[2024 Spring Semester]
지정 날짜 수요일 12:00
운영위원 : 표성인 ( luinn27@ajou.ac.kr, 팔달관 426호 )
감독위원 : 유성현( yoosh0319 @ajou.ac.kr, 팔달관 622호 )
Title : Real toric spaces associated with chordal nestohedra
Abstract : For any chordal building set B, we provide an explicit description of the cohomology ring of the real toric space associated with the nestohedron of B in terms of alternating B-permutations.
Title : Cohomological rigidity of toric manifolds over the connected sum of three n-simplices
Abstract : The cohomological rigidity problem for toric manifold poses the question as to whether two toric manifolds are diffeomorphic if their cohomology rings are isomorphic as graded rings. We solved the cohomological rigidity problem for toric manifolds over the connected sum of three n-simplices.
Title : Strong odd coloring of sparse graphs
Abstract : Recently, various colorings were introduced that relaxing the conditions of square coloring such as odd coloring, proper conflict-free coloring, and strong odd coloring. In this talk, we introduce the definitions of several relaxations and its recent results.
Title : Clustering analysis for multi-dimensional longitudinal data based on Fréchet distance
Abstract : Longitudinal data clustering is not accessable with traditional clustering methods hence structural features of time series data. Longitudinal data consists of multiple tragectories with time points and several data points. Therefore, well-known distance measures used in clustering cannot be applied to measure the distance among tragectories, hence each tragectory contains its time-based trend. In this talk, distance measure which suits to time-based data, called Frechet distance and MFkml(Multi-dimensional Frechet K-means for Longitudinal data) will be introduced.
Title : Deep Learning based Color Regression Model
Abstract : I am conducting research using a deep learning regression model to correct the color of images captured by cameras to more closely match what we see with the human eye. This model aims to reduce color distortions that can occur during camera capture. It takes the captured image data as input and produces an output that adjusts the colors to be closer to human vision. This process aims to achieve a more accurate and natural reproduction of image.
Title : The Fermat's last theorem for regular primes
Abstract : There have been many attempts to prove the Fermat's last Theorem. One partially successful attempt is Kummer's proof. Kummer focused on the case of regular primes by using properties of ideal factorization in cyclotomic extensions. In this talk I will introduce Kummer's proof.
Title : Toric wedge induction
Abstract : A toric space is a topological space equipped with a well-behaved torus action, and a real toric space is its real analogue. It is well-known that they are closely related to simplicial complexes. In this talk, we introduce toric wedge induction, which is a powerful tool for investigating properties on a set of (real) toric spaces in terms of simplicial complexes, and prove the lifting problem in toric topology on the set of real toric spaces associated with piecewise linear spheres with few vertices as an application.
This is joint work with Suyoung Choi and Mathieu Vall\'ee.
Title : Dynamic Word Embeddings for Semantic Analysis
Abstract : In this talk, we introduces a novel approach to studying word evolution, focusing on the changing meanings and associations of words over time. Traditional methods often struggle to capture these shifts effectively. We propose a dynamic statistical model that learns time-aware word vector representations by addressing the alignment problem. Trained on a dataset from The New York Times, our model outperforms existing approaches in both semantic accuracy and alignment quality.
Title : Prediction of Underground Utility Locations Using TDA and YOLO
Abstract : Non-destructive testing is crucial for maintaining and inspecting infrastructure. Among the various methods, Ground Penetrating Radar (GPR) stands out for its effectiveness. This study aims to detect the location of underground utility, epically for pipes. We use Topological Data Analysis (TDA) and the YOLO (You Only Look Once) algorithm. TDA is employed to extract essential features from the GPR data, while YOLO is utilized for object detection and localization. This study reveals features extracted by TDA can improve the accuracy of the predicting the location of underground utilities. The analysis revealed that the integration of TDA and YOLO provides a robust and effective approach for detecting the underground utilities.
Title : Various Methods for Numerical Analysis of Elliptic Partial Differential Equations
Abstract : Partial differential equations can be solved using various numerical methods. In this talk, we will discuss how to solve the Poisson equation using the Finite Element Method (FEM), Discontinuous Galerkin Method (DG), and Hybrid Discontinuous Galerkin Method (HDG). Additionally, we will cover how to implement these methods on a computer to solve the equation.
Title : Deep Learning based PDE Solver
Abstract : Partial differential equations (PDEs) are crucial in modeling various physical phenomena. In this study, we introduce a novel deep learning approach to solve the Poisson equation using convolutional autoencoders. Our method leverages a dataset of function pairs representing source terms and boundary conditions to train the autoencoder model. Once trained, the model can efficiently and rapidly approximate solutions to the Poisson equation for new source terms and boundary conditions without additional training. This approach eliminates the reliance on traditional numerical methods such as the Finite Element Method (FEM), offering significant advantages in terms of inference speed and flexibility. Our results highlight the potential of neural networks to provide accurate solutions for PDEs with non-homogeneous boundary conditions and varying source terms, demonstrating the effectiveness of data-driven models in solving complex physical problems.