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</div> </div> </header> <div id="main" class=" main"> <div id="loop-meta" class=" loop-meta-wrap pageheader-bg-default loop-meta-withtext"> <div class="hgrid"> <div class=" loop-meta archive-header hgrid-span-12" itemscope="itemscope" itemtype="https://schema.org/WebPageElement"> <h1 class=" loop-title entry-title archive-title" itemprop="headline">Lie groups</h1> </div> </div> </div> <div class="hgrid main-content-grid"> <main id="content" class="content hgrid-span-8 has-sidebar layout-wide-right " role="main"> <div id="content-wrap" class=" content-wrap theiaStickySidebar"> <div id="archive-wrap" class="archive-wrap"> <article id="post-2131" class="entry author-uwhitcher post-2131 post type-post status-publish format-standard has-post-thumbnail category-147 category-algebra-and-number-theory category-holley-friedlander category-math-and-the-sciences tag-automorphic-forms tag-e8 tag-lie-groups tag-string-theory archive-block archive-block2 hcolumn-1-2" itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost"> <div class="entry-grid hgrid"> <div itemprop="image" itemscope itemtype="https://schema.org/ImageObject" class="entry-featured-img-wrap"><meta itemprop="url" content="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?resize=690%2C288&ssl=1"><meta itemprop="width" content="690"><meta itemprop="height" content="288"><a href="https://mathvoices.ams.org/featurecolumn/2024/11/01/strung-out-on-automorphic-forms/" class="entry-featured-img-link"><img width="690" height="288" src="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?resize=690%2C288&ssl=1" class="attachment-hoot-large-thumb entry-content-featured-img entry-grid-featured-img wp-post-image" alt="Feature Column" itemscope="" decoding="async" fetchpriority="high" srcset="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?resize=690%2C288&ssl=1 690w, https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?zoom=2&resize=690%2C288&ssl=1 1380w" sizes="(max-width: 690px) 100vw, 690px" itemprop="image" /></a></div> <div class="entry-grid-content"> <header class="entry-header"> <h2 class="entry-title" itemprop="headline"><a href="https://mathvoices.ams.org/featurecolumn/2024/11/01/strung-out-on-automorphic-forms/" rel="bookmark" itemprop="url">Strung Out on Automorphic Forms</a></h2> </header> <div class="screen-reader-text" itemprop="datePublished" itemtype="https://schema.org/Date">2024-11-01</div> <div class="entry-byline"> <div class="entry-byline-block entry-byline-author"> <span class="entry-byline-label">By:</span> <span class="entry-author" itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person"><a href="https://mathvoices.ams.org/featurecolumn/author/uwhitcher/" title="Posts by Ursula Whitcher" rel="author" class="url fn n" itemprop="url"><span itemprop="name">Ursula Whitcher</span></a></span> </div> <div class="entry-byline-block entry-byline-date"> <span class="entry-byline-label">On:</span> <time class="entry-published updated" datetime="2024-11-01T00:01:09-04:00" itemprop="datePublished" title="Friday, November 1, 2024, 12:01 am">November 1, 2024</time> </div> <div class="entry-byline-block entry-byline-cats"> <span class="entry-byline-label">In:</span> <a href="https://mathvoices.ams.org/featurecolumn/category/2024/" rel="category tag">2024</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/algebra-and-number-theory/" rel="category tag">Algebra and Number Theory</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/columnists/holley-friedlander/" rel="category tag">Holley Friedlander</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/math-and-the-sciences/" rel="category tag">Math and the Sciences</a> </div> <div class="entry-byline-block entry-byline-tags"> <span class="entry-byline-label">Tagged:</span> <a href="https://mathvoices.ams.org/featurecolumn/tag/automorphic-forms/" rel="tag">automorphic forms</a>, <a href="https://mathvoices.ams.org/featurecolumn/tag/e8/" rel="tag">E8</a>, <a href="https://mathvoices.ams.org/featurecolumn/tag/lie-groups/" rel="tag">Lie groups</a>, <a href="https://mathvoices.ams.org/featurecolumn/tag/string-theory/" rel="tag">string theory</a> </div> <div class="entry-byline-block entry-byline-comments"> <span class="entry-byline-label">With:</span> <a href="https://mathvoices.ams.org/featurecolumn/2024/11/01/strung-out-on-automorphic-forms/#respond" class="comments-link" itemprop="discussionURL">0 Comments</a> </div><span class="entry-publisher" itemprop="publisher" itemscope="itemscope" itemtype="https://schema.org/Organization"><meta itemprop="name" content="Feature Column"><span itemprop="logo" itemscope itemtype="https://schema.org/ImageObject"><meta itemprop="url" content=""><meta itemprop="width" content=""><meta itemprop="height" content=""></span></span></div> <div class="entry-summary" itemprop="description"><p>An automorphic form is, in the simplest sense, like a trigonometric function. Trigonometric functions are inescapable in both mathematics and physics, so it makes sense that we would see generalizations of them in physics applications... Strung Out on Automorphic Forms Holley Friedlander Dickinson College Automorphic forms are highly symmetric functions<span class="more-link"><a href="https://mathvoices.ams.org/featurecolumn/2024/11/01/strung-out-on-automorphic-forms/">Read More →</a></span></p> </div> </div> </div> </article> <article id="post-1510" class="entry author-uwhitcher post-1510 post type-post status-publish format-standard has-post-thumbnail category-4 category-algebra-and-number-theory category-anil-venkatesh category-real-and-complex-analysis tag-hyperoperations tag-lie-groups archive-block archive-block2 hcolumn-1-2" itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost"> <div class="entry-grid hgrid"> <div itemprop="image" itemscope itemtype="https://schema.org/ImageObject" class="entry-featured-img-wrap"><meta itemprop="url" content="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2022/03/cropped-cropped-mathvoices-banner-feat-col-1.png?resize=690%2C279&ssl=1"><meta itemprop="width" content="690"><meta itemprop="height" content="279"><a href="https://mathvoices.ams.org/featurecolumn/2022/12/01/hyperoperations-distributivity-and-the-unreasonable-effectiveness-of-multiplication/" class="entry-featured-img-link"><img width="690" height="279" src="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2022/03/cropped-cropped-mathvoices-banner-feat-col-1.png?resize=690%2C279&ssl=1" class="attachment-hoot-large-thumb entry-content-featured-img entry-grid-featured-img wp-post-image" alt="Banner for the AMS Feature Column" itemscope="" decoding="async" itemprop="image" /></a></div> <div class="entry-grid-content"> <header class="entry-header"> <h2 class="entry-title" itemprop="headline"><a href="https://mathvoices.ams.org/featurecolumn/2022/12/01/hyperoperations-distributivity-and-the-unreasonable-effectiveness-of-multiplication/" rel="bookmark" itemprop="url">Hyperoperations, Distributivity, and the Unreasonable Effectiveness of Multiplication</a></h2> </header> <div class="screen-reader-text" itemprop="datePublished" itemtype="https://schema.org/Date">2022-12-01</div> <div class="entry-byline"> <div class="entry-byline-block entry-byline-author"> <span class="entry-byline-label">By:</span> <span class="entry-author" itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person"><a href="https://mathvoices.ams.org/featurecolumn/author/uwhitcher/" title="Posts by Ursula Whitcher" rel="author" class="url fn n" itemprop="url"><span itemprop="name">Ursula Whitcher</span></a></span> </div> <div class="entry-byline-block entry-byline-date"> <span class="entry-byline-label">On:</span> <time class="entry-published updated" datetime="2022-12-01T00:01:39-05:00" itemprop="datePublished" title="Thursday, December 1, 2022, 12:01 am">December 1, 2022</time> </div> <div class="entry-byline-block entry-byline-cats"> <span class="entry-byline-label">In:</span> <a href="https://mathvoices.ams.org/featurecolumn/category/2022/" rel="category tag">2022</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/algebra-and-number-theory/" rel="category tag">Algebra and Number Theory</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/columnists/anil-venkatesh/" rel="category tag">Anil Venkatesh</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/real-and-complex-analysis/" rel="category tag">Real and Complex Analysis</a> </div> <div class="entry-byline-block entry-byline-tags"> <span class="entry-byline-label">Tagged:</span> <a href="https://mathvoices.ams.org/featurecolumn/tag/hyperoperations/" rel="tag">hyperoperations</a>, <a href="https://mathvoices.ams.org/featurecolumn/tag/lie-groups/" rel="tag">Lie groups</a> </div> <div class="entry-byline-block entry-byline-comments"> <span class="entry-byline-label">With:</span> <a href="https://mathvoices.ams.org/featurecolumn/2022/12/01/hyperoperations-distributivity-and-the-unreasonable-effectiveness-of-multiplication/#respond" class="comments-link" itemprop="discussionURL">0 Comments</a> </div><span class="entry-publisher" itemprop="publisher" itemscope="itemscope" itemtype="https://schema.org/Organization"><meta itemprop="name" content="Feature Column"><span itemprop="logo" itemscope itemtype="https://schema.org/ImageObject"><meta itemprop="url" content=""><meta itemprop="width" content=""><meta itemprop="height" content=""></span></span></div> <div class="entry-summary" itemprop="description"><p>In 1915, the paper “Note on an Operation of the Third Grade” by Albert A. Bennett appeared in the Annals of Mathematics. A terse two-page note, it was largely neglected until the early 2000s… Hyperoperations, Distributivity, and the Unreasonable Effectiveness of Multiplication Anil Venkatesh Adelphi University Iterated Operations Everyone knows<span class="more-link"><a href="https://mathvoices.ams.org/featurecolumn/2022/12/01/hyperoperations-distributivity-and-the-unreasonable-effectiveness-of-multiplication/">Read More →</a></span></p> </div> </div> </div> </article></div><div class="clearfix"></div> </div> </main> <aside id="sidebar-primary" class="sidebar sidebar-primary hgrid-span-4 layout-wide-right " role="complementary" itemscope="itemscope" itemtype="https://schema.org/WPSideBar"> <div class=" sidebar-wrap theiaStickySidebar"> <section id="search-2" class="widget widget_search"><div class="searchbody"><form method="get" class="searchform" action="https://mathvoices.ams.org/featurecolumn/" ><label class="screen-reader-text">Search</label><i class="fas fa-search"></i><input type="text" class="searchtext" name="s" placeholder="Type Search Term …" value="" /><input type="submit" class="submit" name="submit" value="Search" /><span class="js-search-placeholder"></span></form></div></section><section id="blog_subscription-2" class="widget widget_blog_subscription jetpack_subscription_widget"><h3 class="widget-title"><span>Subscribe to Feature Column via Email</span></h3> <div class="wp-block-jetpack-subscriptions__container"> <form action="#" method="post" accept-charset="utf-8" id="subscribe-blog-blog_subscription-2" data-blog="202620863" data-post_access_level="everybody" > <div id="subscribe-text"><p>Enter your email address to subscribe to Feature Column and receive notifications of new posts by email.</p> </div> <p id="subscribe-email"> <label id="jetpack-subscribe-label" class="screen-reader-text" for="subscribe-field-blog_subscription-2"> Email Address </label> <input type="email" name="email" required="required" value="" id="subscribe-field-blog_subscription-2" placeholder="Email Address" /> </p> <p id="subscribe-submit" > <input type="hidden" name="action" value="subscribe"/> <input type="hidden" name="source" value="https://mathvoices.ams.org/featurecolumn/tag/lie-groups/"/> <input type="hidden" name="sub-type" value="widget"/> <input type="hidden" name="redirect_fragment" value="subscribe-blog-blog_subscription-2"/> <input type="hidden" id="_wpnonce" name="_wpnonce" value="6337b3f234" /><input type="hidden" name="_wp_http_referer" value="/featurecolumn/tag/lie-groups/" /> <button type="submit" class="wp-block-button__link" name="jetpack_subscriptions_widget" > Subscribe </button> </p> </form> </div> </section><section id="block-3" class="widget widget_block"><div class="wp-block-group"><div class="wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow"><h2 class="wp-block-heading">Recent Posts</h2><ul class="wp-block-latest-posts__list wp-block-latest-posts"><li><a class="wp-block-latest-posts__post-title" href="https://mathvoices.ams.org/featurecolumn/2024/11/01/strung-out-on-automorphic-forms/">Strung Out on Automorphic Forms</a></li> <li><a class="wp-block-latest-posts__post-title" href="https://mathvoices.ams.org/featurecolumn/2024/10/01/people-and-computers-compared/">People and Computers Compared</a></li> <li><a class="wp-block-latest-posts__post-title" href="https://mathvoices.ams.org/featurecolumn/2024/09/01/payoffs-and-strategies/">Payoffs and strategies</a></li> <li><a class="wp-block-latest-posts__post-title" href="https://mathvoices.ams.org/featurecolumn/2024/08/01/welcome-to-the-fold/">Welcome to the Fold</a></li> <li><a class="wp-block-latest-posts__post-title" href="https://mathvoices.ams.org/featurecolumn/2024/07/01/looking-ahead/">Looking ahead</a></li> </ul></div></div></section><section id="categories-2" class="widget widget_categories"><h3 class="widget-title"><span>Categories</span></h3> <ul> <li class="cat-item cat-item-2"><a href="https://mathvoices.ams.org/featurecolumn/category/2020/">2020</a> </li> <li class="cat-item cat-item-3"><a href="https://mathvoices.ams.org/featurecolumn/category/2021/">2021</a> </li> <li class="cat-item cat-item-4"><a href="https://mathvoices.ams.org/featurecolumn/category/2022/">2022</a> </li> <li class="cat-item cat-item-112"><a href="https://mathvoices.ams.org/featurecolumn/category/2023/">2023</a> </li> <li class="cat-item cat-item-147"><a href="https://mathvoices.ams.org/featurecolumn/category/2024/">2024</a> </li> <li class="cat-item cat-item-5"><a href="https://mathvoices.ams.org/featurecolumn/category/columnists/adam-a-smith/">Adam A. 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