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 : 13 Aug 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Boaz Klartag, Tel Aviv University and Weizmann Institute of Science

We survey progress from the past five years on the distribution of mass in high-dimensional convex bodies and in probability distributions with convexity properties. The concentration of measure phenomenon has traditionally been studied in highly regular or structured settings, such as spheres, Hamming cubes, Gaussian measures, Markov chains, and martingales. It turns out that convexity assumptions provide an alternative source of regularity in high dimensions with remarkably similar features: Lipschitz functions are highly concentrated, the isoperimetric problem is nearly saturated by half-spaces (up to logarithmic factors), and the central limit theorem is nearly as strong as in the setting of independent random variables. The main developments discussed include the resolution of Bourgain’s slicing problem and the Variance Conjecture, as well as recent progress on the isoperimetric problem for high-dimensional convex bodies. Based on joint work with P. Bizeul and J. Lehec.

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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 : 12 Aug 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Boaz Klartag, Tel Aviv University and Weizmann Institute of Science

We prove there exists a lattice sphere packing in R^n whose density is at least c n^2 / 2^n, where c > 0 is a universal constant. Previously known constructions of sphere packings in R^n had densities of the order of magnitude of n / 2^n, up to logarithmic factors. Our proof utilizes a stochastically evolving ellipsoid that accumulates at least c n^2 lattice points on its boundary, while containing no lattice points in its interior except for the origin.

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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 : 15 Jul 2026 14:00
Venue : S17 #05-11 (Seminar Room 5)
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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