Tuesday, November 22, 2022

2022-11-29 / 17:00 ~ 18:00

IBS-KAIST 세미나 - 대수기하학: A 1-dimensional component of K-moduli of del Pezzo surfaces

by Andrea Petracci(Università di Bologna)

Fano varieties are algebraic varieties with positive curvature; they are basic building blocks of algebraic varieties. Great progress has been recently made by Xu et al. to construct moduli spaces of Fano varieties by using K-stability (which is related to the existence of Kähler-Einstein metrics). These moduli spaces are called K-moduli. In this talk I will explain how to easily deduce some geometric properties of K-moduli by using toric geometry and deformation theory. In particular, I will show how to construct a 1-dimensional component of K-moduli which parametrises certain K-polystable del Pezzo surfaces. * ZOOM information will not be provided. Please send an email to Jinhyung Park if you are interested in.

2022-11-28 / 10:40 ~ 11:40

학과 세미나/콜로퀴엄 - 박사논문심사:

by 김창섭(KAIST)()

2022-11-28 / 09:30 ~ 10:30

학과 세미나/콜로퀴엄 - 박사논문심사:

by 정성구(KAIST)()

2022-11-22 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: A proof of the Elliott-Rödl conjecture on hypertrees in Steiner triple systems

by 임성혁(KAIST / IBS 극단조합및확률그룹)

A linear $3$-graph is called a (3-)hypertree if there exists exactly one path between each pair of two distinct vertices. A linear $3$-graph is called a Steiner triple system if each pair of two distinct vertices belong to a unique edge. A simple greedy algorithm shows that every $n$-vertex Steiner triple system $G$ contains all hypertrees $T$ of order at most $\frac{n+3}{2}$. On the other hand, it is not immediately clear whether one can always find larger hypertrees in $G$. In 2011, Goodall and de Mier proved that a Steiner triple system $G$ contains at least one spanning tree. However, one cannot expect the Steiner triple system to contain all possible spanning trees, as there are many Steiner triple systems that avoid numerous spanning trees as subgraphs. Hence it is natural to wonder how much one can improve the bound from the greedy algorithm. Indeed, Elliott and Rödl conjectured that an $n$-vertex Steiner triple system $G$ contains all hypertrees of order at most $(1-o(1))n$. We prove the conjecture by Elliott and Rödl. This is joint work with Jaehoon Kim, Joonkyung Lee, and Abhishek Methuku.

2022-11-23 / 16:00 ~ 17:00

IBS-KAIST 세미나 - 수리생물학:

by ()

TBD

2022-11-23 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - 정수론:

by ()

Let $E$ be a number field and $X$ a smooth geometrically connected variety defined over a characteristic $p$ finite field. Given an $n$-dimensional pure $E$-compatible system of semisimple $\lambda$-adic representations of the \'etale fundamental group of $X$ with connected algebraic monodromy groups $\bG_\lambda$, we construct a common $E$-form $\bG$ of all the groups $\bG_\lambda$ and in the absolutely irreducible case, a common $E$-form $\bG\hookrightarrow\GL_{n,E}$ of all the tautological representations $\bG_\lambda\hookrightarrow\GL_{n,E_\lambda}$. Analogous rationality results in characteristic $p$ assuming the existence of crystalline companions in $\mathrm{\textbf{F-Isoc}}^{\dagger}(X)\otimes E_{v}$ for all $v|p$ and in characteristic zero assuming ordinariness are also obtained. Applications include a construction of $\bG$-compatible system from some $\GL_n$-compatible system and some results predicted by the Mumford-Tate conjecture. (If you would like to join this seminar please contact Bo-Hae Im to get the zoom link.)

2022-11-22 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - Mathematics & Beyond Seminar:

by 최찬오 세무사(법무법인 태평양)

2022-11-25 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나:

by 문일철,김동준(KAIST 산업및시스템공학과)

Deep generative models (DGM) have been an intersection between the probabilistic modeling and the machine learning communities. Particularly, DGM has impacted the field by introducing VAE, GAN, Flow, and recently Diffusion models with its capability to learn the data density of datasets. While there are many model variations in DGM, there are also common fundamental theories, assumptions and limitations to study from the theoretic perspectives. This seminar provides such general and fundamental challenges in DGMs, and later we particularly focus on the key developments in diffusion models and their mathematical properties in detail.

2022-11-24 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific problems, which has become an emerging field, Scientific Machine Learning (SciML). Many ML techniques, however, are very complex and sophisticated, commonly requiring many trial-and-error and tricks. These result in a lack of robustness and interpretability, which are critical factors for scientific applications. This talk centers around mathematical approaches for SciML, promoting trustworthiness. The first part is about how to embed physics into neural networks (NNs). I will present a general framework for designing NNs that obey the first and second laws of thermodynamics. The framework not only provides flexible ways of leveraging available physics information but also results in expressive NN architectures. The second part is about the training of NNs, one of the biggest challenges in ML. I will present an efficient training method for NNs - Active Neuron Least Squares (ANLS). ANLS is developed from the insight gained from the analysis of gradient descent training.

Events for the 취소된 행사 포함