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)

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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.