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# 解析・幾何セミナー (Salvatori Niccolo 氏)

（今回は微分幾何セミナー世話人の守屋先生にご協力いただき、解析セミナー・微分幾何セミナーの合同で開催いたします。）

日　　時： 7月18日（火） 16時40分 〜 17時40分
場　　所 ： 筑波大学 自然系学系 D棟 D509教室
講 演 者： Salvatori Niccolo (King's College London)

題　 目： The Residue Analytic Torsion and Logarithmic Topological
Quantum Field Theory
講演要旨：
Closed odd-dimensional manifolds with trivial cohomology can be distinguished by their analytic torsion (a secondary topological invariant introduced by Ray and Singer in 1971 that coincides with the Reidemeister torsion). In this talk, we will show that analytic torsion can be equivalently obtained by the (quasi) trace of a log-polyhomogenous operator and, by the use of Wodzicki's residue, we will define and study an exotic torsions: the residue analytic torsion, which turns out to be a smooth invariant in some occasions, with properties that are complementary to those of the analytic torsion. Then, we will define the new concept of LogTQFT and use the residue torsion to provide an example. If time allows, we will present a generalization of the previous results to families of closed manifolds and to manifolds with boundary.

moriya-at-math.tsukuba.ac.jp)