Speaker: Dr. Jia Kong (IAS)

Time: 16:00-17:00  March 14, 2023 (Tuesday)

Place: MCM410

Language: English

Inviter: Prof. Baohua Fu

Title: A deformation of Borel equivariant homotopy

Abstract: The R-motivic stable homotopy category has a close connection to the C2-equivariant category via the C2-equivariant Betti realization map. 

For the bigraded homotopy groups, the C2-equivariant spectra are usually more complicated to compute than the R-motivic ones, due to the existence of the "negative cone". I will first explain this connection; then I will talk about the joint work with Gabriel Angelini-Knoll, Mark Beherens, and Eva Belmont, in which we construct the modified Adams--Novikov spectral sequence (mANSS) aiming to build an odd primary analog of this R-motivic and C2-equivariant relation. Using the mANSS filtration, one can construct a deformation of Borel equivariant homotopy, which agrees with the a-completed Artin—Tate R-motivic category for group C2.

Speaker: Dr. Wenjia Jing (Yau Mathematical Sciences Center, Tsinghua University)

Time: 14:00-15:00  March 16, 2023 (Thursday)

Place: N208

Language: English

Inviter: Prof. Jinping Zhuge

Title: Homogenization of a front propagation model in dynamic environments

Abstract: In this talk I will review the developments of homogenization theory for a front propagation model. It is described by a first order Hamilton-Jacobi equation with a Hamiltonian that grows linearly with respect to the absolute value of the momentum variable. We focus on the case of dynamic environment where the Hamiltonian has highly oscillations in time as well as in space. We present some key steps in the proof of the qualitative homogenization theory and in the quantification of the convergence rate in the periodic setting. The talk is based on several joint works with Souganidis, Tran and Yu.