학과 세미나 및 콜로퀴엄




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A perfect field is said to be Kummer-faithful if the Kummer maps for semiabelian varieties over the field are injective. This notion originates in the study of anabeian geometry. At the same time, our study is also motivated by a conjecture of Frey and Jarden on the structure of Mordell-Weil groups over large algebraic extensions of a number field. I will begin with a review of known results in this direction, as well as a brief discussion on anabelian geometry. Then I will introduce some recent results on the construction of "large" Kummer faithful fields. This is a joint work with Takuya Asayama.
Host: 김완수     영어     2024-09-05 09:59:37
This is a reading seminar to be given by Mr. Jaehong Kim (a graduate student in the department) on foundations of the intersection theory and the classification theory of complex algebraic surfaces. He will give three 2-hour long talks.
Host: 박진현     Contact: 박진현 (2734)     한국어 (필요한 경우 영어 가능) ( )     2024-09-13 16:02:52
I will give a report on the applications of free convolution theory to the singular behavior of random matrix perturbations. This is a joint work with Hari Bercovici and Ping Zhong.
Host: Youngjoon Hong, Junsik Bae     영어     2024-11-08 01:43:38
This is a presentation by Mr. Taeyoon Woo, a graduate student in the department, after his reading course on basics on compact Riemann surfaces. He will concentrate on topics such as degree theory of holomorphic maps, Riemann-Roch theorem, residue theorem, Serre duality, Riemann-Hurtiwz theorem, Hodge decomposition, etc. on the compact Riemann surfaces. If time permits, he will discuss its connections to smooth manifolds and algebraic curves.
Host: 박진현     Contact: 박진현 (2734 박진현)     한국어 (필요한 경우 영어 가능) ( )     2024-11-02 17:04:12

심사위원장: 권순식, 심사위원: 강문진, 변재형, 배명진, 조용근(전북대학교)
미정     2024-11-13 10:33:37
Let (R,m_R) be a d-dimensional, excellent, normal local ring. A divisorial filtration {I_n} is determined by a divisor D on a normal scheme X determined by blowing up an ideal on R, so that I_n are the global sections of nD. Associated to an m_R-primary divisorial filtration, we have the Hilbert function f(n)=\lambda_R(R/I_n), where \lambda_R is the length of an R-module. We discuss how close or far this function is from being a polynomial, focusing on examples which are constructed and analyzed geometrically.
Host: 박진형     Contact: 박진형 (042-350-2747)     영어     2024-10-31 20:38:04
TBA
Host: 박진형     Contact: 박진형 (042-350-2747)     영어     2024-10-31 20:38:53
Given two relatively prime positive integers, p < q, Kunz and Waldi defined a class of numerical semigroups which we denote by KW(p, q) consisting of semigroups of embedding dimension n and type n−1 and multiplicity p by filling in the gaps of the semigroup < a, b >. We study these semigroups, give a criterion for these in terms of principal matrices or their critical binomials and generalize the notion to KW(p, q, w) and prove some results and questions. We will discuss their resolutions and Betti Numbers. Most of this is a joint work with Srishti Singh.
Host: 박진형     Contact: 박진형 (042-350-2747)     영어     2024-10-31 20:41:00

심사위원장: 김재경, 심사위원: 김용정, 정연승, 김진수(포항공과대학교), 이승규(고려대학교)
미정     2024-11-05 15:03:46
This is a reading seminar to be given by Mr. Jaehong Kim (a graduate student in the department) on foundations of the intersection theory and the classification theory of complex algebraic surfaces. He will give three 2-hour long talks.
Host: 박진현     Contact: 박진현 (2734)     한국어 (필요한 경우 영어 가능) ( )     2024-09-13 16:03:52

심사위원장: 안드레아스 홈슨, 심사위원: 박진형, 김은정(전산학부), 엄상일(ibs), 권오정(한양대학교)
미정     2024-10-08 13:43:28
In this talk, we will discuss Leray-Hopf solutions to the two-dimensional Navier-Stokes equations with vanishing viscosity. We aim to demonstrate that when the initial vorticity is only integrable, the Leray-Hopf solutions in the vanishing viscosity limit do not exhibit anomalous dissipation. Moreover, we extend this result to the case where the initial vorticity is merely a Radon measure, assuming its singular part maintains a fixed sign. Our proof draws on several key observations from the work of J. Delort (1991) on constructing global weak solutions to the Euler equation. This is a joint work with Luigi De Rosa (University of Basel).
Host: 권순식     Contact: 김송이 (042-350-2786)     미정     2024-09-09 09:37:15

심사위원장: 홍영준, 심사위원: 김동환, 박노성(전산학부), 박은병(성균관대학교), 윤석배(성균관대학교)
미정     2024-11-11 10:49:33
Ist lecture: Understanding material microstructure Abstract Under temperature changes or loading, alloys can form beautiful patterns of microstructure that largely determine their macroscopic behaviour. These patterns result from phase transformations involving a change of shape of the underlying crystal lattice, together with the requirement that such changes in different parts of the crystal fit together geometrically. Similar considerations apply to plastic slip. The lecture will explain both successes in explaining such microstructure mathematically, and how resolving deep open questions of the calculus of variations could lead to a better understanding. 2nd lecture: Monodromy and nondegeneracy conditions in viscoelasticity Abstract For certain models of one-dimensional viscoelasticity, there are infinitely many equilibria representing phase mixtures. In order to prove convergence as time tends to infinity of solutions to a single equilibrium, it is necessary to impose a nondegeneracy condition on the constitutive equation for the stress, which has been shown in interesting recent work of Park and Pego to be necessary. The talk will explain this, and show how in some cases the nondegeneracy condition can be proved using the monodromy group of a holomorphic function. This is joint work with Inna Capdeboscq and Yasemin Şengül.
Host: 변재형     영어     2024-11-04 17:10:03

심사위원장: 황강욱, 심사위원: 강완모, 정연승, 하우석, 안정연(산업및시스템공학과)
미정     2024-10-08 13:44:31
I will begin by a brief introduction to anabelian geometry. In particular, I will try to explain the distinction between "bi-" and "mono-anabelian" reconstruction. Then I review some of the known (elementary) mono-anabelian reconstruction of invariants of mixed characteristic local fields. Finally, I will explain my (on-going) trial of the mono-anabelian reconstruction of fundamental character and Lubin-Tate character.
Host: 김완수     영어     2024-11-11 10:59:12
In this talk, we consider the self-dual O(3) Maxwell–Chern–Simons-Higgs equation, a semilinear elliptic system, defined on a flat two torus. We discuss about pointwise convergence behavior, which represents the Chern-Simons limit behavior of our system. Building upon this observation, we study the existence, stability, and asymptomatic behavior of solutions.
Host: 권순식     Contact: 김송이 (0423502786)     미정     2024-11-04 16:32:26
Virtual element method (VEM) is a generalization of the finite element method to general polygonal (or polyhedral) meshes. The term ‘virtual’ reflects that no explicit form of the shape function is required. The discrete space on each element is implicitly defined by the solution of certain boundary value problem. As a result, the basis functions include non-polynomials whose explicit evaluations are not available. In implementation, these basis functions are projected to polynomial spaces. In this talk, we briefly introduce the basic concepts of VEM. Next, we introduce mixed virtual volume methods (MVVM) for elliptic problems. MVVM is formulated by multiplying judiciously chosen test functions to mixed form of elliptic equations. We show that MVVM can be converted to SPD system for the pressure variable. Once the primary variable is obtained, the Darcy velocity can be computed locally on each element.
미정     2024-11-06 16:29:08
In this talk, I will discuss the expansion of the free energy of two-dimensional Coulomb gases as the size of the system increases. This expansion plays a central role in proving the law of large numbers and central limit theorems. In particular, I will explain how potential theoretic, topological, and conformal geometric information of the model arises in this expansion and present recent developments.
Host: 남경식     미정     2024-09-05 09:58:29

심사위원장: 백형렬, 심사위원: 박정환, 박지원, 김상현(고등과학원), 임선희(서울대학교)
한국어     2024-10-27 19:15:22
The Gromov-Wasserstein (GW) distance is a generalization of the standard Wasserstein distance between two probability measures on a given ambient metric space. The GW distance assumes that these two probability measures might live on different ambient metric spaces and therefore implements an actual comparison of pairs of metric measure spaces. A metric-measure space is a triple (X,dX,muX) where (X,dX) is a metric space and muX is a fully supported Borel probability measure over X. In Machine Learning and Data Science applications, this distance is estimated either directly via gradient based optimization approaches, or through the computation of lower bounds which arise from distributional invariants of metric-measure spaces. One particular such invariant is the so-called ‘global distance distribution’ which precisely encodes the distribution of pairwise distances between points in a given metric measure space. This invariant has been used in many applications yet its classificatory power is not yet well understood. This talk will overview the construction of the GW distance, the stability of distributional invariants, and will also discuss some results regarding the injectivity of the global distribution of distances for smooth planar curves, hypersurfaces, and metric trees.
Host: 김우진     영어     2024-10-20 15:43:57
This is a reading seminar to be given by Mr. Jaehong Kim (a graduate student in the department) on foundations of the intersection theory and the classification theory of complex algebraic surfaces. He will give three 2-hour long talks.
Host: 박진현     Contact: 박진현 (2734)     한국어 (필요한 경우 영어 가능) ( )     2024-09-13 16:01:55