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2025 KIAS HCMC
Upcoming Talks
Previous Talks
September 29 (Mon) 2025, 14:30~15:30 - HCMC Seminar Room
Speaker: Chenjing Bu (Oxford)
Title: Counting sheaves on curves
Counting sheaves on curves, or more precisely, computing intersection pairings on the moduli space of semistable vector bundles on curves, has been a classical problem in enumerative geometry. The computation was first done by Witten using physical methods; his formula was later proved by Jeffrey–Kirwan, and generalized by Jeffrey–Kiem–Kirwan–Woolf to the case when the rank and the degree are not coprime.
In this talk, I will introduce a new approach to the problem using the wall-crossing formalism developed by Joyce. This allows us to obtain a new formula for these intersection pairings, different from but equivalent to Witten's. The new formula involves a divergent infinite sum in Joyce's vertex algebra. It would be interesting to explore possible geometric or physical interpretations of this formula.
September 29 (Mon) 2025, 16:00~17:00 - HCMC Seminar Room
Speaker: Yaoxiong Wen (KIAS)
Title: Quiver Mutation Conjecture
The quiver mutation conjecture, mathematically formulated by Ruan and also known in the physics literature as Seiberg-like duality, predicts an equivalence between two gauged linear sigma models associated to quivers (with super-potentials) related by mutation. In this talk, I will present a stronger geometric result of quiver mutation, highlighting new structural insights and potential applications. The results are part of ongoing joint work with Yingchun Zhang and Zijun Zhou.
September 4 (Thu) 2025, 16:00~17:00 - HCMC Seminar Room
Speaker: You-Cheng Chou (KIAS)
Title: Genus 1 quantum K-theory over a point
In this talk, I will explain a method for computing the Euler characteristics of the universal cotangent line bundle over \overline{M}_{1,n}. The approach involves a recursive pushforward technique applied to the universal cotangent line bundle and pluri-Hodge sheaf. This technique is combinatorially easier for not using Kawasaki-Hirzebruch-Riemann-Roch theorem. As a result, we obtain a closed formula. This is a joint work with Y.-P. Lee.
September 4 (Thu) 2025, 14:30~15:30 - HCMC Seminar Room
Speaker: Parvez Rasul (KIAS)
Title: Irreducibility and Singularities of Quot Schemes over Curves
Let C be an integral projective curve of arithmetic genus g ⩾ 2 over the field of complex numbers and let E be a vector bundle on C. The Quot scheme QuotC(E,k,d) parametrizes quotients of E of rank k and degree d. Quot schemes play a central role in understanding the geometry of moduli spaces of sheaves and have important applications in enumerative geometry. In this talk, we will discuss geometric properties of the Quot scheme QuotC(E,k,d), focusing on irreducibility and singularities. We will also see results on Nested Quot schemes which parametrize chains of successive quotients.
July 23 (Wed) 2025, 16:00~17:00 - HCMC Seminar Room
Speaker: Leonid Makar-Limanov (Wayne State University)
Title: On potential counterexamples to the two-dimensional Jacobian Conjecture
In the talk I discuss what can be said about algebraic and geometric properties of a counterexample to the two-dimensional Jacobian Conjecture.
July 7 (Mon) 2025, 16:00~17:00 - HCMC Seminar Room
Speaker: Yen-An Chen (KIAS)
Title: Title: Unstable weak del Pezzo surfaces
The geometry of Fano varieties plays a vital role in birational geometry. In this talk, we will explore and classify all canonical weak del Pezzo surfaces with unstable tangent sheaf. The main ingredient is the theory of algebraically integrable foliations. As a byproduct, there exist singular unstable del Pezzo surfaces that admit a weak Kahler-Einstein metric. This is an ongoing collaboration with Ching-Jui Lai.
May 29 (Thu) 2025, 16:00~17:00 - HCMC Seminar Room
Speaker: Haesong Seo (KAIST)
Title: Algebraic hyperbolicity of surfaces in Fano threefolds with Picard number one
By Liouville's theorem, a compact Riemann surface of genus g ≥ 2, or more generally a ball quotient, does not admit a non-constant holomorphic map from the complex plane — such a map is called an entire curve. This motivates the generalized notion of (Brody) hyperbolicity: a complex manifold X is called hyperbolic if it has no entire curve. This concept is closely related to an algebraic nature via the notion of algebraic hyperbolicity, where we require lower bounds of the genera of curves in terms of their degree. In this talk, I will introduce some basic techniques and recent results in the study of algebraic hyperbolicity. I will then present my results on the classification of algebraic hyperbolicity of very general surfaces in general Fano threefolds with Picard number one.
May 29 (Thu) 2025, 14:30~15:30 - HCMC Seminar Room
Speaker: Joonyeong Won (Ewha Womans University)
Title: On singular del Pezzo surfaces embedded in weighted projective spaces
The smooth del Pezzo surfaces are among the most familiar, and fundamental, objects in algebraic geometry. As a generalization of it, we discuss some properies of singular del Pezzo surfaces embedded in weighted projective spaces, in particular, K-stability and the existence of K-polar cylinder.
May 22 (Thu) 2025, 14:30~15:30 - HCMC Seminar Room
Speaker: Meng Chen (SCMS, Fudan)
Title: The Noether inequality for 3-folds and some moduli spaces
In this lecture, I will present a complete proof for the 3-dimensional Noether inequality. As an application of the method, I will introduce the advancement on the study of moduli spaces of some 3-folds of general type.
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. This is a joint work with Jeong-Hoon Ju and Yeongrak Kim.
May 7 (Wed) 2025, 15:00~16:00 - HCMC Seminar Room
Speaker: Jaehyeok Lee (Seoul National University)
Title: Prekosmic Grothendieck/Galois categories
In this talk, I will present a duality between mathematical objects equipped with group structures and the categories of their internal representations. We establish the duality by providing a complete abstract characterization of such categories. The primary motivation is to simultaneously generalize and unify the two categorical concepts, Galois categories and Tannakian categories. I will explain the motivation and a concrete example in detail. Then I will explain that the duality exists in a general context, namely over a prekosmos. This is a joint work with Jae-Suk Park.
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.
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, 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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