Robin Deeley (CU Boulder) Smale Spaces and Group Actions on Them

Sep. 26, 2017 1pm (MATH 220)

Grad Algebra

Agnes Szendrei (CU Boulder) Random finite algebras satisfying idempotent linear Maltsev conditions, Part 1

Sep. 26, 2017 2pm (MATH 350)

Lie Theory

Richard Green (CU) The classification of a(2)-finite Coxeter groups

Sep. 26, 2017 3pm (MATH 350)

Topology

Markus Pflaum (CU Boulder) Introduction to Quantum Field Theory

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I will introduce three examples of Smale spaces (Smale spaces are a class of hyperbolic dynamical systems). Group actions on these three examples will be introduced to motivate the study of group actions on a general Smale space. Finally, I will discuss such actions both in regard to a Smale space itself and the $C}^{*$-algebras associated to it. This talk is based on joint work with Karen Strung.

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We will discuss the following paradox:

Let M be a strong idempotent linear Maltsev condition. Under mild restrictions on M the following statement is true: If A is a random finite algebra whose operations satisfy the identities in M, then asymptotically almost surely, A satisfies much stronger conditions than M.

An example of a strong idempotent linear Maltsev condition is the condition ``There is a ternary operation m which satisfies the identities m(x,x,y)=y=m(y,x,x)''. Every group satisfies this condition with the (derived) operation m(x,y,z)=xy^{-1}z.

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Lusztig's a-function is an integer-valued function on the elements of a Coxeter group, and it is defined in terms of the structure constants of the Kazhdan--Lusztig basis of the associated Hecke algebra. We call a Coxeter group "a(k)-finite" if it has finitely many elements with a-value equal to k. A Coxeter group element has a-value 1 if and only if it is "rigid", meaning that it has a unique reduced expression. The classification of a(1)-finite Coxeter groups is known, and this talk will describe the classification of a(2)-finite Coxeter groups.

[This is a continuation of last week's talk, but it is not necessary to have attended the previous talk.]