[Facets-of-complexity] Invitation to Monday's Lecture & Colloquium Jan.17 - online via Zoom.

["I.Brunke" <i.brunke@fu-berlin.de>]

Dear all,

next Monday's Lecture and Colloquium will take place online via Zoom on January 17.

Please find link to Zoom Meeting here:

https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09

A password is not required!

You all are cordially invited!

Location:

Online via Zoom.

Monday's Lecture: María A. Hernández Cifre (Universitdad de Murcia)

Time: Monday, January 17 - 14:15 h

Title: On discrete Brunn-Minkowski type inequalities

Abstract:

The classical Brunn-Minkowski inequality in the n-dimensional Euclidean space asserts that the volume (Lebesgue measure) to the power 1/n is a concave functional when dealing with convex bodies (non-empty compact convex sets). This result has become not only a cornerstone of the Brunn-Minkowski theory, but also a powerful tool in other related fields of mathematics.
In this talk we will make a brief walk on this inequality, as well as on its extensions to the Lp-setting, for non-negative values of p. Then, we will move to the discrete world, either considering the integer lattice endowed with the cardinality, or working with the lattice point enumerator, which provides with the number of integer points contained in a given convex body: we will discuss and show certain discrete analogues of the above mentioned Brunn-Minkowski type inequalities in both cases.
This is about joint works with Eduardo Lucas and Jesús Yepes Nicolás.


Break

Monday's Colloquium: Ji Hoon Chun (Technische Universität Berlin)

Time: Monday, January 17 - 16:00 h s.t.

Title: The Sausage Conjecture in dimension 4

Abstract:

The Sausage Catastrophe (Jörg Wills) is the observation that in d = 3 and d = 4, the densest packing of n spheres is a sausage for small n and jumps to a full-dimensional packing for large n without passing through any intermediate dimensions. We denote the smallest value of n for which the densest packing is full-dimensional by k_d. We discuss some upper and lower bounds for k_3 and k_4, including k_3 ≤ 56 by Wills (1985) and k_4 < 375,769 by Gandini and Zucco (1992). We present some initial improvements to the upper bound for k_4 via extending the work of Gandini and Zucco.

You all are cordially invited!

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