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UID:MEC-0fe473396242072e84af286632d3f0ff@eur.univ-paris13.fr
DTSTART:20260325T150000Z
DTEND:20260325T170000Z
DTSTAMP:20260323T151200Z
RDATE;VALUE=PERIOD:20260325T150000Z/20260325T170000Z,20260401T140000Z/20260401T160000Z,20260408T140000Z/20260408T160000Z
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SUMMARY:Mini-course by Ulrik Buchholtz
DESCRIPTION:We are delighted to welcome Ulrik Buchholtz (Functional Programming Lab, School of Computer Science, The University of Nottingham) for a mini-course on synthetic homotopy theory.\nIntroduction to Synthetic Homotopy Theory\nWe’ll cover topics in synthetic homotopy theory using homotopy type theory/univalent foundations. First, we’ll give a brief overview of Martin-Löf type theory and an intuitive picture of its interpretation in spaces qua infinity-groupoids. This interpretation motivates Voevodsky’s definition of contractible types, equivalences, homotopy n-types, n-connected types, and the univalence axiom.\nNext, we cover homotopy pushouts as a new type constructor, including variations such as the circle, suspensions, cofibers, joins, and smash products. We’ll look at the type-theoretic formulation of homotopy groups, and the long exact sequence given by a map, leading to the calculation of some homotopy groups.\nThe last lecture will cover the zigzag construction of the path spaces of pushouts, leading to a type-theoretic proof of the Blakers–Massey connectivity theorem. Time permitting, we can touch on other aspects of synthetic homotopy theory, according to the interests of the participants.\nPractical information\nDates: Wednesdays 25 March, 1 April and 8 April 2026\nTimes: 4.00 pm to 6.00 pm\nLocation: Room B405, LAGA, Sorbonne Paris Nord University (99 Av. Jean Baptiste Clément, 93430 Villetaneuse)\nParticipation: The course is available in a hybrid format, either in person or online, via the link here : https://bbb.math.univ-paris13.fr/b/chr-hyw-0rb-jz4\nLecturer’s personal website: https://ulrikbuchholtz.dk/\nFirst Lesson : https://bbb.math.univ-paris13.fr/playback/presentation/2.3/260aa433e092cf0e79b317a48abfe4178f8bd499-1774450535929\nSecond Lesson : https://bbb.math.univ-paris13.fr/playback/presentation/2.3/260aa433e092cf0e79b317a48abfe4178f8bd499-1775053561192\nThird Lesson : https://bbb.math.univ-paris13.fr/playback/presentation/2.3/260aa433e092cf0e79b317a48abfe4178f8bd499-1775657089602\n \nTo watch the video in full screen, click on this icon : \n
X-ALT-DESC;FMTTYPE=text/html:<p>We are delighted to welcome Ulrik Buchholtz (Functional Programming Lab, School of Computer Science, The University of Nottingham) for a mini-course on synthetic homotopy theory.</p>
<p><strong>Introduction to Synthetic Homotopy Theory</strong></p>
<p>We&#8217;ll cover topics in synthetic homotopy theory using homotopy type theory/univalent foundations. First, we&#8217;ll give a brief overview of Martin-Löf type theory and an intuitive picture of its interpretation in spaces qua infinity-groupoids. This interpretation motivates Voevodsky&#8217;s definition of contractible types, equivalences, homotopy n-types, n-connected types, and the univalence axiom.</p>
<p>Next, we cover homotopy pushouts as a new type constructor, including variations such as the circle, suspensions, cofibers, joins, and smash products. We&#8217;ll look at the type-theoretic formulation of homotopy groups, and the long exact sequence given by a map, leading to the calculation of some homotopy groups.</p>
<p>The last lecture will cover the zigzag construction of the path spaces of pushouts, leading to a type-theoretic proof of the Blakers–Massey connectivity theorem. Time permitting, we can touch on other aspects of synthetic homotopy theory, according to the interests of the participants.</p>
<p><strong>Practical information</strong></p>
<p><em>Dates</em>: Wednesdays 25 March, 1 April and 8 April 2026<br />
<em>Times</em>: 4.00 pm to 6.00 pm<br />
<em>Location</em>: Room B405, LAGA, Sorbonne Paris Nord University (99 Av. Jean Baptiste Clément, 93430 Villetaneuse)<br />
<em>Participation</em>: The course is available in a hybrid format, either in person or online, via the link here : <a href="https://bbb.math.univ-paris13.fr/b/chr-hyw-0rb-jz4">https://bbb.math.univ-paris13.fr/b/chr-hyw-0rb-jz4</a><br />
Lecturer’s personal website:<a href="https://ulrikbuchholtz.dk/"> https://ulrikbuchholtz.dk/</a></p>
<p>First Lesson : <a href="https://bbb.math.univ-paris13.fr/playback/presentation/2.3/260aa433e092cf0e79b317a48abfe4178f8bd499-1774450535929">https://bbb.math.univ-paris13.fr/playback/presentation/2.3/260aa433e092cf0e79b317a48abfe4178f8bd499-1774450535929</a><br />
Second Lesson :<a href="https://bbb.math.univ-paris13.fr/playback/presentation/2.3/260aa433e092cf0e79b317a48abfe4178f8bd499-1775053561192"> https://bbb.math.univ-paris13.fr/playback/presentation/2.3/260aa433e092cf0e79b317a48abfe4178f8bd499-1775053561192</a><br />
Third Lesson : <a href="https://bbb.math.univ-paris13.fr/playback/presentation/2.3/260aa433e092cf0e79b317a48abfe4178f8bd499-1775657089602">https://bbb.math.univ-paris13.fr/playback/presentation/2.3/260aa433e092cf0e79b317a48abfe4178f8bd499-1775657089602</a></p>
<p>&nbsp;</p>
<p><strong>To watch the video in full screen, click on this icon : <img loading="lazy" class="alignnone size-full wp-image-2438" src="https://eur.univ-paris13.fr/wp-content/uploads/2026/03/Capture-decran-2026-04-01-155206.png" alt="" width="32" height="29" /></strong></p>

URL:https://eur.univ-paris13.fr/en/events/mini-course-by-ulrik-buchholtz/
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