# MATH 858: Introduction to Dynamics on Moduli Spaces | UW–Madison [View on UW Courses](https://uwcourses.com/courses/MATH_858) ## Dataset ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ### repository twangodev/uwcourses ### schema version 6 ### importer version 7 ### projection id 94468b7d4154126ca413937bb4738a6d21e0c2277f6fa397a6078ad80a32384f ### observed at 2026-09-07T15:55:43.033547+00:00 ### built at 2026-09-10T23:19:01.870283+00:00 ### courses 8951 ### current instructors 5754 ### limited false ### terms * 1272 * 1264 * 1262 * 1254 * 1252 * 1244 * 1242 * 1234 * 1232 * 1224 * 1222 * 1212 * 1204 * 1202 * 1194 * 1192 * 1184 * 1182 * 1174 * 1172 * 1164 * 1162 * 1154 * 1152 * 1144 * 1142 * 1134 * 1132 * 1124 * 1122 * 1114 * 1112 * 1104 * 1102 * 1094 * 1092 * 1084 * 1082 * 1074 * 1072 ### term 1272 ### departments | subject | count | | --------- | ----- | | AAE | 90 | | ABT | 20 | | ACCTIS | 36 | | ACTSCI | 14 | | AFAERO | 10 | | AFRICAN | 87 | | AFROAMER | 71 | | AGROECOL | 21 | | AMERIND | 53 | | ANAT\&PHY | 7 | | ANATOMY | 2 | | ANESTHES | 8 | | ANSCI | 57 | | ANTHRO | 95 | | ART | 125 | | ARTED | 10 | | ARTHIST | 121 | | ASIALANG | 129 | | ASIAN | 109 | | ASIANAM | 28 | | ASTRON | 38 | | ATMOCN | 69 | | BIOCHEM | 51 | | BIOCORE | 10 | | BIOLOGY | 14 | | BIOMDSCI | 18 | | BME | 66 | | BMI | 41 | | BMOLCHEM | 10 | | BOTANY | 69 | | BSE | 44 | | C\&ESOC | 73 | | CBE | 48 | | CHEM | 101 | | CHICLA | 52 | | CIVENGR | 133 | | CLASSICS | 47 | | CNP | 10 | | CNSRSCI | 50 | | COMARTS | 137 | | COMPBIO | 15 | | COMPLIT | 11 | | COMPSCI | 138 | | COUNPSY | 78 | | CRB | 19 | | CS\&D | 71 | | CSCS | 40 | | CURRIC | 193 | | DANCE | 93 | | DERM | 8 | | DS | 88 | | DYSCI | 35 | | ECE | 155 | | ECON | 145 | | EDPOL | 114 | | EDPSYCH | 97 | | ELPA | 70 | | EMA | 53 | | EMERMED | 17 | | ENGL | 206 | | ENTOM | 40 | | ENVIRST | 148 | | EP | 15 | | EPD | 67 | | ESL | 16 | | F\&WECOL | 60 | | FAMMED | 22 | | FINANCE | 50 | | FOLKLORE | 40 | | FOODSCI | 43 | | FRENCH | 63 | | GEN\&WS | 145 | | GENBUS | 72 | | GENECSLR | 17 | | GENETICS | 60 | | GEOG | 113 | | GEOSCI | 83 | | GERMAN | 82 | | GLE | 48 | | GNS | 38 | | GREEK | 27 | | HDFS | 41 | | HEBR-BIB | 13 | | HEBR-MOD | 10 | | HISTORY | 233 | | HISTSCI | 56 | | HONCOL | 13 | | ILS | 43 | | INFOSYS | 9 | | INTEGART | 7 | | INTEGSCI | 22 | | INTER-AG | 18 | | INTER-HE | 11 | | INTER-LS | 22 | | INTEREGR | 16 | | INTLBUS | 21 | | INTLST | 50 | | ISYE | 83 | | ITALIAN | 53 | | JEWISH | 56 | | JOURN | 88 | | KINES | 128 | | LACIS | 26 | | LANDARC | 61 | | LATIN | 24 | | LAW | 120 | | LEGALST | 48 | | LINGUIS | 35 | | LIS | 89 | | LITTRANS | 78 | | LSC | 52 | | M\&ENVTOX | 7 | | MARKETNG | 62 | | MATH | 153 | | MDGENET | 8 | | ME | 130 | | MEDHIST | 43 | | MEDICINE | 60 | | MEDIEVAL | 32 | | MEDPHYS | 39 | | MEDSC-M | 29 | | MEDSC-V | 41 | | MHR | 68 | | MICROBIO | 45 | | MILSCI | 16 | | MM\&I | 22 | | MOLBIOL | 6 | | MS\&E | 59 | | MUSIC | 165 | | MUSPERF | 126 | | NAVSCI | 20 | | NE | 44 | | NEURODPT | 11 | | NEUROL | 7 | | NEURSURG | 4 | | NTP | 11 | | NURSING | 111 | | NUTRSCI | 65 | | OBS\&GYN | 18 | | OCCTHER | 39 | | ONCOLOGY | 14 | | OPHTHALM | 5 | | OTM | 43 | | PATH | 34 | | PATH-BIO | 29 | | PEDIAT | 26 | | PHARMACY | 31 | | PHILOS | 77 | | PHMCOL-M | 11 | | PHMPRAC | 45 | | PHMSCI | 60 | | PHYASST | 37 | | PHYSICS | 88 | | PHYSIOL | 3 | | PHYTHER | 37 | | PLANTSCI | 52 | | PLPATH | 35 | | POLISCI | 192 | | POPHLTH | 58 | | PORTUG | 33 | | PSYCH | 101 | | PSYCHIAT | 22 | | PUBAFFR | 54 | | PUBLHLTH | 23 | | RADIOL | 11 | | REALEST | 41 | | RELIGST | 90 | | RHABMED | 9 | | RMI | 24 | | RP\&SE | 102 | | S\&APHM | 17 | | SCANDST | 73 | | SLAVIC | 89 | | SOC | 149 | | SOCWORK | 87 | | SOILSCI | 46 | | SPANISH | 83 | | SRMED | 21 | | STAT | 94 | | STDYABRD | 52 | | STS | 8 | | SURGERY | 25 | | SURGSCI | 33 | | THEATRE | 91 | | URBRPL | 60 | | UROLOGY | 5 | | ZOOLOGY | 89 | ## course ### run id 20260907T155543-ce3781c4 ### semester 1272 ### observed at 2026-09-07 15:55:43.033547+00:00 ### record version id 808f434dd8e7441d18453b646458df8eaa778967b844a63b80e2bbf80219cd8f ### course id MATH 858 ### course uid course\_eeea463cf7d83d7ea6b95202 ### catalog version id 54fd46dd83de9739183ef2aadc9d9696a466ab2716b6cf2ea7cf1cc349ab7d5a ### course number 858 ### subjects * MATH ### title INTRODUCTION TO DYNAMICS ON MODULI SPACES ### description An introduction to ergodic theory and dynamics on the moduli space of translation surfaces with applications to counting problems in rational billiards and on flat surfaces. Covers dynamical techniques inspired by homogeneous dynamics including the use of Margulis functions to establish quantitative recurrence results; the use of random walks, inspired by work of Benoist and Quint, to prove measure rigidity statements; and the use of Zimmer's theory of the algebraic hull to prove finiteness results. ### requirements text Graduate/professional standing or declared in Mathematics VISP (graduate or dissertator) ### credit offering ids None recorded. ### llm job id enrich-8b774950c2b6adfdc46d1b82 ### llm output id b8730057001252f4a44db17755ce929dc68379b5486cdd7f5140b68138186b3a ### llm model nvidia/Qwen3.6-35B-A3B-NVFP4 ### llm model revision 1355db6a052410cfd62085d94b58866fd0f2c3c5 ### llm task version 14 ### llm search status valid ### llm summary Introduction to ergodic theory and dynamics on the moduli space of translation surfaces ### llm topics * Dynamics on moduli spaces of translation surfaces * Counting problems in rational billiards and flat surfaces * Dynamical techniques from homogeneous dynamics ### llm skills * Establish quantitative recurrence results * Prove measure rigidity statements * Prove finiteness results ### llm assumed background * Graduate standing in Mathematics or VISP ### llm search phrases * ergodic theory dynamics moduli space * translation surfaces rational billiards * Margulis functions quantitative recurrence * measure rigidity random walks * Zimmer algebraic hull finiteness ### llm requirements status valid ### llm student summary status valid ### llm experience status insufficient\_evidence ### catalog variants None recorded. ### student summary #### context hash ddc890781dd14a5f4cdcbf84f9fc20b4796bccf1b09f3987c218269d5b576ee9 #### course id MATH 858 #### current instructors None recorded. #### difficulty workload None recorded. #### errors None recorded. #### historical context None recorded. #### message No course-specific reviews available #### offered false #### profile hash 5cb4dabf887cdbcd8c00d5a1312e10828b95c63f30bc3ea76aea199565390d02 #### quick take Recent recorded grades — Fall 2025: 4.00 GPA, 100.0% A/AB (n=23 letter grades). ```json { "citations": [ { "course_id": "MATH 858", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "b6340fde-aa6a-3725-a43b-469cea73c2e1", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1262", "type": "grade" } ] } ``` #### student experience None recorded. #### task hash 74fb0997943e888960bbc9e47db8c4fd12e4292d55c20509d8d89db6a9910f68 #### teaching history None recorded. #### term id 1272 #### term name 2026 Fall #### version 2 ### requirements #### nodes ```json [ { "children": [ "n1", "n2" ], "condition": null, "course": null, "evidence": "Graduate/professional standing or declared in Mathematics VISP (graduate or dissertator)", "id": "n0", "kind": "any" }, { "children": [], "condition": "Graduate/professional standing", "course": null, "evidence": "Graduate/professional standing", "id": "n1", "kind": "condition" }, { "children": [], "condition": "declared in Mathematics VISP (graduate or dissertator)", "course": null, "evidence": "declared in Mathematics VISP (graduate or dissertator)", "id": "n2", "kind": "condition" } ] ``` #### notes None recorded. #### root n0 #### status parsed ### instructors None recorded. ### offerings None recorded. ### sections None recorded. ### grade instructors ```json [ { "instructor_uid": "instructor_18ef1d7d9b98466965984778", "source": "madgrades", "source_instructor_id": "6396934", "identity_basis": "source_id", "identity_status": "source_identified", "name": "CAGLAR UYANIK", "email": null, "first_observed_at": "2026-09-06 23:14:58.172943+00:00", "last_observed_at": "2026-09-07 15:55:43.033547+00:00", "ratings": { "review_count": 29, "quality": 4.86, "difficulty": 3.28, "quality_count": 29, "difficulty_count": 29, "profile_id": "rmp:2768657", "source_url": "https://www.ratemyprofessors.com/professor/2768657", "match_basis": "exact_name", "observed_at": "2026-09-07 16:50:15.459500+00:00", "courses": { "course_8634dde81cc95f6c58014087": { "review_count": 8, "quality": 4.5, "difficulty": 2.62, "quality_count": 8, "difficulty_count": 8 }, "course_5d98ff5f6adce2207e394dc6": { "review_count": 21, "quality": 5, "difficulty": 3.52, "quality_count": 21, "difficulty_count": 21 } }, "bayesian_quality": 4.370075830019019, "prior_mean": 3.6596857835465957, "prior_weight": 20 }, "grade_statistics": { "gpa": 3.319, "graded": 662, "counts": [ 310, 92, 137, 39, 55, 17, 12 ], "sections": 32 }, "instructor_url": "/instructors/CAGLAR_UYANIK--instructor_18ef1d7d9b98466965984778" } ] ``` ### grades ```json [ { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 858", "course_uid": "course_eeea463cf7d83d7ea6b95202", "term_id": "1262", "term_name": "Fall 2025", "instructors": [ "Caglar Uyanik" ], "a": 23, "ab": 0, "b": 0, "bc": 0, "c": 0, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 23, "source_aliases": [ "MATH 858" ] } ] ``` ### statistics #### gpa 4 #### graded 23 #### counts * 23 * 0 * 0 * 0 * 0 * 0 * 0 ### grade conflicts None recorded. ### evidence #### history * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_eeea463cf7d83d7ea6b95202-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_eeea463cf7d83d7ea6b95202-0.json) #### traces * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_eeea463cf7d83d7ea6b95202-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_eeea463cf7d83d7ea6b95202-0.json) #### results * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_eeea463cf7d83d7ea6b95202-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_eeea463cf7d83d7ea6b95202-0.json) ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ## context ### all #### term #### gpa 4 #### count 23 #### departments | subject | comparison | | ------- | ---------- | | MATH | | ### terms #### 1262 ##### term 1262 ##### gpa 4 ##### count 23 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | ### benchmarks #### all ##### school ###### size 1320 ###### gpa 3.628825763035853 ###### top Share 80.21118846327654 ###### count 70 ##### MATH ###### size 43 ###### gpa 3.2481769276584003 ###### top Share 56.325967864851854 ###### count 81 #### terms ##### 1262 ###### school ###### size 1320 ###### gpa 3.628825763035853 ###### top Share 80.21118846327654 ###### count 70 ###### MATH ###### size 43 ###### gpa 3.2481769276584003 ###### top Share 56.325967864851854 ###### count 81 ## instructor Trends ```json [ { "uid": "instructor_18ef1d7d9b98466965984778", "name": "CAGLAR UYANIK", "count": 23, "terms": [ { "term": "1262", "count": 23, "sections": 1, "gpa": 4 } ] } ] ``` ## following None recorded.