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1<title>Joris Koefler's Website</title><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/animate.css/4.1.1/animate.min.css"/>
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1</head><body class="bg-gradient-to-r from-zinc-100 to-zinc-200 2xl:max-w-[1536px] mx-auto"><header><nav class="flex items-center justify-between px-4 py-8 lg:px-16 lg:py-10"><a class="flex-shrink-0 text-3xl font-extrabold text-black" href="/">Joris Koefler</a><button type="button" class="lg:hidden -m-2.5 inline-flex items-center justify-center rounded-md p-2.5 text-gray-700"><svg xmlns="http://www.w3.org/2000/svg" fill="none" viewBox="0 0 24 24" stroke-width="1.5" stroke="currentColor" aria-hidden="true" data-slot="icon" class="h-6 w-6"><path stroke-linecap="round" stroke-linejoin="round" d="M3.75 9h16.5m-16.5 6.75h16.5"></path></svg></button><div class="hidden lg:flex lg:gap-x-8"><a class="secondary-button" href="/#about">About Me</a><a class="secondary-button" href="/research">Research</a><a class="secondary-button" href="/teaching">Teaching</a><a class="secondary-button" href="/cv">CV</a></div><span hidden="" style="position:fixed;top:1px;left:1px;width:1px;height:0;padding:0;margin:-1px;overflow:hidden;clip:rect(0, 0, 0, 0);white-space:nowrap;border-width:0;display:none"></span></nav><span hidden="" style="position:fixed;top:1px;left:1px;width:1px;height:0;padding:0;margin:-1px;overflow:hidden;clip:rect(0, 0, 0, 0);white-space:nowrap;border-width:0;display:none"></span></header><main><div class="relative"><div class="min-h-[calc(100svh-6.3rem)] flex flex-col lg:flex-row items-center justify-center text-center lg:text-left px-4 py-8 lg:px-8 lg:py-0 gap-8 lg:gap-12 transition-all duration-700 ease-in-out"><div class="h-56 w-56 sm:h-72 sm:w-72 lg:h-[70vh] lg:w-[50vh] flex shrink-0 justify-center"><img src="/headshot_small.jpg" alt="Joris Koefler" class="h-full w-full object-cover rounded-full shadow-lg"/></div><div class="flex flex-col items-center lg:items-start gap-6 max-w-lg"><h1 class="font-black text-4xl lg:text-5xl select-none">Ph.D. candidate</h1><p class="text-balance text-zinc-600 tracking-wider text-lg select-none">Hey, I am Joris Koefler. Starting September 2026, I will be a research fellow at the School of Natural Sciences studying with Nima Arkani-Hamed. I did my PhD under the supervision of Rainer Sinn in Bernd Sturmfels' nonlinear algebra group at the MPI MiS in Leipzig. Before that, I studied with Diane Maclagan at the University of Warwick and Christian Stump at Ruhr University Bochum.</p><p class="text-zinc-600 tracking-wider text-lg">Email:<!-- --> <a href="mailto:[email protected]" class="underline hover:text-black transition">[email protected]</a></p><div class="flex flex-row space-x-6"><button class="primary-button">Research</button><div class="py-2 px-3 rounded-lg hover:bg-black hover:text-white text-base font-semibold leading-7 text-gray-900 flex items-center gap-1"><button>Meet Me</button><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" fill="currentColor" aria-hidden="true" data-slot="icon" class="size-5"><path fill-rule="evenodd" d="M12.53 16.28a.75.75 0 0 1-1.06 0l-7.5-7.5a.75.75 0 0 1 1.06-1.06L12 14.69l6.97-6.97a.75.75 0 1 1 1.06 1.06l-7.5 7.5Z" clip-rule="evenodd"></path></svg></div></div></div></div><div id="about" class="flex flex-col gap-20 px-7 py-12"><div class="flex flex-col gap-9 lg:mx-16"><h1 class="text-balance font-extrabold text-4xl">Research Interest</h1><div class="flex flex-col gap-5"><p class="text-balance tracking-wider lg:tracking-normal text-zinc-600 text-lg select-none">My research is in real algebraic geometry, combinatorics and their application to scattering amplitudes in fundamental particle Physics. In particular, I am interested in semi-algebraic sets appearing as positive geometries, such as the amplituhedron, and their adjoint hypersurfaces. I am also part of the <!-- --> <a class="underline font-bold" href="https://positive-geometry.com/">UNIVERSE+</a> <!-- --> <!-- -->project, where we explore more connections between fundamental Physics and Positive Geometry. I am a contributor to the Math-AI benchmark<!-- --> <!-- --> <a class="underline font-bold" href="https://math.science-bench.ai">science-bench</a>. I also like to organize outreach events, for example our <a class="underline font-bold" href="https://www.youtube.com/watch?v=poUrrdOYzUY">interview</a> with Nima Arkani-Hamed.</p></div><h1 class="text-balance font-bold text-2xl mt-0 mb-0">Highlighted Publication</h1><div class="flex flex-col lg:flex-row items-center justify-start text-center lg:text-left px-4 lg:px-8 gap-12 transition-all duration-700 ease-in-out"><div class="flex justify-center w-1/2 lg:w-1/4"><img src="/3D_DelPezzo.png" alt="Publication Image" class="rounded-xl object-contain w-auto h-auto lg:h-auto mx-auto"/></div><div class="flex-shrink-0 w-full lg:w-1/2 text-center lg:text-left p-4"><a target="_blank" rel="noopener noreferrer" class="text-balance font-semibold text-2xl mb-1 hover:underline" href="https://arxiv.org/abs/2601.11142">Positive Geometries of Positive Genus</a><p class="text-balance text-sm text-gray-600 mt-0">joint work with Dmitrii Pavlov, and Rainer Sinn</p><p class="text-balance text-lg text-gray-700 mt-2">If you thought positive geometries must make genus zero pairs, you will like our Del Pezzo cube
1! It has a nice canonical form, but an elliptic curve in its residual arrangement, so it makes a genus 1 pair.</p></div></div><button class="flex flex-row items-center gap-2 font-bold"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" fill="currentColor" class="size-5"><path fill-rule="evenodd" d="M12.97 3.97a.75.75 0 0 1 1.06 0l7.5 7.5a.75.75 0 0 1 0 1.06l-7.5 7.5a.75.75 0 1 1-1.06-1.06l6.22-6.22H3a.75.75 0 0 1 0-1.5h16.19l-6.22-6.22a.75.75 0 0 1 0-1.06Z" clip-rule="evenodd"></path></svg><a class="text-lg" href="/research">More about my research</a></button></div><div id="events" class="flex flex-col gap-8 mb-4 lg:mx-16"><h1 class="text-balance font-extrabold text-4xl">Upcoming & Recent Events</h1><div class="flex flex-col shadow-lg max-w-2xl"><div class="flex flex-col sm:flex-row rounded-lg bg-black sm:items-center gap-6 p-5 sm:pl-5 sm:pr-9 py-5"><div class="rounded py-4 px-6 border-zinc-100 border-2 sm:border-none sm:bg-zinc-100 flex flex-col justify-center sm:gap-2 text-center sm:w-[150px] sm:self-center"><span class="text-zinc-100 sm:text-black font-semibold text-2xl">28. - 02.</span><span class="text-zinc-100 sm:text-black font-semibold text-2xl">Sep-Oct<!-- --> <!-- -->2026</span></div><div class="text-white flex-1 flex flex-col justify-between gap-4"><div class="flex flex-col gap-1"><a class="font-bold text-xl" href="https://indico.mpp.mpg.de/event/11861">UNIVERSE+ annual meeting</a><span class="font-thin">Cambridge University, UK</span></div><div><button class="flex flex-row items-center gap-2"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" fill="currentColor" class="w-5 h-5" aria-hidden="true"><path fill-rule="evenodd" d="M12.97 3.97a.75.75 0 0 1 1.06 0l7.5 7.5a.75.75 0 0 1 0 1.06l-7.5 7.5a.75.75 0 1 1-1.06-1.06l6.22-6.22H3a.75.75 0 0 1 0-1.5h16.19l-6.22-6.22a.75.75 0 0 1 0-1.06Z" clip-rule="evenodd"></path></svg><a class="text-base" href="https://indico.mpp.mpg.de/event/11861">Visit website</a></button></div></div></div></div></div></div></div></main><footer class=""><nav aria-label="Global" class="flex items-center flex-col gap-12 p-10 lg:px-8"><div class="flex flex-row flex-wrap justify-evenly gap-6 sm:gap-12"><a class="footer-nav" href="/#about">About Me</a><a class="footer-nav" href="/research">Research</a><a class="footer-nav" href="/teaching">Teaching</a><a class="footer-nav" href="/cv">CV</a><a class="footer-nav" href="/">Contact</a></div><div class="flex flex-row mx-auto items-center space-x-10"><a href="https://www.linkedin.com/in/joris-köfler-88009a255/?originalSubdomain=uk"><svg aria-hidden="true" focusable="false" data-prefix="fab" data-icon="linkedin-in" class="svg-inline--fa fa-linkedin-in fa-lg " role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" style="color:#8b919c"><path fill="currentColor" d="M100.28 448H7.4V148.9h92.88zM53.79 108.1C24.09 108.1 0 83.5 0 53.8a53.79 53.79 0 0 1 107.58 0c0 29.7-24.1 54.3-53.79 54.3zM447.9 448h-92.68V302.4c0-34.7-.7-79.2-48.29-79.2-48.29 0-55.69 37.7-55.69 76.7V448h-92.78V148.9h89.08v40.8h1.3c12.4-23.5 42.69-48.3 87.88-48.3 94 0 111.28 61.9 111.28 142.3V448z"></path></svg></a><a href="mailto:[email protected]"><svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="envelope" class="svg-inline--fa fa-envelope fa-lg " role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" style="color:#8b919c"><path fill="currentColor" d="M48 64C21.5 64 0 85.5 0 112c0 15.1 7.1 29.3 19.2 38.4L236.8 313.6c11.4 8.5 27 8.5 38.4 0L492.8 150.4c12.1-9.1 19.2-23.3 19.2-38.4c0-26.5-21.5-48-48-48L48 64zM0 176L0 384c0 35.3 28.7 64 64 64l384 0c35.3 0 64-28.7 64-64l0-208L294.4 339.2c-22.8 17.1-54 17.1-76.8 0L0 176z"></path></svg></a></div><div class="flex-row mx-auto items-center text-xs font-extralight text-gray-500"><span>© 2024 Joris Koefler, All rights reserved.</span></div></nav></footer>
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