Bilbao – Iberian Cosmological Meeting

Quantum Gravity is so difficult subject, because we don’t have so far any experimental data from the Planck scale. We need to solve many different issues simultaneously as nonlocality, background independence, or dimensional reduction for solving this problem. We claim that it is possible to formulate a different approach from all known paradigms, which is based on ideas of causal set approach, loop quantum gravity and string theory. We present the basic idea.

Seminar in Torino

There are many approaches to Quantum Gravity. We have string theory (ST), loop quantum gravity (LQG), causal dynamical triangulations (CDT), causal set approach (CSA) and many others. There are some common features for all of these theories. We discussed them briefly. We claim that the mathematical apparatus for Quantum Gravity is hidden in foundations of ST, LQG and CSA. We formulate the RT-paradigm and we wrote a list of open issues.

One mathematical problem in combinatorical topology: my lecture at the conference Group 32 in Prague

We formulate one mathematical problem, which will be useful in Quantum Gravity problematics. We will call, that a circle with finite length and finite circumference, which could be deformed, is a ring: let’s have a finite collection of N rings, which could not touch. Derive a formula for number of non-homeomorphic structures, which could be constructed from this finite collection of rings; Every two rings could be linked only once, they could not be knotted or twisted. We don’t consider the Brunnian type of ring.