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Members – enjoy special offers! </a> </h4> </div>   <div class="clearfix"><br></div> <div class="row homepagecontent" id="main-content"> <script> $(document).ready(function() { var hash = window.location.hash; if (hash) { $('.nav-tabs a[href="' + hash + '"]').tab('show'); if(hash.includes("tab")){ FocusOnTab(); } } // Change hash for page-reload $('.nav-tabs a').on('click', function (e) { window.location.hash = this.hash; }); // Navigate to tab on history back/forward window.addEventListener('hashchange', function() { var changedHash = window.location.hash; if (changedHash) { $('.nav-tabs a[href="' + changedHash + '"]').tab('show'); } }); }); function FocusOnTab(){ $('html,body').animate({ scrollTop: $("#homepageTabs").offset().top - 220 }); } </script> <link as="style" href="/css/2022_website_homepage.css" rel="stylesheet preload" /> <div class="container-fluid"><style> .jumbotron{ font-family: 'Open Sans', sans-serif;} </style> <header class="jumbotron"> <h1>Advancing Research. Creating Connections.</h1> <p class="catchphrase">The American Mathematical Society is dedicated to advancing research and connecting the diverse global mathematical community through publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs.</p> <p><a class="btn btn-info" href="/membership" role="button">Join us today »</a></p> </header>  <main> <section id="uppertier"> <ul class="nav nav-tabs" id="homepageTabs" role="tablist"> <li class="h4 active" role="presentation"><a aria-controls="tab-research" data-target="#researchTab" data-toggle="tab" href="#tab-research" role="tab">Research</a></li> <li class="h4" role="presentation"><a aria-controls="tab-news" data-target="#newsTab" data-toggle="tab" href="#tab-news" role="tab">News</a></li> <li class="h4" role="presentation"><a aria-controls="tab-calendar" data-target="#calendarTab" data-toggle="tab" href="#tab-calendar" role="tab">Events</a></li> <li class="h4" role="presentation"><a aria-controls="tab-deadlines" data-target="#deadlinesTab" data-toggle="tab" href="#tab-deadlines" role="tab">Deadlines</a></li> </ul>  <div class="tab-content"> <div class="tab-pane fade in active" id="researchTab" role="tabpanel"> <div> <article class="row"> <p class="sectionhead">From Bulletin of the AMS</p> <h2><a href=" https://www.ams.org/journals/bull/2024-61-04/S0273-0979-2024-01808-4/viewer/"> Functoriality in categorical symplectic geometry </a></h2> <figure class="pull-right" style="max-width: 300px;"><img alt=" The multiplihedra $J_2$ and $J_3$." class="img-responsive" src="/images/fig3.2-functoriality-300pw.png" style="margin-left:5px" /></figure> <p class="AMS_gray_foreground small">by <a href="https://mathscinet.ams.org/mathscinet/mrauthorid/734175"> Mohammed Abouzaid </a><br /> <a href="https://mathscinet.ams.org/mathscinet/mrauthorid/883870"> Nathaniel Bottman </a></p> <p><strong>Abstract</strong></p> <p>Categorical symplectic geometry is the study of a rich collection of invariants of symplectic manifolds, including the Fukaya $A_\infty$-category, Floer cohomology, and symplectic cohomology. Beginning with work of Wehrheim and Woodward in the late 2000s, several authors have developed techniques for functorial manipulation of these invariants. We survey these functorial structures, including Wehrheim and Woodward's quilted Floer cohomology and functors associated to Lagrangian correspondences, Fukaya's alternate approach to defining functors between Fukaya $A_\infty$-categories, and the second author's ongoing construction of the symplectic $(A_\infty,2)$-category. In the last section, we describe a number of direct and indirect applications of this circle of ideas, and propose a conjectural version of the Barr—Beck monadicity criterion in the context of the Fukaya $A_\infty$-category. </p> <p><small><a href="https://www.ams.org/journals/bull/2024-61-04/S0273-0979-2024-01808-4/viewer/">Read more»</a></small></p> <dl> <dt><strong>Also in Bulletin</strong></dt> <dd><a href="https://www.ams.org/journals/bull/2024-61-04/S0273-0979-2024-01835-7/viewer/">Algebraic solutions of linear differential equations: An arithmetic approach</a></dd> <dd><a href="https://www.ams.org/journals/bull/2024-61-04/S0273-0979-2024-01845-X/viewer">Spectral theory and self-similar blowup in wave equations</a></dd> </dl> <div class="clearfix"> </div> <p class="pull-right"><a class="btn btn-default" href="https://www.ams.org/journals/bull/2024-61-04/?active=current" role="button">More from Bulletin»</a></p> </article> </div> </div> <div class="tab-pane" id="newsTab" 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