8th TT-UU Mini Symposium: Mathematics Breakout Session

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The 8th joint mini symposium between Tokyo Tech - Uppsala University will be conducted virtually on zoom. The Mathematics Breakout Session consists of four 30 minute talks. All talks will be streamed on zoom, but the UU speakers will give the talks from the room, and you are free to attend physically if you want. 

Time and Venue

  • Date: Wednesday 11 January 2023
  • Time: 09:00-11:30 (Uppsala time, GMT+1) // 17:00-19:30 (Tokyo time, GMT+9)
  • Room in Uppsala: Ångström 101258
  • Zoom: Link to meeting

Schedule

Time Speaker
9:05 (GMT+1) // 17:05 (GMT+9) Thomas Kragh (Uppsala University)
Title: Topological refinements of invariants in geometry.
 
9:40 (GMT+1) // 17:40 (GMT+9) Yuri Yatagawa (Tokyo Tech)
Title: Euler characteristic and ramification of a constructible sheaf
 

10:15 (GMT+1) // 18:15 (GMT+9)

Anna Sakovich (Uppsala University)
Title: Towards a spacetime intrinsic flat convergence
10:50 (GMT+1) // 18:50 (GMT+9) Hidetoshi Masai (Tokyo Tech)
Title: Visualizing deformations of hyperbolic and complex structures on 4-punctured spheres
 

Abstracts

Anna Sakovich (Uppsala University)
Title: Towards a spacetime intrinsic flat convergence
Abstract: How can we compare spacetimes with stars, black holes and other singularities – for example our Universe – to standard cosmological models that are symmetric and smooth? One can argue that for answering this kind of questions, where the manifolds that one wants to compare are not close in a smooth sense and possibly not even diffeomorphic, it is necessary to rely on notions of distance from metric geometry that are based on comparison of distances rather than metric tensors.  The intrinsic flat distance of Sormani and Wenger is an example of such a notion of distance which has been successfully applied to address a number of questions in Riemannian geometry and mathematical general relativity, such as stability of torus rigidity and stability of Riemannian positive mass theorem. I will report on our ongoing work with Christina Sormani whose ultimate goal is to develop the analogue of intrinsic flat distance and intrinsic flat convergence for Lorentzian manifolds. One of the difficulties in achieving this goal is that, unlike Riemannian manifolds, Lorentzian manifolds are not natural metric spaces. In this connection, our recent breakthrough is developing a canonical procedure which allows one to convert spacetimes into metric spaces, in such a way that it is possible to recover the Lorentzian structure back. This motivates a very promising notion of spacetime intrinsic flat distance that I will discuss along with some potential applications.


Organisers: Tamas Kalman (TT) and Georgios Dimitroglou Rizell (UU)

Last modified: 2023-01-09