https://pzhou.org/ 2026-10-19T22:41:05+00:00 https://pzhou.org/ https://pzhou.org/lib/tpl/dokuwiki/images/favicon.ico text/html 2026-10-17T06:59:19+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/zh/2026-10-16?rev=1792220359&do=diff 2026-10-16 yes, i watched the movie 'edge of tomorrow'. yes, they win. i don't believe i can win, but i have no other choice but fight, keep fighting, till i die. text/html 2026-10-08T17:33:39+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/notes/difference-between-kleisili-and-eilenberg-moore-reconstruction?rev=1791480819&do=diff Difference between Kleisili and Eilenberg-Moore reconstruction 1. The question Suppose $F:C\to D$ is a conservative functor admitting a left adjoint $F^L:D\to C$. We obtain a monad $$ T=FF^L:D\to D. $$ Under the Barr--Beck hypotheses, we have $$ C\simeq \operatorname{Alg}_T(D). $$ text/html 2026-10-08T17:21:40+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/notes/2026-10-08?rev=1791480100&do=diff A Counterexample to the Barr–Beck Monadicity Theorem Without Preservation of Split Colimits 1. The Barr–Beck theorem Suppose $F:\mathcal C\to\mathcal D$ admits a left adjoint $F^L:\mathcal D\to\mathcal C$. Then $$ T=FF^L:\mathcal D\to\mathcal D $$ text/html 2026-10-08T17:13:52+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/start?rev=1791479632&do=diff Hi, welcome! My name is Peng Zhou 周鹏. I do research in math, currently work in UC Berkeley math department as a postdoc. I am on job market this year for tenure track position, here is my [ research statement], and here is my Curriculum Vitae . recent notes * A Natural Transformation that vanishes on generator objects * What is Borisov-Batyrev Mirror Construction * An example to show case Barr-Beck's preservation of some split coequalizer recent papers text/html 2026-09-25T08:13:00+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/blog/2026-09-24-ii?rev=1790323980&do=diff 2026-09-24 (II) last time, we ended at: if the input's intersections are within certain range, and all the possible output's intersections are present, then we have associative product. why is that? if we can show that all the newly created conicalization output intersections are impossible, then we should be able to do it. text/html 2026-09-25T05:48:41+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/zh/2026-09-24?rev=1790315321&do=diff 2026-09-24 我今天看了2小时15分钟小红书 text/html 2026-09-25T04:30:59+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/blog/2026-09-24?rev=1790310659&do=diff 2026-09-24 what is the problem? * Consider a flat symplectic fibration $\pi: E \to B$, $B$ is complex 1-dim, no singular fiber, no curvature, but may have non-trivial monodromy. Suppose $(B, \omega_B = -d\lambda_B$ is a Liouville domain. pick a reference point $b_0 \in B$, and reference fiber $F = \pi^{-1}(b_0)$. Assume $F_0$ is also a Liouville domain, with $\lambda_F$, and symplectic parallel transport preserves the fiberwise Liouville 1-form structure near the boundary. A fibered Lagrang… text/html 2026-09-23T23:00:39+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/blog/2026-09-23?rev=1790204439&do=diff 2026-09-23 something just clicked, felt very happy. 1. We all know the classical story, $[x, p] = \hbar $ (sorry, I will drop $i$ as math people don't care about constant...). We can realize this algebra (or faithful representation) of it in two ways (view $\hbar$ as some complex number) text/html 2026-09-17T05:47:51+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/zh/2026-09-16?rev=1789624071&do=diff 2026-09-16 到底要不要学proof formalization？我已经觉得学代数是sell the soul to devil, 而不是追求几何直觉或者物理，再让我去做formalization？不如去写诗。 每天在跟G老师学习。今天学的是Oh-Tanaka的Local system of categories given by Liouville manifold bundle. 挺好。之前真的是思而不学则怠。 text/html 2026-09-04T23:54:09+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/klrw-fukaya/start?rev=1788566049&do=diff Fukaya Category of Zastava Space and Quantum Group Here we organize some notes. * The rank-one setup: We discuss $sl_2$ space, nil-Hecke algebra. text/html 2026-09-04T23:52:57+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/klrw-fukaya/sl2-setup?rev=1788565977&do=diff The rank-one setup We begin with \(\mathfrak g=\mathfrak{sl}_2\) and fix \(d\geq 0\). On the algebraic side, we consider the \(\hbar\)-deformed nilHecke algebra \(NH_d^\hbar\) over \(\mathbb Z[\hbar]\). It is generated by dots \(x_1,\ldots,x_d\) and elementary crossings \(s_1,\ldots,s_{d-1}\), subject to \[ \begin{gathered} x_a x_b=x_b x_a,\qquad s_a^2=0,\qquad s_a s_b=s_b s_a\quad\text{if }|a-b|>1,\cr s_a s_{a+1}s_a=s_{a+1}s_a s_{a+1},\qquad s_a x_b=x_b s_a\quad\text{if }b\neq a,a+1,\cr x_a s_… text/html 2026-07-12T13:56:58+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/zh/2026-07-12?rev=1783864618&do=diff 2026-07-12 什么是proposal？是那种你看到了，别人还没看到，你要去耐心真诚的说服别人跟着你走的事。我是说去云南旅游，你是不是想到了劝别人花钱支持你的科研追求？这么看来也差不太多。 text/html 2026-06-12T06:18:06+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/zh/2026-06-11?rev=1781245086&do=diff 2026-06-11 课代表讲“穿越不确定性”。这些所谓的软实力，其实非常非常重要。这些不是技术，而是mindset，是人之所以为人，不是工具的闪光点。我需要把它记下来，而不是仅仅几个金句。not today，not yet text/html 2026-06-12T04:46:11+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/blog/2026-06-11?rev=1781239571&do=diff 2026-06-11 I am thinking about proving multiplicatve - multiplicative HMS, with Spencer, and with quantization. text/html 2026-06-10T18:08:15+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/notes/fukaya-with-b-field?rev=1781114895&do=diff From B-fields to the Quantum Torus: a Toy Model in Wrapped Fukaya Categories 0. The question Start with the mirror pair $$ \operatorname{Coh}( ( \mathbb C^* )^2 ) \quad\leftrightarrow\quad \operatorname{Fuk}(T^*T^2). $$ On the B-side, quantization of $( \mathbb C^* )^2$ should replace the commutative Laurent polynomial algebra text/html 2026-04-01T21:22:08+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/?image=fuksym_gl11.pdf&ns=&rev=1775078528&tab_details=history&mediado=diff&do=media text/html 2026-04-01T21:21:07+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/?image=note_may_4_2024_gluing_along_stop.pdf&ns=&rev=1775078467&tab_details=history&mediado=diff&do=media text/html 2026-03-15T20:40:33+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/?image=notes%3Alaumon_nilpotent_cone.pdf&ns=notes&rev=1773607233&tab_details=history&mediado=diff&do=media text/html 2026-03-06T18:21:36+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/?image=projects%3Aclusterhms%3Apasted%3A20260306-182136.png&ns=projects%3Aclusterhms%3Apasted&rev=1772821296&tab_details=history&mediado=diff&do=media <img src="https://pzhou.org/_media/projects/clusterhms/pasted/20260306-182136.png?w=500&h=79&t=1772821296&amp;tok=00db3d" alt="projects:clusterhms:pasted:20260306-182136.png" /> text/html 2026-02-27T19:23:54+00:00 pzhou (pzhou@undisclosed.example.com) https://pzhou.org/?image=blog%3Apasted%3A20260227-192354.png&ns=blog%3Apasted&rev=1772220234&tab_details=history&mediado=diff&do=media <img src="https://pzhou.org/_media/blog/pasted/20260227-192354.png?w=500&h=144&t=1772220234&amp;tok=7ecccd" alt="blog:pasted:20260227-192354.png" />