{"id":49882169,"url":"https://github.com/chenle02/directed-polymers-shenzhen-2026","last_synced_at":"2026-05-15T15:34:56.791Z","repository":{"id":356001621,"uuid":"1230588555","full_name":"chenle02/directed-polymers-shenzhen-2026","owner":"chenle02","description":"Slide deck: A class of d-dimensional directed polymers in a Gaussian environment (CUHK-Shenzhen, May 6 2026)","archived":false,"fork":false,"pushed_at":"2026-05-06T06:36:00.000Z","size":17316,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"main","last_synced_at":"2026-05-06T08:39:22.288Z","etag":null,"topics":["directed-polymers","mathematics","mathjax","presentation-slides","reveal-js","spde"],"latest_commit_sha":null,"homepage":"https://chenle02.github.io/directed-polymers-shenzhen-2026/","language":"HTML","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/chenle02.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2026-05-06T06:22:26.000Z","updated_at":"2026-05-06T06:36:03.000Z","dependencies_parsed_at":null,"dependency_job_id":null,"html_url":"https://github.com/chenle02/directed-polymers-shenzhen-2026","commit_stats":null,"previous_names":["chenle02/directed-polymers-shenzhen-2026"],"tags_count":null,"template":false,"template_full_name":null,"purl":"pkg:github/chenle02/directed-polymers-shenzhen-2026","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/chenle02%2Fdirected-polymers-shenzhen-2026","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/chenle02%2Fdirected-polymers-shenzhen-2026/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/chenle02%2Fdirected-polymers-shenzhen-2026/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/chenle02%2Fdirected-polymers-shenzhen-2026/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/chenle02","download_url":"https://codeload.github.com/chenle02/directed-polymers-shenzhen-2026/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/chenle02%2Fdirected-polymers-shenzhen-2026/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":33071314,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-05-15T11:35:32.926Z","status":"ssl_error","status_checked_at":"2026-05-15T11:35:31.362Z","response_time":103,"last_error":"SSL_connect returned=1 errno=0 peeraddr=140.82.121.5:443 state=error: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["directed-polymers","mathematics","mathjax","presentation-slides","reveal-js","spde"],"created_at":"2026-05-15T15:34:55.160Z","updated_at":"2026-05-15T15:34:56.781Z","avatar_url":"https://github.com/chenle02.png","language":"HTML","funding_links":[],"categories":[],"sub_categories":[],"readme":"\u003cdiv align=\"center\"\u003e\n\n# A Class of *d*-Dimensional Directed Polymers in a Gaussian Environment\n\n### Workshop on PDEs and Stochastic PDEs in Material Science and Statistical Mechanics\n\n**The Chinese University of Hong Kong, Shenzhen** \u0026middot; May 4–8, 2026\n\n[![View Slides](https://img.shields.io/badge/▶%20View%20Slides-chenle02.github.io%2Fdirected--polymers--shenzhen--2026-2EA44F?style=for-the-badge)](https://chenle02.github.io/directed-polymers-shenzhen-2026/)\n\n[![Reveal.js](https://img.shields.io/badge/Reveal.js-5.0.5-9CC?style=flat-square)](https://revealjs.com)\n[![MathJax](https://img.shields.io/badge/MathJax-3-005A9C?style=flat-square)](https://www.mathjax.org/)\n[![Manim](https://img.shields.io/badge/Manim-Community-FF7A00?style=flat-square)](https://www.manim.community/)\n[![arXiv](https://img.shields.io/badge/arXiv-2603.06574-b31b1b?style=flat-square)](https://arxiv.org/abs/2603.06574)\n[![License: CC BY 4.0](https://img.shields.io/badge/License-CC%20BY%204.0-blue.svg?style=flat-square)](https://creativecommons.org/licenses/by/4.0/)\n\n\u003c/div\u003e\n\n---\n\n## ▶ View the Slides\n\n**Live deployment:** \u003chttps://chenle02.github.io/directed-polymers-shenzhen-2026/\u003e\n\n| Key | Action |\n|-----|--------|\n| `→` `Space` | Advance |\n| `←` | Back |\n| `Esc` / `O` | Overview (jump by clicking a tile) |\n| `S` | Speaker view (clock, timer, next-slide preview) |\n| `F` | Fullscreen |\n| `?` (Shift+/) | Help dialog |\n\n---\n\n## 🎤 The Talk\n\nA research-colloquium slide deck by **Le Chen** ([Auburn University](https://chenle02.github.io)), joint work with\n\n| Co-author | Affiliation |\n|-----------|-------------|\n| **Cheng Ouyang** | University of Illinois at Chicago |\n| **Samy Tindel** | Purdue University |\n| **Panqiu Xia** | Cardiff University |\n\n**Wednesday, May 6, 2026 \u0026middot; 16:00–17:00 \u0026middot; CUHK-Shenzhen, Conference Complex II 202 \u0026 203**\n\n---\n\n## 📄 Preprint\n\n\u003e L. Chen, C. Ouyang, S. Tindel, P. Xia,\n\u003e *A class of d-dimensional directed polymers in a Gaussian environment.*\n\u003e [**arXiv:2603.06574**](https://arxiv.org/abs/2603.06574) (2026).\n\n---\n\n## 📖 About the Talk\n\nThe talk introduces a class of *d*-dimensional **continuous directed polymers**\nin a general Gaussian environment — white in time, homogeneous in space —\ncovering both trace-class and non-trace-class regimes.\n\n### Central results\n\n1. **Singularity dichotomy.**\n   The quenched polymer measure $\\mathbb{P}^W_\\beta$ is mutually singular with the Wiener measure $\\mathbb{P}_0$ for almost every realization of the noise $W$ if and only if the spatial covariance is *not* trace-class, i.e. $\\widehat{f}(\\mathbb{R}^d) = \\infty$. The criterion is **sharp** and holds for every $\\beta \u003e 0$.\n\n2. **Diffusive CLT in $d \\ge 3$ at high temperature.**\n   Under Dalang's spectral integrability $\\Upsilon(0) \u003c \\infty$ and weak disorder $\\beta \u003c \\beta_0$, the rescaled polymer endpoint converges to a Gaussian limit.\n\n3. **Local Brownian behavior.**\n   Despite the global singularity, the polymer path agrees with a Brownian motion at every fixed scale — singularity emerges only in the limit.\n\n### Manim animations\n\nThree Manim-rendered scenes carry the main ideas:\n\n- **Scene A** — Discrete → continuous polymer via Donsker refinement\n- **Scene B** — Brownian motion vs. polymer path (locally identical, globally singular)\n- **Scene C** — Martingale collapse on a dyadic skeleton\n\n---\n\n## 🏗️ Built With\n\n- [**Reveal.js 5.0.5**](https://revealjs.com) — slide framework, `night` theme\n- [**MathJax 3**](https://www.mathjax.org/) — TeX rendering (CDN)\n- [**Manim Community**](https://www.manim.community/) — open-source mathematical animations\n- [**edge-tts**](https://github.com/rany2/edge-tts) — narration\n\n### Local preview\n\n```bash\ngit clone https://github.com/chenle02/directed-polymers-shenzhen-2026.git\ncd directed-polymers-shenzhen-2026\npython3 -m http.server 8000\n# Open http://localhost:8000 in your browser\n```\n\n---\n\n## 🗂️ Repository Layout\n\n```\n.\n├── index.html              ← The slide deck\n├── mystyle_polymer.css     ← Custom styling (overrides night theme)\n├── dist/                   ← Reveal.js core\n├── plugin/                 ← Reveal.js plugins (notes, math, highlight)\n├── assets/                 ← Images (Jupiter, team, Bessel, SPDE landscapes)\n└── videos/                 ← Manim animations (scene_A–D.mp4)\n```\n\n---\n\n## 🙏 Acknowledgments\n\nThis work is supported by:\n\n- **U.S. National Science Foundation** \u0026mdash; CAREER Award\n  [No. 2443823](https://www.nsf.gov/awardsearch/showAward?AWD_ID=2443823) (2025–2030)\n- **Simons Foundation** \u0026mdash; Travel Support for Mathematicians\n  No. 959981 (2022–2027)\n\nThe mathematical animations were built with the\n[**Manim Community**](https://www.manim.community/) open-source library —\nwarm thanks to the community of contributors who maintain it.\n\nI am grateful to the **Workshop on PDEs and SPDEs in Material Science and Statistical Mechanics** organizers at CUHK-Shenzhen — *Yuan Chen*, *Cheuk Yin Lee*, and *Xuefeng Wang* — for the kind invitation, and to **Bella Lin** (SSE) for impeccable logistics support.\n\nSpecial thanks to my coauthors **Cheng Ouyang**, **Samy Tindel**, and **Panqiu Xia** for the long collaboration that produced this work, and to the broader SPDE community whose ideas this talk builds upon.\n\n---\n\n\u003cdiv align=\"center\"\u003e\n\n*Slides © 2026 Le Chen — released under [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).*\n*Reveal.js, MathJax, Manim, and other third-party code retain their respective licenses.*\n\n**谢谢 · Thank You**\n\n\u003c/div\u003e\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fchenle02%2Fdirected-polymers-shenzhen-2026","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fchenle02%2Fdirected-polymers-shenzhen-2026","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fchenle02%2Fdirected-polymers-shenzhen-2026/lists"}