# Topology and Geometry Seminar

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Wed., Sep. 20, 2023 2:00 p.m.
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Location: CL 305
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**Speaker: **Allen Herman, University of Regina

**Title: **Classical Deformation Theory of Algebras

**Abstract: **

If *A* is an algebra over a field *k*, and *R* is an augmented commutative *k*-algebra, then an *R*-deformation of *A* is (intuitively) an *R*-algebra *B* whose underlying *k*-algebra structure is isomorphic to that of *A*. Two *R*-deformations of *A* are considered equivalent when there is an *R*-algebra isomorphism between the two that reduces to the expected isomorphism of their underlying *k*-algebra structures. In this talk we will see that in the cases *R* = *k*[[*t*]] (formal deformations) and *R*=*k*[*t*]/(*t*^{2}) (infinitesimal deformations), the equivalence classes of *R*-deformations of *A* can be understood using tools from Hochschild cohomology.

Topology and Geometry Seminar: https://www.reginatopology.ca/seminar