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Infinite Analysis Seminar Tokyo
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|
2016/12/22
14:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Yuta Nozaki (Graduate School of Mathematical Sciences, the University of Tokyo) 14:00-15:30
Homology cobordisms over a surface of genus one (JAPANESE)
Generalization of Schur partition theorem (JAPANESE)
Yuta Nozaki (Graduate School of Mathematical Sciences, the University of Tokyo) 14:00-15:30
Homology cobordisms over a surface of genus one (JAPANESE)
[ Abstract ]
Morimoto showed that some lens spaces have no genus one fibered knot,
and Baker completely determined such lens spaces.
In this talk, we introduce our results for the corresponding problem
formulated in terms of homology cobordisms.
The Chebotarev density theorem and binary quadratic forms play a key
role in the proof.
Shunsuke Tsuchioka (Graduate School of Mathematical Sciences, the University of Tokyo) 16:00-17:30Morimoto showed that some lens spaces have no genus one fibered knot,
and Baker completely determined such lens spaces.
In this talk, we introduce our results for the corresponding problem
formulated in terms of homology cobordisms.
The Chebotarev density theorem and binary quadratic forms play a key
role in the proof.
Generalization of Schur partition theorem (JAPANESE)
[ Abstract ]
The celebrated Rogers-Ramanujan partition theorem (RRPT) claims that
the number of partitions of n whose parts are ¥pm1 modulo 5
is equinumerous to the number of partitions of n whose successive
differences are
at least 2. Schur found a mod 6 analog of RRPT in 1926.
We will report a generalization for odd $p¥geq 3$ via representation
theory of quantum groups.
At p=3, it is Schur's theorem. The statement for p=5 was conjectured by
Andrews in 1970s
in a course of his 3 parameter generalization of RRPT and proved in 1994
by Andrews-Bessenrodt-Olsson with an aid of computer.
This is a joint work with Masaki Watanabe (arXiv:1609.01905).
The celebrated Rogers-Ramanujan partition theorem (RRPT) claims that
the number of partitions of n whose parts are ¥pm1 modulo 5
is equinumerous to the number of partitions of n whose successive
differences are
at least 2. Schur found a mod 6 analog of RRPT in 1926.
We will report a generalization for odd $p¥geq 3$ via representation
theory of quantum groups.
At p=3, it is Schur's theorem. The statement for p=5 was conjectured by
Andrews in 1970s
in a course of his 3 parameter generalization of RRPT and proved in 1994
by Andrews-Bessenrodt-Olsson with an aid of computer.
This is a joint work with Masaki Watanabe (arXiv:1609.01905).
