Monday, September 16, 2019

Jami Workshop: Riemann-Roch in characteristic one and related topics

The Johns Hopkins Mathematics Department jointly with the Japan-U.S. Mathematics
Institute (JAMI) plan to organize a workshop on the weekend of October 18-20 2019.

The interactions between the fields of noncommutative arithmetic geometry, tropical geometry, the theory of toposes and mathematical logic, optimization and game theory have matured quite rapidly in the last few years and have produced very exciting results.
The goal of the workshop is thus that of coordinating these diverse research areas and with a common aim that is deeply related to the Riemann Hypothesis (RH).
The Noncommutative Geometry approach to RH has  unveiled the exotic nature of the adele class space of the rationals, based on the theory of Grothendieck toposes on one hand and tropical geometry on the other. The search of a suitable Riemann-Roch formula on the square of the Scaling Site seems to require the development of algebraic geometry in characteristic one and of refinements of the tropical Riemann-Roch theory as developed so far and its connections to game and potential theory.
On the other hand, the theory of Segal's Gamma-rings provides a natural extension of the theory of rings and of semirings:  the clear advantage of working with Gamma-rings is  that this category forms the natural groundwork where cyclic homology is rooted (this means that de Rham theory is here naturally available). In fact, much more holds,  since the simplicial version of modules over Gamma-rings (ie the natural set-up for homological algebra in this context) forms the core of the local structure of algebraic K-theory. In arithmetic geometry, the new Gamma-ring arising as the stalk of the structure sheaf of the Arakelov compactification of Spec Z at the archimedean place, is intimately related to hyperbolic geometry and the Gromov norm.  The theory of Gamma-rings in fact culminates with the development of a new theory of ABSOLUTE ALGEBRAIC GEOMETRY
All these developments are thus part of a general program for a workshop that brings together researchers from these different fields.

K. Consani

Friday, January 18, 2019

for a dead friend

It is not surprising that all the honourable men who are manning (what else) this blog did not find it proper to comment on the passing of Sir Michael Atiyah, so I am offering a link to my own:

Friday, August 3, 2018

Master Class on Noncommutative geometry: spaces, bundles and connections

Registration is now open for this master class. For more details please check their website  here.

Wednesday, March 7, 2018

Noncommutative Geometry and Index Theory for Group Actions and Singular Spaces

This weeklong workshop will be an opportunity for young researchers in noncommutative geometry to share their ideas with their peers and with some of the leaders of the field. Apart from lectures by young researchers there will be mini-courses by Pierre Albin, Nigel Higson and Shmuel Weinberger. Topics will include the analysis and geometry of hypoelliptic operators, group actions on aspherical manifolds, index theory on singular spaces, and secondary invariants.

Some funding is available for participants, and there are still opportunities for contributed talks. For further information, see the link below.