Ambidexterity Learning Seminar

This page contains information for the Fall 2025 learning seminar on (Twisted) Ambidexterity at UIUC, organized by myself under the supervision of Dr. Dan Berwick-Evans.

The (current) reading plan for the seminar can be found here. The primary references are:

• [CSY20] Carmeli, S., Schlank, T.M., Yanovski, L.: Ambidexterity and Height, http://arxiv.org/abs/2007.13089, (2020)
• [CSY18] Carmeli, S., Schlank, T.M., and Yanovski, L.: “Ambidexterity in Chromatic Homotopy Theory.” arXiv:1811.02057. Preprint, arXiv, September 16, 2020. https://doi.org/10.48550/arXiv.1811.02057.
• [Cno24] Bastiaan Cnossen. “Twisted Ambidexterity in Equivariant Homotopy Theory: Two Approaches.” Phd, Rheinische Friedrich-Wilhelms-Universität Bonn, 2024. https://hdl.handle.net/20.500.11811/11281.
• [CLS24] Cnossen, B., Lenz, T., and Linskens, S.: “Parametrized (Higher) Semiadditivity and the Universality of Spans.” arXiv:2403.07676. Preprint, arXiv, September 27, 2024. https://doi.org/10.48550/arXiv.2403.07676.
• [HKK24] Hilman, K., Kirstein, D., and Kremer, C.: “Parametrised Poincaré Duality and Equivariant Fixed Points Methods.” arXiv:2405.17641. Preprint, arXiv, May 27, 2024. https://doi.org/10.48550/arXiv.2405.17641.
• [LH13] Lurie, J., and Hopkins, M.: “Ambidexterity in K(n)-Local Stable Homotopy Theory in nLab.” Accessed April 11, 2025. https://people.math.harvard.edu/~lurie/papers/Ambidexterity.pdf.
• [Har20] Harpaz, Y. (2020), Ambidexterity and the universality of finite spans. Proc. London Math. Soc., 121: 1121-1170. https://doi.org/10.1112/plms.12367.

Schedule of Speakers and Talks

• Week 1 (9/8). Organization and Planning Meeting
• Week 2 (9/15). Ea E T: Introduction to Semiadditivity
  • Refs: [CSY18] Section 2, [CSY20] Section 2, [CLS24]
• Week 3 (9/22). Ea E T: Cardinalities and Semiadditive Height
  • Refs: [CSY18] Section 2, [CSY20] Sections 2-3, [CLS24]
• Week 4 (9/29). Fredrick Mooers: Parameterized Infinity Categories (related notes)
  • Refs: [Cno24] Section I.2, [CLS24] Section 2,
• Week 5 (10/6). Fredrick Mooers: Parameterized Higher Semiadditivity
  • Refs: [CLS24] Section 3,
• Week 6 (10/13). Fredrick Mooers: Twisted Ambidexterity
  • Refs: [Cno24] Section I.3
• Week 7 (10/20). No Talk
• Week 8 (10/27). Yigal Kamel: Equivariance in Twisted Ambidexterity
  • Refs: [Cno24] Sections I.3-I.4
• Week 9 (11/3). Yigal Kamel: Equivariance in Twisted Ambidexterity
  • Refs: [Cno24] Sections I.3-I.4
• Week 10 (11/10). Ea E T: Twisted Ambidexterity via Spivak Data
  • Refs: [HKK24] Section 3
• Week 11 (11/17). Ea E T: Applications and Examples in Equivariant Poincare Duality
  • Refs: [HKK24] Section 4
• Week 12 (11/24). Fall Break
• Week 13 (12/1). Langwen Hui: Applications of Ambidexterity to Chromatic Homotopy Theory
  • Refs: [LH13] Section 5
• Week 14 (12/8). Fredrick Mooers: Universality of Spans and Applications to TQFTs
  • Refs: [Har20], [CLS24]