Really shocked after the end of parliamental election. Really depressed, felt hopeless at that result.
Only one thing heals my mind now: God is working for all goodness all the time.
Even if we made the great victory, it cannot be an ultimate hope.
Even if it seems that justice has been faded away, His light has not been diminished. Definitely!!

God is the strength in my depression.
God is the only hope in His world.
I put my life on Him again. Have mercy on me, have Your mercy on this country!!

While having dinner in the lounge, got to meet a seminary student, Frank, who is from Pakistan.

Very luckily, he was born in the Christian family. After he graduated university, he came to US, worked in Iowa for two years, and then came to the seminary to study.

He told that there were many hardships in keeping the religion in his country. He was rather lucky anyway, but people who converted to Christianityhave suffered from family's persecution and something like that. Frank just said, "God works tediously."

May God bless Christians in hardships.

(The chai he made for me was great!)

When we define equivariant matrix factorizations, P_1 and P_0 may have distinct group actions. For instance, if Z_3 acts on the complex line, then the action on the function ring(namely, C[z]) is naturally induced. Then let w=z^n, and think of the matrix factorization of w. Then P_1 and P_0 are both C[z] which are free C[z]=modules. To have nontrivial objects, we need to give different actions on each "module", not just taking a priori defined action on C[z].

Let X be an affine scheme of ring A. Then the category of coherent sheaves on X is equivalent to the category of finitely generated A-modules, and for quasi-coherent sheaves correspond to general A-modules. Via this equivalence, locally free sheaves correspond to projective modules.

This notion generalizes usual notion of categories.
When we say that C is an enriched category over a monoidal category M, we consider Hom(A,B) of C as an object of M. In other words, instead of considering Hom as sets, we take into account more structures or even different structures from sets for Homs, as we take them in M, which may have more refined structures than Sets. To define composition-like structures,we need to force M to be monoidal.

For example, ordinary categories are enriched over Sets.
DG categories are enriched over category of chain complexes. ...

키보드를 샀다.

로지텍걸로 샀다.

Textouch가 나름 괜찮다. 비싸긴 하지만, 그덕에 온라인 컴파일링을 제대로 지원한다. 언제까지 잘될지는 장담 못하지만..

암튼 그렇게 텍을 치려고 산 키보드로 블로깅중 ㅋㅋ

섹션 하나 이해함. 그래도 감지덕지.

ideal 계산은 역시 쉽지가 않네.

아무도 찾지않는 집이라도 그래도 나라도 잘 들어와 살아야지.

Dyckerhoff논문 읽는중이고, 이사람의 nonlocal ambient ring이 뭘 뜻하는지 헷갈리는중. 분명 essentially finite type over k랬는데, 그러니까 우리가 생각하는 rational function으로 주어지는 superpotential을 생각하기 위한거 아닌지? 근데 그럼 이미 이 ring이 local인것 아닌가? 아마도 내 추측으로는 Laurent polynomial ring 말고 진짜 local information을 주는 ring을 이 사람이 nonlocal ambient ring으로 부르는게 아닌가 이런 생각인데.. 아닐수도 있고.. 헷갈린다.


He deals with polynomial ring later...