10 August 2020, 18:30 - (UTC+3)

Title : Clasp diagrams

Speaker : J. Mostovoy

Organization : Knots and representation theory

Abstract:

I will describe a new coding for knots and some of its applications.

This is a joint work with Michael Polyak.

This talk will be given by skype @knots-in-moscow.

12 August 2020, 15:30 - (UTC+3)

Notice that the time changes due to the time difference.

Title: Splitting cobordism orientations

Speaker Sanath Devalapurkar (Harvard University)

Organization : Seminar in Moscow and Beijing by zoom

Abstract :

The cobordism invariants given by the mod 2 Euler characteristic, signature, and A-hat genus all define maps MO -> HF_2, MSO -> HZ, and MSpin -> ko of spectra. Each of these maps of spectra admits a splitting, which implies the existence of manifolds with given cobordism invariants. In this talk, I will describe a program to reprove the splitting of the A-hat genus, by describing a universal property for mapping out of ko. This program has the advantage of also working (with some modifications) for splitting the Ando-Hopkins-Rezk orientation MString -> tmf. The methods suggest many further directions of investigation, and we hope to highlight some of them in this talk.

About the speaker:

Sanath Devalapurkar was born in India in 2000. He is a rising star in the field of algebraic topology. Though he recently graduated from MIT, he has many publications, see his homepage: https://sanathdevalapurkar.github.io

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

Meeting ID: 831 5020 0580

Password: 141592

13 August 2020, 17:30 - (UTC+3)

Title: Outer billiards outside regular polygons: sets of full measure and aperiodic points

Speaker: Fillip Rukhovich

Organizatinon: Mathematical colloquium in BMSTU

Abstract:

Draw a tangent line to $\Gamma$ through point $p$ and reflect $p$ with respect to tangency point. Such a map is called \it outer billiard map}. In terms of consecutive applying of outer billiard, the point can be {\it periodic} (i.e. return to itself at some moment), aperiodic (never return itself) and also {\it boundary} (outer billiard can be applied only finite number of times).

An important case of $\Gamma$ is regular $n$-gon. In case $n=3,4,6$, a structure of points is simple (no aperiodic points); also a structure was researched by S.Tabachnikov in case $n=5$ and partially $n = 10$ (there exists an aperiodic point, but set of aperiodic points is of zero Lebesgue measure). In his Ph.D. author proved results for cases $n=8,12,10$.

Topics of report are following:

\begin{itemize}

\item structure of periodic, aperiodic and boundary points;

\item what interesting fractal structures arise;

\item how to describe all possible periodic components;

\item what algorithms can be useful for search and proof of self-similarity;

\item why computer occurs necessary for full research.

\end{itemize}

Join Zoom Meeting

Meeting ID: 896 7076 5101

Passcode: 203624