https://sfb-higher-invariants.app.uni-regensburg.de/index.php?action=history&feed=atom&title=Interactions_between_homotopy_theory_and_CAlgebraic_KTheory
Interactions between homotopy theory and CAlgebraic KTheory - Revision history
2026-10-25T18:55:08Z
Revision history for this page on the wiki
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https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=Interactions_between_homotopy_theory_and_CAlgebraic_KTheory&diff=2992&oldid=prev
Dub22449 at 08:29, 10 February 2025
2025-02-10T08:29:31Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:29, 10 February 2025</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Week 2:'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Week 2:'''</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Ulrich Bunke:''' Homotopy theory for K-theory of crossed products<del style="font-weight: bold; text-decoration: none;">; </del>; [https://youtu.be/9AnRxbVMICo Video], [[Media: Ulrich_Bunke_2.pdf | Notes]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Ulrich Bunke:''' Homotopy theory for K-theory of crossed products; [https://youtu.be/9AnRxbVMICo Video], [[Media: Ulrich_Bunke_2.pdf | Notes]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>If a group G acts on a C*-algebra A, then one can form the crossed product A ⋊ G.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>If a group G acts on a C*-algebra A, then one can form the crossed product A ⋊ G.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Marius Dadarlat:''' Asymptotic Homotopy, Asymptotic Commutants, and K-Theoretic Duality</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Marius Dadarlat:''' Asymptotic Homotopy, Asymptotic Commutants, and K-Theoretic Duality<ins style="font-weight: bold; text-decoration: none;">; [https://www.youtube.com/watch?v=GgjJdsvMMj0 Video]</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The talk aims to highlight connections between certain asymptotic properties of C*-algebras and KK-theory. It draws on joint work with Loring, Pennig, Willett, and Wu.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The talk aims to highlight connections between certain asymptotic properties of C*-algebras and KK-theory. It draws on joint work with Loring, Pennig, Willett, and Wu.</div></td></tr>
</table>
Dub22449
https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=Interactions_between_homotopy_theory_and_CAlgebraic_KTheory&diff=2969&oldid=prev
Brv60445 at 12:50, 29 January 2025
2025-01-29T12:50:25Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:50, 29 January 2025</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The normal registration period has passed. To receive a Zoom-link, please reach out to one of the organizers. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The normal registration period has passed. To receive a Zoom-link, please reach out to one of the organizers. </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">==Conference Poster==</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><div class="res-img">[[File:Interactions.png| center]]</div></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">You can download the conference poster [[Media:Interactions_6_2.pdf| <b>here</b>]].</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Organizers==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Organizers==</div></td></tr>
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Brv60445
https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=Interactions_between_homotopy_theory_and_CAlgebraic_KTheory&diff=2968&oldid=prev
Brv60445 at 08:30, 27 January 2025
2025-01-27T08:30:47Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:30, 27 January 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l249">Line 249:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The normal registration period has passed. To receive a Zoom-link, please reach out to one of the organizers. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The normal registration period has passed. To receive a Zoom-link, please reach out to one of the organizers. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Conference Poster==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><div class="res-img">[[File:Interactions.png| center]]</div></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">You can download the conference poster [[Media:Interactions_6_2.pdf| <b>here</b>]].</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Organizers==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Organizers==</div></td></tr>
</table>
Brv60445
https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=Interactions_between_homotopy_theory_and_CAlgebraic_KTheory&diff=2964&oldid=prev
Dub22449 at 21:45, 22 January 2025
2025-01-22T21:45:37Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:45, 22 January 2025</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Alexander Engel:''' C*-Categories; [https://youtu.be/KrvBSjeXCjU Video]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Alexander Engel:''' C*-Categories; [https://youtu.be/KrvBSjeXCjU Video<ins style="font-weight: bold; text-decoration: none;">], [[Media: AlexE_slides.pdf|Notes]</ins>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>After giving a brief introduction to C*-categories I will explain how to extend KK-theory from C*-algebras to C*-categories and why this is useful. In the second half of my talk I will focus on the (2,1)-categorical nature of C*-categories arising from considering unitary equivalences.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>After giving a brief introduction to C*-categories I will explain how to extend KK-theory from C*-algebras to C*-categories and why this is useful. In the second half of my talk I will focus on the (2,1)-categorical nature of C*-categories arising from considering unitary equivalences.</div></td></tr>
</table>
Dub22449
https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=Interactions_between_homotopy_theory_and_CAlgebraic_KTheory&diff=2963&oldid=prev
Dub22449 at 21:42, 22 January 2025
2025-01-22T21:42:49Z
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Alexander Engel:''' C*-Categories</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Alexander Engel:''' C*-Categories<ins style="font-weight: bold; text-decoration: none;">; [https://youtu.be/KrvBSjeXCjU Video]</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>After giving a brief introduction to C*-categories I will explain how to extend KK-theory from C*-algebras to C*-categories and why this is useful. In the second half of my talk I will focus on the (2,1)-categorical nature of C*-categories arising from considering unitary equivalences.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>After giving a brief introduction to C*-categories I will explain how to extend KK-theory from C*-algebras to C*-categories and why this is useful. In the second half of my talk I will focus on the (2,1)-categorical nature of C*-categories arising from considering unitary equivalences.</div></td></tr>
</table>
Dub22449
https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=Interactions_between_homotopy_theory_and_CAlgebraic_KTheory&diff=2962&oldid=prev
Dub22449 at 21:41, 22 January 2025
2025-01-22T21:41:13Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<col class="diff-marker" />
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<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:41, 22 January 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l182">Line 182:</td>
<td colspan="2" class="diff-lineno">Line 182:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Ralf Meyer:''' Classifying C*-algebras up to KK-equivalence; [[Media: Ralf_Meyer.pdf | Notes]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Ralf Meyer:''' Classifying C*-algebras up to KK-equivalence; <ins style="font-weight: bold; text-decoration: none;">[https://youtu.be/QnlBhZk-v7U Video], </ins>[[Media: Ralf_Meyer.pdf | Notes]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Several classification results for C*-algebras say that an equivalence between two C*-algebras in a suitable bivariant KK-theory that encodes extra structure such as ideals or a group action, lifts to an isomorphism of those C*-algebras, suitably compatible with the extra structure. This leads to the question how to classify objects in a bivariant KK-theory up to isomorphism using some simpler K-theoretic invariant. One method to produce prove that an invariant works for this is to show that any object has a projective resolution of length 1 in a certain sense. There are several examples where this exists. A rather sophisticated theorem about this due to my doctoral student Köhler is for C*-algebras with an action of a group of prime order. More generally, if an object has a projective resolution of length 2, then one may use a more general classification result proven by Bentmann and me. Besides the invariant used to set up the projective resolutions, this invariant contains an extra piece of information, which we call the obstruction class. This classification method applies, for instance, to C*-algebras with an action of the circle group or to graph C*-algebras with finite ideal lattice.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Several classification results for C*-algebras say that an equivalence between two C*-algebras in a suitable bivariant KK-theory that encodes extra structure such as ideals or a group action, lifts to an isomorphism of those C*-algebras, suitably compatible with the extra structure. This leads to the question how to classify objects in a bivariant KK-theory up to isomorphism using some simpler K-theoretic invariant. One method to produce prove that an invariant works for this is to show that any object has a projective resolution of length 1 in a certain sense. There are several examples where this exists. A rather sophisticated theorem about this due to my doctoral student Köhler is for C*-algebras with an action of a group of prime order. More generally, if an object has a projective resolution of length 2, then one may use a more general classification result proven by Bentmann and me. Besides the invariant used to set up the projective resolutions, this invariant contains an extra piece of information, which we call the obstruction class. This classification method applies, for instance, to C*-algebras with an action of the circle group or to graph C*-algebras with finite ideal lattice.</div></td></tr>
</table>
Dub22449
https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=Interactions_between_homotopy_theory_and_CAlgebraic_KTheory&diff=2959&oldid=prev
Dub22449 at 22:15, 16 January 2025
2025-01-16T22:15:43Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:15, 16 January 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l155">Line 155:</td>
<td colspan="2" class="diff-lineno">Line 155:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Ivo Dell'Ambrogio:''' Tensor triangular geometry for equivariant KK-theory; [https://youtu.be/ucTOJsXT5qM Video]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Ivo Dell'Ambrogio:''' Tensor triangular geometry for equivariant KK-theory; [https://youtu.be/ucTOJsXT5qM Video<ins style="font-weight: bold; text-decoration: none;">], [[Media: Ivo_DellAmbrogio.pdf | Notes]</ins>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In 2006, Ralf Meyer and Ryszard Nest proved that the equivariant KK-theory of a locally compact group G carries the structure of a tensor triangulated category. As with any tensor triangulated category, one can then try to apply the methods of Paul Balmer's tensor triangular geometry to it. In this talk I will introduce these ideas and explain their latest applications to KK-theory, in the form of classifications of thick and localizing subcategories inside the G-equivariant bootstrap class for certain finite groups G (joint work with Rubén Martos).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In 2006, Ralf Meyer and Ryszard Nest proved that the equivariant KK-theory of a locally compact group G carries the structure of a tensor triangulated category. As with any tensor triangulated category, one can then try to apply the methods of Paul Balmer's tensor triangular geometry to it. In this talk I will introduce these ideas and explain their latest applications to KK-theory, in the form of classifications of thick and localizing subcategories inside the G-equivariant bootstrap class for certain finite groups G (joint work with Rubén Martos).</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l182">Line 182:</td>
<td colspan="2" class="diff-lineno">Line 182:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Ralf Meyer:''' Classifying C*-algebras up to KK-equivalence</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Ralf Meyer:''' Classifying C*-algebras up to KK-equivalence<ins style="font-weight: bold; text-decoration: none;">; [[Media: Ralf_Meyer.pdf | Notes]]</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Several classification results for C*-algebras say that an equivalence between two C*-algebras in a suitable bivariant KK-theory that encodes extra structure such as ideals or a group action, lifts to an isomorphism of those C*-algebras, suitably compatible with the extra structure. This leads to the question how to classify objects in a bivariant KK-theory up to isomorphism using some simpler K-theoretic invariant. One method to produce prove that an invariant works for this is to show that any object has a projective resolution of length 1 in a certain sense. There are several examples where this exists. A rather sophisticated theorem about this due to my doctoral student Köhler is for C*-algebras with an action of a group of prime order. More generally, if an object has a projective resolution of length 2, then one may use a more general classification result proven by Bentmann and me. Besides the invariant used to set up the projective resolutions, this invariant contains an extra piece of information, which we call the obstruction class. This classification method applies, for instance, to C*-algebras with an action of the circle group or to graph C*-algebras with finite ideal lattice.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Several classification results for C*-algebras say that an equivalence between two C*-algebras in a suitable bivariant KK-theory that encodes extra structure such as ideals or a group action, lifts to an isomorphism of those C*-algebras, suitably compatible with the extra structure. This leads to the question how to classify objects in a bivariant KK-theory up to isomorphism using some simpler K-theoretic invariant. One method to produce prove that an invariant works for this is to show that any object has a projective resolution of length 1 in a certain sense. There are several examples where this exists. A rather sophisticated theorem about this due to my doctoral student Köhler is for C*-algebras with an action of a group of prime order. More generally, if an object has a projective resolution of length 2, then one may use a more general classification result proven by Bentmann and me. Besides the invariant used to set up the projective resolutions, this invariant contains an extra piece of information, which we call the obstruction class. This classification method applies, for instance, to C*-algebras with an action of the circle group or to graph C*-algebras with finite ideal lattice.</div></td></tr>
</table>
Dub22449
https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=Interactions_between_homotopy_theory_and_CAlgebraic_KTheory&diff=2958&oldid=prev
Dub22449 at 22:12, 16 January 2025
2025-01-16T22:12:38Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<col class="diff-marker" />
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:12, 16 January 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l155">Line 155:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Ivo Dell'Ambrogio:''' Tensor triangular geometry for equivariant KK-theory</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Ivo Dell'Ambrogio:''' Tensor triangular geometry for equivariant KK-theory<ins style="font-weight: bold; text-decoration: none;">; [https://youtu.be/ucTOJsXT5qM Video]</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In 2006, Ralf Meyer and Ryszard Nest proved that the equivariant KK-theory of a locally compact group G carries the structure of a tensor triangulated category. As with any tensor triangulated category, one can then try to apply the methods of Paul Balmer's tensor triangular geometry to it. In this talk I will introduce these ideas and explain their latest applications to KK-theory, in the form of classifications of thick and localizing subcategories inside the G-equivariant bootstrap class for certain finite groups G (joint work with Rubén Martos).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In 2006, Ralf Meyer and Ryszard Nest proved that the equivariant KK-theory of a locally compact group G carries the structure of a tensor triangulated category. As with any tensor triangulated category, one can then try to apply the methods of Paul Balmer's tensor triangular geometry to it. In this talk I will introduce these ideas and explain their latest applications to KK-theory, in the form of classifications of thick and localizing subcategories inside the G-equivariant bootstrap class for certain finite groups G (joint work with Rubén Martos).</div></td></tr>
</table>
Dub22449
https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=Interactions_between_homotopy_theory_and_CAlgebraic_KTheory&diff=2957&oldid=prev
Dub22449 at 22:07, 16 January 2025
2025-01-16T22:07:05Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:07, 16 January 2025</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Devarshi Mukherjee:''' Rigid categories in functional analysis </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Devarshi Mukherjee:''' Rigid categories in functional analysis<ins style="font-weight: bold; text-decoration: none;">; [https://youtu.be/AQxiO1IwOq0 Video]</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In this talk, I will introduce a category of nuclear modules associated to a complete bornological algebra. In a sense that will be made precise, this category is a rigid symmetric monoidal category, and therefore serves as an input for continuous K-theory. We will then use this category to define a version of A<sup>1</sup>-invariant noncommutative motives, which admits a functor from KK-theory. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In this talk, I will introduce a category of nuclear modules associated to a complete bornological algebra. In a sense that will be made precise, this category is a rigid symmetric monoidal category, and therefore serves as an input for continuous K-theory. We will then use this category to define a version of A<sup>1</sup>-invariant noncommutative motives, which admits a functor from KK-theory. </div></td></tr>
</table>
Dub22449
https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=Interactions_between_homotopy_theory_and_CAlgebraic_KTheory&diff=2956&oldid=prev
Dub22449 at 22:05, 16 January 2025
2025-01-16T22:05:15Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:05, 16 January 2025</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Markus Land:''' K- and L-theory of C*-algebras; [https://youtu.be/ics2Ikk2DEk]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Markus Land:''' K- and L-theory of C*-algebras; [https://youtu.be/ics2Ikk2DEk <ins style="font-weight: bold; text-decoration: none;">Video</ins>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>I will explain how to use the ∞-categorical enhancement of Kasparov’s KK-cateogry to study the relation between (topological) K- and L-theory spectra of (complex) C*-algebras. This is largely motivated by the quest for a comparison of the Baum-Connes conjecture and the (L-theoretic) Farrell-Jones conjecture, and I will explain how to obtain such a comparison. Furthermore, I will explain that the comparison between K- and L-spectra is slightly more subtle than was initially expected. Finally, if time permits, I will indicate how to describe L-theory of arbitrary real C*-algebras in terms of topological K-theory; in contrast to the complex case, the L-groups of real C*-algebras have not previously been described in terms of topological K-groups.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>I will explain how to use the ∞-categorical enhancement of Kasparov’s KK-cateogry to study the relation between (topological) K- and L-theory spectra of (complex) C*-algebras. This is largely motivated by the quest for a comparison of the Baum-Connes conjecture and the (L-theoretic) Farrell-Jones conjecture, and I will explain how to obtain such a comparison. Furthermore, I will explain that the comparison between K- and L-spectra is slightly more subtle than was initially expected. Finally, if time permits, I will indicate how to describe L-theory of arbitrary real C*-algebras in terms of topological K-theory; in contrast to the complex case, the L-groups of real C*-algebras have not previously been described in terms of topological K-groups.</div></td></tr>
</table>
Dub22449