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 : 15 Jul 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Wang Hao, Sichuan University

Solid-state phase transitions typically follow a Minimum Energy Path (MEP). Classical methods such as G-SSNEB compute the MEP in the full high-dimensional configuration space, which becomes prohibitive when paths must be scanned over pressures, defect types, and system sizes. We propose the Preset Structure Strain Path (PSSP) method, which uses feature extraction and transfer learning to compute MEPs efficiently across these conditions. PSSP is based on the fact that in defective systems, lattice strain sets the direction of the MEP, while the local atomistic environment changes little but governs the energy. PSSP fully exploits this separation by presetting the displacement field as a transferable feature and optimizing only the lattice evolution in a low-dimensional space. By doing this, the strain paths learned in one setting can be reused under different pressures, defects and system sizes. The advantage of PSSP is verified that it reduces the energy and force evaluations to less than 2% of G-SSNEB but preserving the accuracy of the energy barrier in a satisfactory level.

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Date/Time : 15 Jul 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Luca Makowiec, Leipzig University

In this talk, we consider a special instance of a random spanning tree in random environment on the complete graph. Each edge is given weight infinity with probability 1/|V| and weight one otherwise. We will discuss a result about the approximate order of the diameter of this tree. In particular, we will explain how a critical Erdős–Rényi graph formed by the infinite-weight edges influences the geometry of the spanning tree. Along the way, we will encounter interesting results and proof techniques associated with the birthday problem and their relation to (weighted) uniform spanning trees (USTs).

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Date/Time : 08 Jul 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Jean-Bernard Lasserre, LAAS-CNRS

Anomaly detection plays a critical role in identifying unusual patterns across domains such as fraud detection, network intrusion, and system fault diagnosis. Relatively recently, Christoffel Function (CF) based methods have emerged as powerful and easy-to-use tools for support inference and outlier (or anomaly) detection in data mining.  However in their original form, their suffer from a scalability issue even for moderate data dimension. In this talk we describe two ways of addressing this challenge.

In a first direction we briefly describe how to construct a Christoffel-like rational function when $\mu satisfies a correlative sparsity pattern associated with a graphical model. Its computational complexity is parametrized by the tree-width of the associated graph. In a second direction we consider the general cas with no assumption on the underlying measure $\mu$ associated with the data cloud. One introduces the mapping $y\mapsto g_x(y):=norm(x-y)^2$ and the CF associated the univariate pushforward $\nu_x$ of $\mu$ by $g_x$. The score function is now the CF of $\nu_x$ evaluated at $z=0$ (and so must be recomputed when $x$ changes). We describe its remarkable properties for support inference and density approximation, and Its efficiency on a large set of benchmarks.

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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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