank 1 is 1/6351, uniquely realized by a normal rational stable surface previously constructed from P^2 with 4 lines by Valery Alexeev and Wenfei Liu.

In the proof of the minimum, we use various filters to narrow down the possible basket of singularities on such a surface.

The last and very crucial one, the so-called pluricanonical product-dimension filter, was suggested to us by the AI!

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Date/Time : 28 Jul 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Tianqi Wang, Yale University

We introduce notions of ending currents for properly discontinuous isometric actions of hyperbolic groups on Gromov hyperbolic spaces, generalizing Thurston’s ending laminations from the setting of Kleinian surface groups. In contrast with the 3-dimensional picture, we construct an example of geometrically finite representations of a closed surface group into $SO^+(4,1)$ whose parabolicity appears only at a non-simple closed geodesic, and an example of hyperbolic group extensions where different notions of ending currents, which coincide in the 3-dimensional setting, become distinct. This is joint work with Yair Minsky.

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Date/Time : 24 Jul 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Tsuyoshi Kato, Kyoto University

We associate to each proper discrete metric space X a Lie algebra that acts by locally generated derivations on an infinite tensor product of matrix algebras indexed by the points of X. We compute the homology of this Lie algebra with trivial scalar coefficients when X is the integer lattice in n-dimensional Euclidean space.

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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 : 30 Jun 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Yujie Luo, National University of Singapore

We explore the essential dimension of polarized endomorphisms on abelian varieties and its relation with algebraic dynamics. This talk is based on joint work with Keiji Oguiso and De-Qi Zhang.

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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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