Thursday, November 27, 2025

2025-12-03 / 16:00 ~ 18:00

학과 세미나/콜로퀴엄 - 위상수학 세미나: Symmetries on equivariant Khovanov homology

by Taketo Sano(RIKEN)

Khovanov homology is a knot homology theory, introduced by M. Khovanov in 2000 as a categorification of the Jones polynomial. Equivariant versions of Khovanov homology are also known, and they play an important role in understanding the Rasmussen invariant. In this talk, I will present the results established in my joint work with M. Khovanov in September 2025 (arXiv:2509.03785): (i) an order-two symmetry inherent in equivariant Khovanov homology, (ii) the existence of a signed Shumakovitch operator, and (iii) its relationship to the Rasmussen invariant.

2025-12-02 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 박사학위심사: 3차원 쌍곡다양체의 부피와 천-사이먼스 불변량의 재정규화

by 이동하(KAIST)

We renormalize the Chern-Simons invariant for convex-cocompact hyperbolic 3-manifolds, finding the explicit asymptotics along an equidistance foliation. We prove that the divergent terms are completely expressed in terms of the data from the Weitzenböck geometry of hyperbolic ends and the conformal boundary. For this, it is essential to extend the framework of submanifolds in Riemannian geometry to Riemann-Cartan geometry, which addresses connections with torsion. This procedure naturally introduces a complex-valued geometric quantity consisting of mean curvature and torsion 2-form, which appears in the leading coefficient of the asymptotics. We also obtain several geometric results regarding the complex-valued quantity that generalize classical minimal surface theory.

2025-12-01 / 16:00 ~ 17:30

편미분방정식 통합연구실 세미나 - 편미분방정식:

by ()

I will discuss recent progress on the vanishing-viscosity limit of the two-dimensional Navier–Stokes equation. Our approach is Lagrangian and probabilistic: 1. We develop a stochastic counterpart of the DiPerna–Lions theory to construct and control stochastic Lagrangian flows for the viscous dynamics. 2. We also establish a large-deviation principle that quantifies convergence to the Euler dynamics. This talk is based on joint work with Chanwoo Kim, Dohyun Kwon, and Jinsol Seo.

2025-12-02 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 조성웅(인하대학교 데이터사이언스학과)

Neural networks have become increasingly effective for approximating solutions to partial differential equations (PDEs). This talk presents three advances that improve both accuracy and computational efficiency. First, I introduce an augmented Lagrangian formulation of the physics-informed loss that strengthens constraint enforcement and improves accuracy near domain boundaries. Second, I develop efficient architectures based on hypernetworks and graph neural networks that learn PDE solution operators with markedly small model sizes. Finally, I describe Neural-Galerkin schemes with low rank approximations for operator learning, which achieves a favorable accuracy-efficiency trade-off.

2025-12-04 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나: Invariants for Persistence Homology

by 김동한(KAIST)

TBA

2025-12-04 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 오병권(서울대학교 수리과학부)

A (positive definite and integral) quadratic form $f$ is called irrecoverable (from its subforms) if there is a quadratic form $F$ that represents all proper subforms except for $f$ itself, and such a quadratic form $F$ is called an isolation of $f$. In this talk, we present recent advances on irrecoverable quadratic forms and discuss their possible generalizations.

Events for the 취소된 행사 포함