TopMath Talk with Jamico Schade

Lower bounds on the flatness constant

25 July 2022 16:15 – 18:00
Graphic from Jamico Schade's research

On Monday, 25th July 2022 at 16:15, Jamico Schade from the Research group Discrete Mathematics, Optimization, and Convexity will give a talk on "Lower bounds on the flatness constant" (hybrid event).

Lower bounds on the flatness constant

When trying to fit a convex set between the points of a lattice, it becomes apparent that such a set always has to be somewhat flat. The lattice-width of a convex body is a quantity that measures this flatness with regard to the lattice that constricts the body. The well-known Flatness Theorem states that the lattice-width of a d-dimensional lattice-free convex set is bounded from above by a constant Flt(d) that only depends on the dimension d. While there have been lots of results concerned with upper bounds to this constant, only few techniques are known to obtain lower bounds and so far, the best known lower bound was Flt(d) ≥ 1.138d. In this talk, we will discuss a construction of a series of simplices that yields the lower bound Flt(d) ≥ 2d - O(sqrt(d)).

The talk will take place in room FMI 02.06.011. Moreover, you can watch it online.

TopMath Talks

As part of the TopMath talks, TopMath students and doctoral students present parts of their research. They provide an understandable insight into their current area of interest, enabling students and staff to broaden their mathematical background knowledge. The talks are open to the public and last about an hour, followed by discussion. You are cordially invited!