Геометрија, образовање и визуализација са применама, 11. октобар 2018.

Наредни састанак Семинара биће одржан у четвртак, 11. октобра 2018. у сали 301ф Математичког института САНУ са почетком у 17:15.

Предавач: Dmitri Polyakov
Center for Theoretical Physics, College of Physical Science and Technology Sichuan University, Chengdu 6100064, China;
Institute of Information Transmission Problems (IITP) Moscow, Russia

Наслов предавања: EXACT FORMULA FOR A NUMBER OF RESTRICTED PARTITIONS FROM CONFORMAL FIELD THEORY

Apstract: A partition of a number N of length p is a decomposition

$N=n_1+ ... +n_p$, where $0<n_1\leq{n_2}...\leq{n_p}$, $1\leq{p}\leq{N}$.

Finding an exact formula for a number of such partitions is a long-standing problem in number theory. For a total number of partitions, various approximations are known, such as Ramanujan-Hardy formula, as well as its improvements. If the length $p$ is fixed (restricted partitions) the problem becomes even more complicated, and no exact solution to it has been known. In my talk, I show how to derive exact analytic formula for the number of restricted partitions from corelators of irregular vertex operators in conformal field theory (CFT), that I will describe in the talk.


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