Eli will discuss the construction/definition of the Chevalley groups over arbitrary fields. This is based on Chapter 3 of Steinberg's notes.
As usual, there is a problem/example session as usual on Tuesday from 4:05-4:55pm in Math 350. The starting point for our session this week is a worksheet discussing the universal enveloping algebra U=U(g) of a semisimple Lie algebra g and its Kostant form, a lattice which acts integrally on all representations of g. If you would like a copy of the worksheet, please email me at michael.woodbury@colorado.edu.
The Chevalley Groups
Mar. 10, 2022 2:30pm (MATH 3…
Functional Analysis
Robin Deeley (CU Boulder)
X
I will discuss three aspects of KK-theory. First, I will show that KK(C,C) is isomorphic to the integer via an index map. Then I will prepare us for the definition of equivariant KK-theory by discussing group actions in the C*-algebraic context. Finally, if time permits, I will outline some of the issues with the construction of the Kasparov product.
KK(C,C), group actions on C*-algebras, and background for the product
Mar. 10, 2022 3pm (Zoom)
Probability
Janos Englander (CU Boulder)
X
In our previous paper, the ``coin turning walk'' has been introduced on . It is a non-Markovian process where the steps form a (possibly) time-inhomogeneous Markov chain. In this talk we follow up the investigation by introducing analogous processes in : at time the direction of the process is ``updated'' with probability ; otherwise the next step repeats the last one. We study the fundamental properties of these walks, such as transience/recurrence and scaling limits. This is joint work with S. Volkov from Lund, Sweden.
The multi-dimensional coin-turning walk
Mar. 10, 2022 3pm (Zoom)
Topology
Joel Ornstein (CU Boulder)
X
This talk will be an overview of Chen-Freedman's paper "Quantifying Homology Classes", which discusses a certain algorithm for choosing bases of homology groups.
The Chevalley Groups