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Conference Higher Invariants: interactions between arithmetic geometry and global analysis, October 6.-10., 2025 organized by Ulrich Bunke, Denis-Charles Cisinski and Guido Kings
List of Speakers
- Federico Binda
- Dustin Clausen
- Hélène Esnault
- Hokuto Konno
- Manuel Krannich
- Akhil Mathew
- Thomas Nikolaus
- Viktoriya Ozornova
- Maxime Ramzi
- Charanya Ravi
- Tomer Schlank
- Peter Scholze
- Georg Tamme
- Inna Zakharevich
Abstracts
Hélène Esnault - On the restriction map in $p$-adically complete de Rham or prismatic cohomology (joint work with Mark Kisin and Alexander Petrov)
For X smooth proper over Z_p and U a smooth affine, we show that the restriction homomorphism $H_{prism}^i(X) \to H^i_{prism}(U)^{sep}$ in the separated quotient of prismatic cohomology $H^i_{prism}(U)$ dies if $H^0(X mod p, \Omega^i)=0$, so likewise for $p$-adically complete de Rham cohomology: under the same assumption the restriction homomorphism $H^i_{dR}^i( \hat X) \to H^i_{dR( \hat U)^{sep}$ in the separated quotient of $p$-adically complete de Rham cohomology $H^i_{prism}(U)$ dies. This already produces classes in algebraic de Rham cohomology of $X$ which die in $p$-adically complete de Rham cohomology $H^i( \hat U )$ of $U$. In particular it shows that no $p$-adic method, even if we take into account almost all $p$, can shed light on Grothendieck’s conjecture. Caro-D’Addezio lifted the vanishing of $H^i_{dR}^i( \hat X) \to H^i_{dR( \hat U)^{sep}$ to the vanishing of $H^i_{dR}^i( \hat X) \to H^i_{dR}( \hat U)_{\mathbb Q}$ under the extra assumption $H^1(X, \Omega^{i-1})=0$. May be by the time of the conference we’ll know the precise condition to lift their result to prismatic cohomology.
Hokuto Konno - Family gauge theory and diffeomorphism groups
One of the major advances in topology over the past decade has concerned diffeomorphism groups of higher-dimensional manifolds. On the other hand, it has long been known that dimension 4 is special in the classification of manifolds. Such special phenomena are detected using gauge theory. Recent advances in gauge theory for families have revealed that similar phenomena in dimension 4 also appear in diffeomorphism groups, in striking contrast with results in higher dimensions. In this talk, I will survey these new phenomena in dimension 4.
Akhil Mathew - Sheared Witt vectors (after V. Drinfeld, E. Lau, and T. Zink)
Motivated by Dieudonné theory, V. Drinfeld and E. Lau introduced a "decompletion" of the ring of Witt vectors W(R) of a derived p-complete ring R such that (R/p)_{red} is perfect, extending a construction of T. Zink. I will explain various characterizations of this decompletion (called the sheared Witt vectors) and some examples. (Joint work in progress with Bhargav Bhatt, Vadim Vologodsky, and Mingjia Zhang.)
Program and Schedule
The list of talks and abstracts will appear here before the conference.
Practical Information
City of Regensburg: Regensburg is a Unesco World Heritage site that is famous for its well-preserved medieval city center and its beautiful Gothic cathedral.
Further information about Regensburg can be found here.
Internet: Access to eduroam and BayernWLAN is available throughout the Mathematics Building.
Accomodation: Regensburg is a tourist destination and we encourage guests to book their rooms as early as possible. Here is a list of hotels in the area:
- Hotel Münchner Hof (In the city center, one must take a bus to the University.)
- Hotel Kaiserhof am Dom (In the city center, one must take a bus to the University.)
- Hotel Jakob (In the city center, one must take a bus to the University.)
- Hotel Wiendl (Between the city center and the University.)
- Hotel Central (Between the city center and the University, one must take a bus to the University.)
Family Friendly Campus: Our UR family service offers various rooms for families and services. If you need further information look here.
Venue
TBA
Registration and financial support
To register for this event, please use the following link: https://s2survey.net/1085/ Registration is open until 31 August 2025. (The deadline for financial support queries is 22 July 2025.)
Conference Poster
You can download the conference poster here.
Organizers
Ulrich Bunke, Denis-Charles Cisinski and Guido Kings
Conference Picture
TBA
Sponsors of the conference
This conference is funded by SFB 1085 "Higher Invariants"
