31 citations · 113 across the 46 of their papers we have counts for
49 papers
HypLTSF: A Hyperbolic Geometric View of Multi-Scale Hierarchies for Long-Term Time Series Forecasting
Namwoo Kim, Hyungryul Baik, Yoonjin Yoon
Multi-scale modeling has become an effective approach for long-term time series forecasting, capturing temporal patterns that range from fine-grained local dynamics to coarse globa…
Lean-GAP: A Dataset of Formalized Graduate Algebra Problems
Seewoo Lee, Byung-Hak Hwang, Hyojae Lim +10
We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pi…
Co-Hopfianity is not a profinite property
Hyungryul Baik, Wonyong Jang
We exhibit two finitely generated residually finite groups and with isomorphic profinite completions , such that is co-Hopfian while …
Random Groups at Density : Sharp Length Inequalities for Generalized Torsion and a Fixed-width Exclusion via First-order Transfer
Hyungryul Baik
Let be a random group in Gromov's density model with . We prove a sharp quantitative constraint on products of conjugates equal to the identity: for ever…
Optimizing the Upper-Bound Constant for the Crossing Number of Polynomial Curve Systems
Hyungryul Baik
Baader, Jörg, and Parlier recently established an upper bound for the crossing number of curve systems of size on a genus surface, obtaining a leading coeffic…
Uniform Perfectness and Centers in Sublinearly Morse Boundaries
Hyungryul Baik
The --Morse boundary was introduced for CAT(0) spaces by Qing and Rafi and extended to proper geodesic spaces by Qing, Rafi, and Tiozzo. Motivated by Han and Liu's work on unifo…
Normal generators for mapping class groups
Hyungryul Baik, Dongryul M. Kim
In this chapter, we discuss normal generators for mapping class groups of surfaces. Especially, we focus on the relation between normal generation of a mapping class with its asymp…
TopoCL: Topological Contrastive Learning for Time Series
Namwoo Kim, Hyungryul Baik, Yoonjin Yoon
Universal time series representation learning is challenging but valuable in real-world applications such as classification, anomaly detection, and forecasting. Recently, contrasti…
Reconstruction of Anosov flows from infinity
Hyungryul Baik, Chenxi Wu, Bojun Zhao
Every pseudo-Anosov flow in a closed -manifold gives rise to an action of on a circle from infinity \cite{Fen12}, with a pair of invariant \…
Acylindrical hyperbolicity of outer automorphism groups of right-angled Artin groups
Hyungryul Baik, Junseok Kim
We study the acylindrical hyperbolicity of the outer automorphism group of a right-angled Artin group . When the defining graph has no SIL-pair (separating intersection of…
On the kernel of actions on asymptotic cones
Hyungryul Baik, Wonyong Jang
Any finitely generated group acts on its asymptotic cones in natural ways. The purpose of this paper is to calculate the kernel of such actions. First, we show that when is…
Monodromy through bifurcation locus of the Mandelbrot set
Hyungryul Baik, Juhun Baik
We investigate the behavior of itinerary sequence of each point of the Julia set of when the parameter in the shift locus is allowed to pass through points i…
On Translation Lengths of Pseudo-Anosov Maps on the Curve Graph
Hyungryul Baik, Changsub Kim
We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We a…
Groups acting on veering pairs and Kleinian groups
Hyungryul Baik, Hongtaek Jung, KyeongRo Kim
We show that some laminar group which has an invariant veering pair of laminations is a hyperbolic 3-orbifold group. On the way, we show that from a veering pair of laminations, on…
Topological entropy of pseudo-Anosov maps on punctured surfaces vs. homology of mapping tori
Hyungryul Baik, Juhun Baik, Changsub Kim +1
We investigate the relation between the topological entropy of pseudo-Anosov maps on surfaces with punctures and the rank of the first homology of their mapping tori. On the surfac…
Reducible normal generators for mapping class groups are abundant
Hyungryul Baik, Dongryul M. Kim, Chenxi Wu
In this article, we study the normal generation of the mapping class group. We first show that a mapping class is a normal generator if its restriction on the invariant subsurface…
Random walks on mapping class groups
Inhyeok Choi, Hyungryul Baik
This survey is concerned with random walks on mapping class groups. We illustrate how the actions of mapping class groups on Teichmüller spaces or curve complexes reveal the nature…
Characterization of Fuchsian groups as laminar groups & the structure theorem of hyperbolic 2-orbifolds
Hyungryul Baik, KyeongRo Kim
Thurston and Calegari-Dunfield showed that the fundamental group of some tautly foliated hyperbolic 3-manifold acts on the circle in a distinctive way that the action preserves som…
Foliations from left orders
Hyungryul Baik, Sebastian Hensel, Chenxi Wu
We describe a construction which takes as an input a left order of the fundamental group of a manifold, and outputs a (singular) foliation of this manifold which is analogous to a…
Minimal asymptotic translation lengths on curve complexes and homology of mapping tori
Hyungryul Baik, Dongryul M. Kim, Chenxi Wu
Let be a closed orientable surface of genus . Consider the minimal asymptotic translation length on the Teichmüller space of , among pseud…
On the finiteness property of hyperbolic simplicial actions: the right-angled Artin groups and their extension graphs
Hyungryul Baik, Donggyun Seo, Hyunshik Shin
We study the right-angled Artin group action on the extension graph. We show that this action satisfies a certain finiteness property, which is a variation of a condition introduce…
Linear growth of translation lengths of random isometries on Gromov hyperbolic spaces and Teichmüller spaces
Hyungryul Baik, Inhyeok Choi, Dongryul M. Kim
We investigate the translation lengths of group elements that arise in random walks on the isometry groups of Gromov hyperbolic spaces. In particular, without any moment condition,…
Simple length spectra as moduli for hyperbolic surfaces and rigidity of length identities
Hyungryul Baik, Inhyeok Choi, Dongryul M. Kim
In this article, we revisit classical length identities enjoyed by simple closed curves on hyperbolic surfaces. We state and prove the rigidity of such identities over Teichmüller…
On the asymptotic translation lengths on the sphere complexes and the generalized fibered cone
Hyungryul Baik, Dongryul M. Kim, Chenxi Wu
In this paper, we study the asymptotic translation lengths on the sphere complexes of monodromies of a manifold fibered over the circle. Given a compact mapping torus, we define a…