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2025 KIAS HCMC
Upcoming Talks
April 17 (Thu) 2025, 16:00~17:00 - HCMC Seminar Room
Speaker: Sanghyeon Lee (Ajou University)
Title: Quasimaps and quasisections to the moduli space of sheaves
For a threefold X = C x S, D. Nesterov developed a theory of quasimaps from C to the moduli space of sheaves over S, and compared the moduli space of quasimaps and the moduli space of sheaves over the threefold X and also compared their obstruction theories. In an ongoing project with Yaoxiong Wen, we generalized Nesterov's theory for the case when the threefold X is a smooth fibration over C. As an application, we computed Vafa-Witten invariant of elliptic surfaces, which are smooth fibration over C. In this talk, I will introduce these theories of quasimaps and quasisections. Moreover, for the case when the elliptic surface has nodal fibers, we will discuss how we can generalize the theory of quasisections.
May 7 (Wed) 2025, 15:00~16:00 - HCMC Seminar Room
Speaker: Jaehyeok Lee (Seoul National University)
May 7 (Wed) 2025, 16:30~17:30 - HCMC Seminar Room
Speaker: Jong In Han (KIAS)
Title: Recursive Koszul flattenings of determinant and permanent tensors
We investigate new lower bounds on the tensor rank of the determinant and the permanent tensors via recursive usage of the Koszul flattening method introduced by Landsberg-Ottaviani and Hauenstein-Oeding-Ottaviani-Sommese. Our lower bounds on the rank of the determinant tensor of order n completely separate the determinant and the permanent tensors by their tensor ranks. Furthermore, we determine the exact tensor ranks of the determinant tensor of order 4 and the permanent tensor of order 4 over arbitrary field of characteristic ≠ 2.
Previous Talks
March 20 (Thu) 2025, 14:00~15:00 - HCMC Seminar Room
Speaker: Woonam Lim (Yonsei University)
Title: Nekrasov’s gauge origami via DT4 theory
The study of the classical instantons on the spacetime has led to many interesting mathematics. In a series of papers, Nekrasov introduced and studied the generalised ADHM equations, whose solutions are instantons on the “origami spacetime”. In this talk, I will explain how to interpret Nekrasov’s gauge origami via DT4 theory. Our main result computes the orientation in the Oh-Thomas localisation formula and matches it with the definition from physics. If time permits, I will discuss some applications and a conjectural sheaf-theoretic description of the gauge origami theory. This is joint work in progress with N. Arbesfeld and M. Kool.
Organizers
Junho Choe, Jong In Han, In-Kyun Kim, Jeong-Seop Kim, Hyeonjun Park
supported by June E Huh Center for Mathematical Challenges at Korea Institute for Advanced Study
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