### Seminars

### on knot theory and related topics

18 January 2021, 18:30 - (UTC+3)

Title : Unexpected applications of homotopical algebra to knot theory.

Speaker : Victoria Lebed

Organization : Knots and representation theory (by Zoom)

Abstract:Interactions between knot theory and homotopical algebra are numerous and natural. But the connections unveiled in this talk are rather unexpected. Following a recent preprint with Markus Szymik, I will explain how homotopy can help one to compute the full homology of racks and quandles. These are certain algebraic structures, useful in knot theory and other areas of mathematics. Their homology plays a key role in applications. Although very easy to define, it is extremely difficult to compute. Complete computations have been done only for a few families of racks. Our methods add a new family to this list, the family of permutation racks. The necessary background on racks and quandles, and their role in braid and knot theories, will be given.

Join Zoom Meeting

https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09

Meeting ID: 818 6674 5751

Passcode: 141592

13 January 2021, 10:30 - (UTC+3)

Title: Interlocking structures

Speaker: A.J.Kanel-Belov, I.A.Ivanov-Pogodaev

Organization : Seminar in Moscow and Beijing by zoom

Abstract: Consider a set of contacting convex figures in $R^2$. It can be proven that one of these figures can be moved out of the set by translation without disturbing others. Therefore, any set of planar figures can be disassembled by moving all figures one by one.

However, attempts to generalize it to $R^3$ have been unsuccessful and finely quite unexpectedly of convex bodies were found. Author proposed a follows mechanical use of this effect. In a small grain there is no room for cracks, and crack propagation should be arrested on the boundary of the grain. On the other hand, grains keep each other. So it is possible to get "materials without crack propagation" and get new use of sparse materials, say ceramics. Quite unexpectedly, such structures can be assembled with any type of platonic polyhedra, and they have a geometric beauty.

The talk is devoted to the different structures.

This is the work by A.Ya.Kanel-Belov (jointly with Estrin, Dyskin, Ivanov-Pogodaev, Pesin, E. Pasternak).

The seminar will be held during 15:30--17:00 (Beijing time) on Zoom.

Meeting ID: 831 5020 0580

Password: 141592

21 January 2021, 17:30 - (UTC+3)

Title: On disproving 4-dimensional Smale Conjecture

Speaker: Selman Akbulut (Gokova Geometry Topology Institute)

Organization: Mathematical colloquium in BMSTU

Abstract: We present the construction of a self diffeomorphism of S4 which is not isotopic to identity. This disproves a 4-dimensional version of the Smale Conjecture.

Идентификатор конференции: 948 341 6153

Код доступа: 2SXtEz