학과 정기특강입니다.

1. 일시 : 2021년 10월 29일 (금) 15:30-16:30
2. 장소 : Zoom을 이용한 실시간 온라인 강연
3. 연사 : 안재만 교수 (공주대학교 수학교육과)
4. 제목 : Multivariate Hermite Interpolation via Explicit Groebner Basis of Fat Points Ideals

5. 초록 : Multivariate Hermite interpolation problem asks to find a “small” polynomial that has given values of several partial derivatives at given points. It has numerous applications in science and engineering. Thus, naturally, it has been intensively studied, resulting in various beautiful ideas and techniques. One approach is to choose a basis of the vector space of interpolating polynomials and to translate the interpolating conditions into a system of linear equations.

A fundamental challenge in this approach is to find a “nice” basis so that the resulting system of linear equations is “easy” to solve. In this talk, we will give a “nice” basis in that
(1) it is explicit,
(2) The resulting linear system is block diagonal,
(3) Each block is triangular, and
(4) The diagonal elements of each block are all one.

We found such a basis by first deriving an explicit Groebner basis of fat points ideal and by imitating the shape. This is a joint work with Hoon Hong (NCSU).

학과 정기특강입니다.

1. 일시 : 2021년 10월 22일 (금) 15:30-16:30
2. 장소 : Zoom을 이용한 실시간 온라인 강연
3. 연사 : 송경환 교수 (선문대학교 AI소프트웨어학과)
4. 제목 : Some variations of the Riemann-zeta function and Multiple Zeta Values

5. 초록 : The Riemann-zeta function appears in many contexts in mathematics. Firstly, we explain some results regarding the Riemann zeta function and its variations. Next, we see why a reciprocal sum related to the Riemann-zeta function for some natural numbers s. Also, we give some bounds of the inverses of tails of the Riemann-zeta function on 0 < s < 1 and compute the integer parts of the inverses of tails of the Riemann-zeta function for some real numbers between 0 and 1. In addition to this, we look some properties related to the Multiple Zeta Values and Finite Multiple Zeta Values. Finally, if time permits, we talk about the strategy to get an academic job for ordinary students.

————(연사 개인 사정으로 연기되었습니다)—————–

December 14 (Tuesday) 19:00-21:00 (KST),
15 (Wednesday) & 16 (Thursday) 16:00-18:00 (KST, GMT +9)

————————————————————-

고등과학원에서 주관하는 집중강연입니다.
https://sites.google.com/view/eag-seminar

DATE: 2021 October 25, 27, 29
TIME: 16:00-18:00
PLACE: Online
SPEAKER: Michel Brion

Lecture 1: Actions and representations of algebraic groups (October 25)
– Overview; basic notions and results on actions and representations of algebraic groups; toric varieties.

Lecture 2: Properties and examples of spherical varieties (October 27)
– Further background on the structure and representations of linear algebraic groups; projective homogeneous varieties; spherical varieties: definition, first properties, local structure.

Lecture 3: Embeddings of spherical homogeneous spaces (October 29)
– Embeddings of spherical homogeneous spaces; wonderful varieties; open questions.

Spherical varieties form a remarkable class of algebraic varieties equipped with an action of an algebraic group, which contains several classes of interest: toric varieties, projective homogeneous varieties, symmetric spaces, wonderful varieties. Toric varieties are classified by fans, which provide a well-developed dictionary between their geometry and combinatorics. This makes toric varieties an excellent testing ground for algebro-geometric questions, even if they form a very special class. Spherical varieties are much more general, and include many examples from classical projective geometry. They also admit a combinatorial classification, whose relation to geometry is less understood. The lectures will present basic results on spherical varieties, together with the relevant background on the structure, actions and representations of algebraic groups. They will conclude with open questions.

학과 정기특강입니다.

일시 : 2021년 10월 1일 (금) 15:30-16:30
장소 : Zoom을 이용한 실시간 온라인 강연
연사 : 고영우 교수 (공주대학교 수학교육과)

제목 : Introduction to the operator splitting method
초록 : In this talk, we introduce the operator splitting method for some nonlinear equations. For any time, the method gives an approximation solution depending only on initial data for the nonlinear equation. In this argument, we divide the nonlinear equation into computable parts and consist of the approximation solution by composing these computable parts. This method is widely used for numerical computation. However, it remains a very fundamental question to converge between the approximation with the original solution. In this talk, we study some convergence results which applying harmonic analysis tools to numerical analysis. This work is joint with Hyung Jun Choi and Woocheol Choi.

2021년도 SMMC 입니다.

일시: 2021년 10월 9일 토요일 10:00 – 1:00, 2:30 – 5:30.
장소: 아산이학관 5층

smmc flyer2021

자세한 내용은 대회 홈페이지를 참고하세요
https://www.simonmarais.org/

학과 정기특강입니다.

일시 : 2021년 9월 17일 (금) 15:30-16:30
장소 : Zoom을 이용한 실시간 온라인 강연

연사 : 조장환 박사 (오스트리아 빈 공과대학)
제목 : 평면 곡선의 변환에서 비롯되는 가적분이산화에 대하여

초록 : 가적분이산화(integrable discretization)는 최근 큰 반향을 얻고 있는 이산미분기하학(discrete differential geometry)의 핵심입니다. 본 발표에서는 접근성이 뛰어난 평면 곡선의 예를 통해 적분가능계(integrable systems)의 중심 개념인 변환이론(transformation theory)과 중첩원리(superposition principle)를 살펴보고, 이에 기반한 가적분이산화를 소개합니다.

문의: 허야용 교수

문과대 대학혁신지원사업에서 주관하는 인문고전 심화학습 프로그램입니다.

정규 교과목에서 읽기 어려운 인문고전을 선별하여 학부생들이 인문고전을 원전으로 직접 학습할 수 있도록 지원합니다. 21년 2학기에는 13개 강좌를 개설하였으니 많은 참여 바랍니다.

1. 운영 원칙: 해당 언어 학습 및 고전 텍스트 원어 강독

2. 수강 자격: 고려대학교 구성원 누구나

3. 운영 기간 및 시간: 2021년 9월 ~ 2022년 1월, 온라인 실시간 강의

4. 수강료 및 교재 : 학부 및 대학원생 재학생에 한하여 문과대 대학혁신지원사업 제공

5. 신청 방식 및 기한:  2021. 08. 16(월) 

https://docs.google.com/forms/d/1jZ1srzf-qofrGivpuNgOEVVQ5D8DOMuPBMKaT1J_3LE/edit

고등과학원 개원 25주년 기념 강연입니다.
http://25th.kias.re.kr/

Time : July 30 (Friday), 3 – 4 pm
Speaker : Prof. Caucher Birkar (Tsinghua, Cambridge)
Title : Classification of algebraic varieties
Abstract : The classification of algebraic varieties is at the heart of algebraic geometry. With roots in the ancient world the theory saw great advances in dimensions one and two in the 19th century and the first half of 20th century. It was only in the 1970-80’s that a general framework was formulated, and by the early 1990’s a satisfactory theory was developed in dimension 3. The last 30 years has seen great progress in all dimensions. In this talk I will try to give a historical perspective and discuss the theory in general terms. I will explain how the theory is based on birational transformations and moduli considerations.

Time : July 30(Friday), 5 – 6 pm
Speaker : Prof. Caucher Birkar (Tsinghua, Cambridge)
Title : Boundedness and moduli of algebraic varieties
Abstract : Boundedness and moduli spaces play important roles in algebraic geometry. The subject has evolved in different directions depending on the type of objects being parameterized. In this talk I will focus on boundedness and moduli of algebraic varieties. In particular, I will discuss Fano and Calabi-Yau varieties as well as minimal models of arbitrary Kodaira dimension.

수학과 동아리 서로소에서 여름방학 대수학 관련 세미나를 합니다. 논의를 통해 책을 선정하고,각자 공부한 후 발표하는 형식으로 진행합니다. 대수학1을 수강한 학부 3학년생이 주 대상입니다만 전공에 관심있는 2학년도 환영합니다.

사전회의 2021년 7월 2일 금요일 2시입니다. 자세한 문의는 이메일로 주기 바랍니다.

1. 방정식 해법 (김상집) 7/6, 7/8, 7/13.
2. Algebraic sets and regular functions (윤마리) 7/15, 7/22, 7/29, 8/5.
3. Invariant theory (허진, 윤정빈) 7/20, 7/27, 8/3, 8/10.

학과 세미나입니다.

연사: 고태희 (Pennsylvania State University 박사과정)
일시: 2021년 7월 19일 월요일 오후 2시
장소: 이학관 620호 / Zoom 온라인 세미나

제목: Mixing Schemes for Fixed-Point Problems with Application to Self-Consistent Calculations of Electronic Structures

초록: In the self-consistent calculations of electronic structures, mixing schemes are widely used to improve the convergence of the iteration. With a fixed-point problem arisen from such a calculation, I will review on the past and present results on deterministic mixing schemes such as the simple mixing and Anderson mixing. Secondly, I will give an overview of the simple mixing scheme towards convergence in mean-square and stochastic stability based on the Lyapunov functional approach. I also hope to describe about our results on convergence and stability of general mixing schemes.

서울대학교 모듈과 공간의 양자구조 연구센터(QSMS)에서 주관하는 클러스터 대수 관련 학회입니다.
http://qsms.math.snu.ac.kr/QSMS2021CART

A brief introduction to cluster algebras
Sangjib Kim

Reflections in Coxeter groups and cluster algebras I-IV
Su Ji Hong, Jeongwoo Yu, Kyu-Hwan Lee, Kyungyong Lee

Seeds many Lagrangian fillings for Legendrian links I-III
Youngjin Bae, Eunjeong Lee, Byung Hee An

Wall-crossing in Lagrangian Floer theory and cluster transformations
Hansol Hong

Generalized skein algebra and decorated Teichmuller space
Han-Bom Moon

Fock-Goncharov duality conjecture and tropical integer points of cluster A-varieties
Hyun Kyu Kim

Categorification and cluster algebra
Euiyong Park

Monoidal categorification of quantum cluster algebras and quantum affine algebras
Se-jin Oh

2021년 7월 23일, 24일 실시하는 산업수학관련 여름학교입니다.

포스터링크:
https://www.notion.so/pssc2021/2021-PSSC-Summer-School-3fe07ecf12ec4ac3b8b0b9606b9c0720

신청링크:
http://m.site.naver.com/0OEqD

고등과학원 특강입니다.

TIME: July 08 (Thu), 2021, 10:00-11:00/ 14:00-15:00
SPEAKER: 채동호 (중앙대)
TITLE: Mathematical Challenges in Fluid Mechanics I, II

Abstract : In this lecture we discuss some mathematical problems in the fluid mechanics. Many of the physical systems are described partial differential equations, and the mathematical study of these equations could have important and direct physical significances. In general, in the cases when the equations are nonlinear and nonlocal systems the study of solutions to the equations are much more difficult than the other cases. The fluid equations we are interested in corresponds to these cases. Among others we are particularly interested in the problem of singularities in the incompressible Navier-Stokes and the Euler equations. We emphasize that singularities in the solution of partial differential equations has direct physical importance in many cases. One fashionable example is the singularity of the Einstein field equation, which is nothing but the black hole. The other one is the singularities in the compressible Euler equations, which correspond to the shock waves. The singularities in the Navier-Stokes and the Euler equations are less understood than the two above cases. In the rest part of this lecture we introduce, in general terms, the problem of singularities in the fluids. In the second part we focus on some of the recent studies on the problem, related to the scenario of Type I singularities.

Zoom Link : https://us02web.zoom.us/j/89261183867

고려대학교 데이터과학원에서 주관하는
2021년 인공지능과 데이터과학 여름특강입니다.

7월 9일 희소최적화의 딥러닝적 접근방법, 정원주(인공지능학과/컴퓨터학과)
7월 16일 치매의 조기진단과 예측을 위한 AI기반 뉴로이미징, 성준경(바이오의공학부/인공지능학과)
7월 23일 의료영상 인공지능과 연구사례, 조용원(안암병원 영상의학과 AI센터)
7월 30일 딥러닝 시대의 융합-언어연구, 송상헌(언어학과)
8월 6일 Can Machine Learning Tell Us Anything About the Neurobiological Basis for Learning?, Andrew G. Barto (University of Massachusetts, Amherst)

데이터과학원 온라인(유투브) 강의 특강 링크입니다.

데이터과학원 주간 특강 (2020.11.3~)

심리학과 최준식 교수: 인공지능처럼 생각하기
언어학과 송상헌 교수: 파이썬 프로그래밍 기초다지기
전기전자공학부 김중헌 교수: 딥러닝 프로그래밍 기초다지기
컴퓨터학부 임희석 교수: 인공지능의 언어능력
인공지능학과 성준경 교수: 영상을 대상으로 하는 기계학습
컴퓨터학과 김현우 교수: 인공지능은 물체를 어떻게 이해할까?
인공지능학과 석흥일 교수: 의료인공지능
수학과 이동헌 교수: AI 밑에 감춰진 수학 들춰보기-목적함수

데이터과학원특강

2021 q-day

고등과학원에서 열리는 q-series 관련 학회입니다.
일시: 2021년 6월 30일 수요일
장소: 온/오프라인

세부적인 프로그램 내용과 등록은 학회 홈페이지를 참고하세요.
https://sites.google.com/view/2021qday

2021년도 국가수리과학연구소NIMS 산업수학 학부연수생 모집 안내

1. 연수 기간
   ◦ 2021년 7월 5일(월)부터 8월 13일(금), (6주, 30일. 매일 09:00~18:00)
2. 연수 내용
   ◦ 산업수학 연수 및 문제 해결 실습
   ◦ 산업수학문화 확산 활동
3. 모집대상자
   ◦ 산업수학에 관심 있는 국내대학 학부생 8명 이내
   ◦ 수학 학부 저학년 전공 지식 및 기초적인 컴퓨터 코딩 지식 필요
4. 모집기간
   ◦ 2021년 6월 9일(수)부터 6월 21일(월)까지

이외 자세한 내용은 국가수리과학연구소(https://www.nims.re.kr/) 공지사항을 참고하기 바랍니다.

수학과 정기특강입니다

Operations preserving polynomially chi-boundedness

1. 일시 : 2021년 6월 4일 (금) 16:00-17:00

2. 장소 : 아산이학관 526호 및 Zoom을 이용한 실시간 온라인 강연 동시 진행

3. 연사 : 김린기 교수 (인하대 수학과)

4. 제목 : Operations preserving polynomially chi-boundedness

5. 초록 : A coloring of a graph G is a coloring of vertices of G so that no pair of adjacent vertices receive the same color, and the chromatic number of G is the minimum number of colors needed for a coloring of G. The main question regarding graph coloring in structural graph theory is the following: how can we control the chromatic number by controlling local structures of graphs? (…)

수학과 정기특강입니다

Data-driven modeling for stochastic systems with machine learning

1. 일시 : 2021년 5월 28일 (금) 11:00-12:00
2. 장소 : 아산이학관 526호 및 Zoom을 이용한 실시간 온라인 강연 동시 진행
3. 연사 : 최민석 교수 (포항공대 수학과)
4. 제목 : Data-driven modeling for stochastic systems with machine learning
5. 초록 : Models of physical systems typically involve uncertainty in the input data such as those associated with coefficients initial or boundary conditions, geometry, etc. Estimating the propagation of this uncertainty into model output predictions is crucial to provide more insight to the true physics and produce predictions with high fidelity. This often leads to solve partial differential equations with many parameters. We discuss machine learning based algorithms to solve parametric PDEs and present numerical examples to demonstrate the effectiveness of the proposed methods.

고등과학원 특강입니다.

TIME: 10:00-10:50 May 20 (Thu), 2021
PLACE: Online
SPEAKER: Huh, June(Stanford University)
TITLE: Lorentzian polynomials

ABSTRACT: Lorentzian polynomials link continuous convex analysis and discrete convex analysis via tropical geometry. The tropical connection is used to produce Lorentzian polynomials from discrete convex functions. The talk will be accessible to undergraduate students in mathematics: The audience will need no specific background beyond linear algebra and multivariable calculus to enjoy the presentation. In addition, I advertise the talk and the corresponding paper to people with interests in at least one of the following topics: graphs, convex bodies, stable polynomials, projective varieties, Potts model partition functions, tropicalizations, Schur polynomials, highest weight representations. Based on joint work with Petter Branden.

고등과학원 특강입니다.

DATE: May 12 (Wed), 2021
TIME: 14:00-15:30
PLACE: 고등과학원 8101
SPEAKER: Rak-Kyeong Seong (Samsung SDS)
TITLE: The Mathematics and Physics of Explainable AI

ABSTRACT:
Machine Learning has been a useful tool in recent years for solving computationally costly problems in the natural sciences. However, often too much focus has been on what computation Machine Learning can do for us rather than on how AI can teach us about new interesting natural phenomena. By highlighting the strong connections that Machine Learning fundamentally has with mathematics and physics, the colloquium will outline the challenging problem of explainability of AI and how we might use it in order to make new scientific discoveries. The colloquium will make connections to problems in industry, where explainable AI is quintessential for risk reduction, as well as to problems in a wide range of research areas such as molecular biology, medicine, electronic design automation or material science. At the heart of the colloquium will be our pioneering work in string theory and AI since 2017 and how explainable AI is paving the way for new groundbreaking discoveries at the interface of mathematics and physics.

학과 정기특강입니다.

제목: Invitation to Birational Geometry (Minimal model program)
연사: 최성락 교수님 (연세대학교 수학과)
일시: 2021년 5월 14일 (금) 16:00-17:00

초록: In this talk, I will introduce the brief history and recent progress in the birational algebraic geometry, including the work of Birkar Caucher who won the Fields medal in 2018. I will also introduce my ongoing work with Dr. Jinhyung Park in the related area.

이번 특강은 Zoom을 이용한 실시간 온라인 강연으로 박의성 교수님께서 주관하십니다.

참여방법은 학과홈페이지를 참고하거나 메일을 주기 바랍니다.

교수학습개발원(kuctl@korea.ac.kr)에서 주관하는
자기주도 창의설계 프로그램(CCP)입니다.

” 학부생 3~5명이 그룹을 형성하여 지도교수와 함께 관심분야에 대해 문제 해결 과정을 수행할 수 있는 연구 환경을 지원 함으로써 창의적 사고방식을 갖춘 인재를 양성하는 프로그램입니다.”

제 13회 CCP 서류모집 5월 13일 목요일까지.
자세한 내용은 교수학습개발원 홈페이지(ctl.korea.ac.kr) 상단메뉴 “학습지원” 참조.

고등과학원 특강입니다
KIAS Quadranscentennial Lectures

DATE: April 15 (Thu), April 22 (Thu) 2021
TIME: 10:00-11:30
SPEAKER: Danny Calegari (University of Chicago)
TITLE: Sausages and Butcher Paper I, II

ABSTRACT:
The shift locus S_d is the space of conjugacy classes of degree d polynomials f(z) in one complex variable for which all the critical points tend to infinity under repeated application of f. When d=2 this is the complement of the Mandelbrot set. Although S_d is a very complicated space geometrically, it turns out one can get a surprisingly concrete description of its topology; for example, S_2 is homeomorphic to an open annulus (this is equivalent to the famous theorem of Douady-Hubbard that the Mandelbrot set is connected). I would like to discuss two very explicit ways to capture the topology of S_d, one via the combinatorics of laminations (Butcher paper) and one via algebraic geometry (sausages). As a corollary of this explicit description one can show that S_d is a K(pi,1) with the homotopy type of a complex of half its real dimension.

줌을 이용한 온라인 강연입니다. 고등과학원 세미나 게시판을 참고하세요.

수학과 정기 특강입니다.

1. 일시 : 2021년 4월 2일 (금) 16:00-17:00
2. 장소 : Zoom을 이용한 실시간 온라인 강연
3. 연사 : 정재훈 교수 (포항공대 수학과)
4. 제목 : Topological data analysis and its application to Korean music (Jeong-Ak) data

5. 초록 : Topological Data Analysis (TDA) is rising field useful for the analysis of high-dimensional data structure. The main tool in TDA is persistent homology, introduced by Edelsbrunner et al. in 2002, where snapshots of the topological structure of the data set is taken at many different scales and the results are compared from one scale to the next. TDA via persistent homology provides an efficient way of analyzing the cycle or loop structures embedded in multi-dimensional data. Particularly the one-dimensional homology structure is closely related to the repeating patterns in music flow when it mapped to the proper topological space. In this talk, we first explain TDA and related research. Then we apply TDA to Korean Jeong-Ak music data written in Jeongganbo, particularly to Suyeonjang, Songuyeo, and Taryong, those well-known pieces played at the palace and among noble community. We define and determine the node elements of each music, characterized uniquely with its pitch and length. Then we transform the music into a graph and define the distance between the nodes as their adjacent occurrence rate. The graph is used as a point cloud whose homological structure is investigated by measuring the hole structure in each dimension. We identify cycles of each music, match those in Jeongganbo, and show how those cycles are interconnected. Finally, we will demonstrate a music piece composed by the machine based on the patterns found through TDA.

이 강연은 박의성 교수님께서 주관하십니다

2021-1학기 고려대학교 문과대 대학혁신지원사업
｢인문고전 심화학습 프로그램(Veritas Forum)｣ 참여학생 모집

문과대 대학혁신지원사업에서는 인문고전에 대한 학생들의 지적 열망을 충족시켜주기 위해 인문고전 심화학습 프로그램(Veritas Forum)을 시행합니다. Veritas Forum(‘진리 광장’을 뜻하는 라틴어)은 정규 교과목과는 차별화된 비정규 교육프로그램으로서, 학부생들이 인문고전을 원전으로 직접 학습할 수 있도록 지원합니다.

1. 운영 원칙
– 해당 언어 학습 및 고전 텍스트 원어 강독

2. 수강 자격
– 고려대학교 구성원 누구나
(단, 교재 지원은 학부 및 대학원 재학생에 한함. 휴학생 및 졸업생은 지원 불가.)

3. 운영 기간 및 시간(2021년 1학기)
– 운영 기간 : 2021년 4월~8월 (각 반별 10회)
– 운영 방식 : 온라인 실시강 강의

4. 지원 사항
– 수강료 및 교재 : 문과대 대학혁신지원사업 제공

5. 신청 방식 및 기한
– 신청 기한 : 2021. 03. 31(수)

고등과학원 특강입니다.

일시: 2021년 2월 26일 금요일 (1) 11:00-12:00, (2) 2:00-3:00.
장소: 고등과학원 8101
연사: 김영훈 교수(서울대)
제목: Enumerative geometry, before and after string theory

초록: Throughout its long history, algebraic geometry has been enriched by influences from abstract algebra, number theory, analysis and so on. One of the most recent influences came from string theory circa 1990 which revolutionalized enumerative geometry in particular. In this informal survey talk, I will discuss classical enumerative geometry before string theory and improvements after string theory as well as some recent advances.

학과 세미나입니다.

제목: Deep Reinforcement Learning for Legged Robots
연사: 황보제민 (KAIST 기계공학과)
장소: 이학관 525호 – 줌을 이용한 실시간 온라인 동시진행
일시: 2021년 2월 26일 (금) 13:00-14:00

초록: Legged robots pose one of the greatest challenges in robotics. Dynamic and agile maneuvers of animals cannot be imitated by existing methods that are crafted by humans. A compelling alternative is reinforcement learning, which requires minimal craftsmanship and promotes the natural evolution of a control policy. However, so far, reinforcement learning research for legged robots is mainly limited to simulation, and only few and comparably simple examples have been deployed on real systems. The primary reason is that training with real robots, particularly with dynamically balancing systems, is complicated and expensive. Recent algorithmic improvements have made simulation even cheaper and more accurate at the same time. Leveraging such tools to obtain control policies is thus a seemingly promising direction. However, a few simulation-related issues have to be addressed before utilizing them in practice. The biggest obstacle is the so-called reality gap — discrepancies between the simulated and the real system. Hand-crafted models often fail to achieve a reasonable accuracy due to the complexities of actuation systems of existing robots. This talk will focus on how such obstacles can be overcome. The main approaches are twofold: a fast and accurate algorithm for solving contact dynamics and a data-driven simulation-augmentation method using deep learning. These methods are applied to the ANYmal robot, a sophisticated medium-dog-sized quadrupedal system. Using policies trained in simulation, the quadrupedal machine achieves locomotion skills that go beyond what had been achieved with prior methods: ANYmal is capable of precisely and energy-efficiently following high-level body velocity commands, running faster than ever before, and recovering from falling even in complex configurations.