Algebra Seminar: Lai

Chun-Ju Lai (Academia Sinica) will be speaking in the algebra seminar.  We will go out
for lunch after the talk---all are welcome to join! 

When: 12-1pm Friday September 4 

Where: Carslaw 275 

Title: Foundations and Applications of Quantum Wreath Products 

Abstract: Roughly speaking, a quantum wreath product is a deformation algebra of the
classical wreath product of a monoid (or group) by the symmetric group, where the
relation coefficients are in a tensor product algebra rather than in the ground field.
From this perspective, algebras admitting a Bernstein-Lusztig presentation are quantum
wreath products.  This framework encompasses (1) Vigneras' pro-p Hecke algebras and
their metaplectic analogs, (2) Kleshchev and Muth's affine zigzag algebras, and (3) the
``Hecke algebra'' for the wreath products between symmetric groups arising from the work
of Jun Hu.  I'll speak about recent progress in seemingly unrelated directions using
general theory of quantum wreath products.  They are (A) realization problem of
imaginary strata of affine Khovanov-Lauda-Rouquier algebras in positive characteristic,
(B) failure of Local Shimura correspondence at the pro-p level, (C) the
Ginzburg-Guay-Opdam-Rouquier conjecture on constructing highest weight covers for
non-semisimple Hecke algebras of complex reflection groups, and (D) categorification
perspective of towers of quantum wreath products.  The talk is based on joint work with
Buciumas (Pohang), Cailan Li (Academia Sinica), Minets (Bonn), Nakano (Georgia), and
Xiang (Shenzhen).