1. Essential dimension of simple algebras

    The notion of essential dimension was introduced by Buhler and Reichstein in the late 90s. Roughly speaking, the essential dimension of an algebraic object is the minimal number of algebraically independent parameters one needs to define the...
    Category수학강연회 소속KAIST 강연자백상훈
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  2. Restriction theorems for real and complex curves

    We will talk about the Fourier restriction theorems for non-degenerate and degenerate curves in Euclidean space Rd. This problem was first studied by E. M. Stein and C. Fefferman for the circle and sphere, and it still remains an unsolved pr...
    Category수학강연회 소속포항공과대학교 강연자박종국
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  3. Recommendation system and matrix completion: SVD and its applications (학부생을 위한 강연)

    이 강연에서는 최근 음악, 영화 추천 등 다양한 Recommendation System의 기본 아이디어인 Matrix Completion 문제와, 이를 해결하기 위해 Singular Value Decomposition을 통한 차원 축소 및 내재 공간 학습이 어떤 원리로 이루어 지는지 설명합니다. 그리고 ...
    Category수학강연회 소속서울대 전기공학부 강연자정교민
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  4. Deformation spaces of Kleinian groups and beyond

    From 1980’s, the study of Kleinian groups has been carried out in the framework of the paradigm of “Thurston’s problems”. Now they are all solved, and we can tackle deeper problems; for instance to determine the topological types of the defo...
    Category수학강연회 소속Osaka University 강연자Kenichi Ohshika
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  5. Idempotents and topologies

    A classical theorem of Jacobs, de Leeuw and Glicksberg shows that a representation of a group on a reflexive Banach space may be decomposed into a returning subspace and a weakly mixing subspace. This may be realized as arising from the idem...
    Category수학강연회 소속University of Waterloo 강연자Nico Spronk
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  6. Recent progress on the Brascamp-Lieb inequality and applications

    In his survey paper in the Bulletin of the AMS from 2002, R. J. Gardner discussed the Brunn-Minkowski inequality, stating that it deserves to be better known and painted a beautiful picture of its relationship with other inequalities in anal...
    Category수학강연회 소속Saitama University 강연자Neal Bez
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  7. Existence of positive solutions for φ-Laplacian systems

    Category수학강연회 소속이용훈 강연자수학강연회,특별강연,대중강연
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  8. Riemann-Hilbert correspondence for irregular holonomic D-modules

    The original Riemann-Hilbert problem is to construct a liner ordinary differential equation with regular singularities whose solutions have a given monodromy. Nowadays, it is formulated as a categorical equivalence of the category of regular...
    Category수학강연회 소속서울대학교/RIMS 강연자Masaki Kashiwara
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  9. Normal form reduction for unconditional well-posedness of canonical dispersive equations

    Normal form method is a classical ODE technique begun by H. Poincare. Via a suitable transformation one reduce a differential equation to a simpler form, where most of nonresonant terms are cancelled. In this talk, I begin to explain the not...
    Category수학강연회 소속KAIST 강연자권순식
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  10. Random conformal geometry of Coulomb gas formalism

    Several cluster interfaces in 2D critical lattice models have been proven to have conformally invariant scaling limits, which are described by SLE(Schramm-Loewner evolution) process, a family of random fractal curves. As the remarkable achie...
    Category수학강연회 소속서울대학교 강연자강남규
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  11. Categorification of Donaldson-Thomas invariants

    In 1980s, Donaldson discovered his famous invariant of 4-manifolds which was subsequently proved to be an integral on the moduli space of semistable sheaves when the 4-manifold is an algebraic surface. In 1994, the Seiberg-Witten invariant w...
    Category수학강연회 소속서울대학교 강연자김영훈
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  12. Noncommutative Surfaces

    Many aspects of the differential geometry of embedded Riemannian manifolds, including curvature, can be formulated in terms of multi-linear algebraic structures on the space of smooth functions. For matrix analogues of embedded surfaces, one...
    Category수학강연회 소속서강대학교 강연자Jens Hoppe
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  13. The Shape of Data

    Creating information and knowledge from large and complex data sets is one the fundamental intellectual challenges currently being faced by the mathematical sciences. One approach to this problem comes from the mathematical subdiscipline cal...
    Category수학강연회 소속Stanford University 강연자Gunnar E. Carlsson
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  14. Topological Mapping of Point Cloud Data

    One of the important problems in understanding large and complex data sets is how to provide useful representations of a data set. We will discuss some existing methods, as well as topological mapping methods which use simplicial complexes ...
    Category특별강연 소속Stanford University 강연자Gunnar E. Carlsson
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  15. Structures on Persistence Barcodes and Generalized Persistence

    Persistent homology produces invariants which take the form of barcodes, or nite collections of intervals. There are various structures one can imposed on them to yield a useful organization of the space of all barcodes. In addition, there...
    Category특별강연 소속Stanford University 강연자Gunnar E. Carlsson
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  16. Persistent Homology

    Homology is a method for assigning signatures to geometric objects which reects the presence of various kinds of features, such as connected components, loops, spheres, surfaces, etc. within the object. Persistent homology is a methodology...
    Category특별강연 소속Stanford University 강연자Gunnar E. Carlsson
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  17. Topological aspects in the theory of aperiodic solids and tiling spaces

    After a review of various types of tilings and aperiodic materials, the notion of tiling space (or Hull) will be defined. The action of the translation group makes it a dynamical system. Various local properties, such as the notion of "Finit...
    Category수학강연회 소속Georgia Institute of Technology, School of Mathematics and School of Physics 강연자Jean V. Bellissard
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  18. Subgroups of Mapping Class Groups

    The mapping class group of a surface S is the component group of orientation-preserving homeomorphisms on S. We survey geometric and algebraic aspects of this group, and introduce a technique of using right-angled Artin groups to find geomet...
    Category수학강연회 소속서울대학교 강연자김상현
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  19. Irreducible Plane Curve Singularities

    It is very interesting to study what problems can be computed in irreducible plane curve singularities in algebraicgeometry? Then, the aim of this talk is to compute the explicit algorithm for finding the correspondence between the family of...
    Category특별강연 소속서울대학교 강연자강정혁
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  20. Analytic torsion and mirror symmetry

    In the early 90's, physicists Bershadsky-Cecotti-Ooguri-Vafa conjectured that the analytic torsion was the counterpart in complex geometry of the counting problem of elliptic curves in Calabi-Yau threefolds. It seems that this conjecture is ...
    Category수학강연회 소속Kyoto University 강연자Ken-ichi Yoshikawa
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