Frontiers in Mathematical Sciences 7th Conference University of Isfahan - January 1-3, 2020
 Title: On splitting Madsen-Tillmann spectra Speaker: Hadi Zare, University of Tehran Date, Time, and Venue:  Wednesday, January 1 | 11:45-12:30 | Hall 1 Abstract: For a given compact Lie group $G$ with an embedding of Lie groups $G\hookrightarrow O(n)$ one can associate a Thom spectrum, known as a Madsen-Tillman spectrum, $MTG=BG^{-\gamma}$ where $\gamma$ is the pull back of the universal bundle over $BO(n)$. We show that upon choosing suitable compact subgroups $H\leq G$ then $MTH$ splits off $MTG$. We also hint on some recent results on splitting $MTO(n)$ using Steinberg idempotents. These results are based on joint work with Takuji Kashiwabara.