This is a joint talk with the topology seminar. The space of mixed states of a quantum system can be decomposed by ranks. For purposes of differential topology and geometry, one wants subspaces in a decomposition to fit together in a natural way, in which case it is called a stratification and the pieces called strata. Moreover, in order to have a useful notion of stratified tangent bundle, certain regularity conditions such as Whitney (a)- and (b)-regularity are considered. In this talk, we discuss the necessary background in stratification theory and discuss the regularity conditions satisfied by the decomposition of mixed states by rank.
State spaces in quantum mechanics Part 2: Stratifications
Wed, Sep. 23 3:30pm (MATH 3…
Topology
Howy Jordan (CU Boulder)
X
This is a joint talk with the mathematical physics seminar. The space of mixed states of a quantum system can be decomposed by ranks. For purposes of differential topology and geometry, one wants subspaces in a decomposition to fit together in a natural way, in which case it is called a stratification and the pieces called strata. Moreover, in order to have a useful notion of stratified tangent bundle, certain regularity conditions such as Whitney (a)- and (b)-regularity are considered. In this talk, we discuss the necessary background in stratification theory and discuss the regularity conditions satisfied by the decomposition of mixed states by rank.
State spaces of quantum systems Part 2: Stratifications
Wed, Sep. 23 4:40pm (MATH 3…
Grad Student Seminar
Taylor Rogers (CU Boulder)
X
"Homotopy coherent algebra provides a family of fields interpolating between characteristic 0 and p for each prime p. Finite group representation theory extends to these higher categorical contexts, as do generalizations of finite groups called -finite spaces. In this talk we will translate representation theory to these homotopical contexts. Further, time permitting, we will see how some properties of representation theory change over these higher categorical fields and why one might care... and I may tell a joke or two. "
State spaces in quantum mechanics Part 2: Stratifications