1<!DOCTYPE html> 2<html> 3 4<head> 5 <meta charset="utf-8"> 6 <meta name="viewport" content="width=device-width, initial-scale=1.0, shrink-to-fit=no"> 7 <title>Ross Paterson's Homepage</title> 8 <meta name="google-site-verification" content="OI8flXvZduaZqEK203xSYTqscLSfa8WOSwYYRhnf7a8"> 9 <meta name="keywords" content="Ross Paterson, maths, math, Number Theory, Arithmetic Statistics, Elliptic Curves, Galois Module"> 10 <meta name="title" content="Ross Paterson"> 11 <meta name="description" content="Homepage of Ross Paterson, a number theorist at the University of Bristol"> 12 <link rel="icon" type="image/png" sizes="460x460" href="../assets/img/Farey.png"> 13 <link rel="icon" type="image/png" sizes="460x460" href="../assets/img/Farey.png"> 14 <link rel="icon" type="image/png" sizes="460x460" href="../assets/img/Farey.png"> 15 <link rel="icon" type="image/png" sizes="460x460" href="../assets/img/Farey.png"> 16 <link rel="icon" type="image/png" sizes="460x460" href="../assets/img/Farey.png"> 17 <link rel="stylesheet" href="../assets/bootstrap/css/bootstrap.min.css"> 18 <link rel="stylesheet" href="../assets/fonts/ionicons.min.css"> 19 <link rel="stylesheet" href="../assets/css/bss-overrides.css"> 20 <link rel="stylesheet" href="../assets/css/Footer-Basic.css"> 21 <link rel="stylesheet" href="../assets/css/Navigation-Clean.css">
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36 37</head> 38 39<body> 40 <div></div> 41 <div class="container" style="max-width: 800px;"> 42 <nav class="navbar navbar-light navbar-expand-md navigation-clean"> 43 <div class="container"><img src="../assets/img/Farey.png" style="width: 80px;"><a class="navbar-brand" href="#" style="padding: 0px;padding-left: 0px;margin-left: 10px;">Ross Paterson</a><button class="navbar-toggler" data-toggle="collapse" data-target="#navcol-1"><span class="sr-only">Toggle navigation</span><span class="navbar-toggler-icon"></span></button> 44 <div class="collapse navbar-collapse" id="navcol-1"> 45 <ul class="navbar-nav ml-auto"> 46 <li class="nav-item"><a class="nav-link border rounded" href="../">Home</a></li> 47 <li class="nav-item"><a class="nav-link border rounded" href="../Research/">Research</a></li> 48 <li class="nav-item"></li> 49 <li class="nav-item"><a class="nav-link disabled active border rounded" href=".">Notes</a></li> 50 <li class="nav-item"><a class="nav-link border rounded" href="../Teaching/">Teaching</a></li> 51 <li class="nav-item"><a class="nav-link border rounded" href="../Code/">Code</a></li> 52 <li class="nav-item"><a class="nav-link border rounded" href="../Misc/">Misc.</a></li> 53 </ul> 54 </div> 55 </div> 56 </nav> 57 <p>When attending courses on research topics, I have tried to maintain a habit of typesetting the lectures live. The notes below are the product of this, which is a lazy excuse for poor typesetting. Please be aware that little effort has been made to check for errors, and you are welcome to let me know of any so that I can resolve them.</p> 58 <div> 59 <h4 style="margin-right: 10px;margin-left: 10px;"></h4> 60 <h4 style="margin-right: 10px;margin-left: 10px;">Reading Group Notes</h4> 61 <p style="margin: 0px 10px 5px;">Below are notes that I have taken during reading groups.</p> 62 <ul> 63 <li><a href="Reading_Groups/ModelsOfCurves.pdf">Models of Curves</a> (University of Bristol, Spring 2024)</li> 64 <li><a href="Reading_Groups/Etale_Cohomology.pdf">Ãtale Cohomology</a> (University of Bristol, Autumn 2023)</li> 65 </ul> 66 </div> 67 <div id="maintext-2"> 68 <h4 style="margin-right: 10px;margin-left: 10px;">Research School Notes</h4> 69 <div> 70 <h5 style="margin-right: 10px;margin-left: 10px;">Introduction to Smith's Methods (2026)</h5> 71 <p style="margin: 0px 10px 5px;">In April 2026, <a href="https://webspace.science.uu.nl/~koyma001/">Peter Koymans</a> gave a 10-lecture series on the groundbreaking techniques of <a href="https://www.asmith-math.org/">Alex Smith</a> at the University of Bristol via a Heilbronn International Visitors Scheme grant. The webpage is <a href="../Koymanslectures2026/index.html">here</a>, please note that exercise sheet 1 below is an exercise sheet of Matthew Emerton from a course in 2012.</p> 72 <ul> 73 <li><a href="../Koymanslectures2026/materials/notes.pdf">Live Lecture Notes</a></li> 74 <li><a href="../Koymanslectures2026/materials/primer.pdf">Galois Cohomology Primer</a></li> 75 <li><a href="../Koymanslectures2026/materials/Genus.pdf">Exercise sheet 1</a>, <a href="../Koymanslectures2026/materials/Exercises2.pdf">Exercise sheet 2</a>, <a href="../Koymanslectures2026/materials/Exercises3.pdf">Exercise sheet 3</a>, <a href="../Koymanslectures2026/materials/Exercises4.pdf">Exercise sheet 4</a></li> 76 </ul> 77 </div> 78 <div> 79 <h5 style="margin-right: 10px;margin-left: 10px;">LMSI Thematic Programme on Rational Points, Algebraic Cycles and the Local-Global Principle Minicourses (2026)</h5> 80 <p style="margin: 0px 10px 5px;">The official webpage is <a href="https://lmsi.org/programmes/thematic-programme-on-rational-points/">here</a>.</p> 81 <ul> 82 <li>Martin Bright & Alexander Molyakov -- <a href="LMSI_2026/BrightMolyakovBrauer.pdf">Characteristic p Phenomena in Brauer Groups</a></li> 83 <li>
83Julian Demeio -- <a href="LMSI_2026/DemeioGrunwald.pdf">The Grunwald Problem and Solvable Descent</a></li> 84 <li>Adam Morgan -- <a href="LMSI_2026/MorganKummer.pdf">Rational Points on Kummer Varieties and Swinnerton-Dyer's Method</a></li> 85 </ul> 86 </div> 87 <div> 88 <h5 style="margin-right: 10px;margin-left: 10px;">CIRM Arithmetic Statistics Spring School (2023)</h5> 89 <p style="margin: 0px 10px 5px;">The official webpage is <a href="https://conferences.cirm-math.fr/2679.html">here</a>, Samuele Anni hosts the materials for the courses <a href="https://sites.google.com/view/samuele-anni/home/research-school-arithmetic-statistics?authuser=0">here</a>.</p> 90 <ul> 91 <li>Peter Stevenhagen & René Schoof -- <a href="AS_2023/ClassFieldTheory.pdf">Class Field Theory</a></li> 92 <li>Eugenia Rosu & Jan Vonk -- <a href="AS_2023/ComplexMultiplication.pdf">Complex Multiplication</a><br></li> 93 <li>Kiran Kedlaya & Andrew Sutherland -- <a href="AS_2023/FrobeniusDistributions.pdf">Frobenius Distributions</a><br></li> 94 <li>Samuele Anni & René Schoof -- <a href="AS_2023/GaloisReps.pdf">Galois Representations</a><br></li> 95 </ul> 96 </div> 97 <div> 98 <h5 style="margin-right: 10px;margin-left: 10px;">CIRM SAGA Spring School (2023)</h5> 99 <p style="margin: 0px 10px 5px;">The official webpage is <a href="https://conferences.cirm-math.fr/2801.html">here</a>, Samuele Anni hosts the materials for the courses <a href="https://sites.google.com/view/samuele-anni/home/research-school-introduction-to-saga">here</a>.</p> 100 <ul> 101 <li>Rachel Newton -- <a href="SAGA_CIRM_2023/LocalGlobal.pdf">Local-Global Principles (Part II)</a><br></li> 102 <li>Tim Dokchitser -- <a href="SAGA_CIRM_2023/JacobiansII.pdf">Models and Jacobians of Curves (Part II)</a><br></li> 103 <li>Anna Medvedovsky & Alexandru Ghitza -- <a href="SAGA_CIRM_2023/GaloisRepresentations.pdf">Galois Representations and Modular Forms</a><br></li> 104 </ul> 105 </div> 106 <div> 107 <h5 style="margin-right: 10px;margin-left: 10px;">CMI-HIMR Computational Number Theory (2019)</h5> 108 <p style="margin: 0px 10px 5px;">Tim Dokchitser hosts the official webpage <a href="https://people.maths.bris.ac.uk/~matyd/Jen/">here</a>, where there are official notes for some courses. </p> 109 <ul> 110 <li>Rachel Newton -- <a href="CNT_Bristol_2019/RNewton.pdf">The Hasse Norm Principle</a><br></li> 111 <li>Adam Morgan -- <a href="CNT_Bristol_2019/AMorgan.pdf">Local Arithmetic of Curves and Jacobians</a><br></li> 112 <li>Celine Maistret -- <a href="CNT_Bristol_2019/CMaistret.pdf">Computational Aspects of the Birch and Swinnerton-Dyer Conjecture</a><br></li> 113 <li>John Voight -- <a href="CNT_Bristol_2019/JVoight.pdf">Computing Endomorphism Rings of Jacobians</a><br></li> 114 <li>Steffen Muller -- <a href="CNT_Bristol_2019/SMueller.pdf">Rational Points on Curves</a><br></li> 115 </ul> 116 </div> 117 </div> 118 </div> 119 <div class="footer-basic"> 120 <footer> 121 <div class="social"><a href="https://github.com/ramifiedprime"><i class="icon ion-social-github-outline"></i></a></div> 122 </footer> 123 </div> 124
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