Juvitop seminar (Fall 2025)
We are an informal pedagogical seminar concerning algebraic topology and homotopy theory, localized at Harvard and MIT. For Fall 2025, talks will proceed on Thursdays at 1:30 - 2:30 pm ET, located in SC 309a.
This seminar is organized by Thomas Brazelton and Logan Hyslop. Email us for questions or to get on the mailing list!
References:
- Our main reference is the book The norm residue theorem in motivic cohomology by Haesemeyer and Weibel [HW19]. Other references include:
- [MVW06] Lecture notes on motivic cohomology, Mazza-Voevodsky-Weibel, 2006.
- Developments in algebraic $K$-theory and quadratic forms after the work of Milnor by Merkurjev (this is a great survey paper)
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Abstract: We will give an overview of ideas for the semester.
References:
- Intro to [HW19]
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Abstract: tbd - define étale cohomology and Milnor $K$-theory. Give examples. Discuss residue homomorphisms on Milnor $K$-theory, and define norm residue maps
References:
- Algebraic $K$-theory and quadratic forms, Milnor, 1970
- Introduction to algebraic $K$-theory (Section 15), Milnor
- Étale cohomology, Milne
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Abstract: tbd - explain the primary reductions we have
References:
- [HW19], Chapter 1
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Abstract: tbd - explain sheaves with transfers, and what properties their cohomology enjoys. Give examples. Explain chain complexes of sheaves, and hypercohomology. Define (if possible) the motivic complexes $\mathbb{Z}(q)$ and $\mathbb{Z}/\ell(q)$
References:
- Lectures 2-5 of Mazza-Voevovsky-Weibel
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Abstract: tbd
References:
- [HW19], Chapters 2-3
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Abstract: tbd
References:
- [HW19], Chapter 4
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Abstract: tbd
References:
- [HW19], Chapters 8 and 14
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Abstract: tbd
References:
- [HW19], Chapter 13
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Abstract: tbd
References:
- [HW19], Chapters 10-11
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Abstract: tbd
References:
- [HW19], Chapters 5-7
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Abstract: tbd
References:
- [HW19], Chapters 1 and 15
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🦃 Thanksgiving 🦃
(no talk)
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Abstract: tbd
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Abstract: tbd