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 Events
UCLA
Wed 10 Mar 2021, 3:00pm
Topology and related seminars
Zoom (see Notes for Attendees)
An equivariant Thom isomorphism theorem and equivariant fundamental classes
Zoom (see Notes for Attendees)
Wed 10 Mar 2021, 3:00pm-4:00pm

Abstract

Let C_2 denote the cyclic group of order two. Given a manifold with a C_2-action, we can consider its equivariant Bredon RO(C_2)-graded cohomology. In this talk, we give an overview of RO(C_2)-graded cohomology in constant Z/2 coefficients, and then explain how a version Thom isomorphism theorem in this setting can be used to develop a theory of fundamental classes for equivariant submanifolds.
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UBC
Wed 17 Mar 2021, 3:00pm
Topology and related seminars
Zoom (see Notes for Attendees)
Construction of nonsingular bilinear maps
Zoom (see Notes for Attendees)
Wed 17 Mar 2021, 3:00pm-4:00pm

Abstract

Let R^n denote n-dimensional Euclidean space. A bilinear map F: R^r X R^s --> R^n  is said to be nonsingular if F(x,y)=0 implies x = 0 or y = 0.  In the 1840's Hamilton looked for such an F when r=s=n=3 without success. He did, however, find one such F for r=s=n=4: the multiplication map of "quaternions". In a sense it signifies the birth of sympletic geometry. The general question is: for what triples (r,s,n) will there exist a nonsingular bilinear map F? This remains unanswered up to the present day. In this talk I shall present some new examples of nonsingular bilinear maps, constructed via factorization theory of polynomials whose coefficients come from a non-commutative ring. I shall then discuss the geometry and topology behind these new examples, and explain their potential use for constructing elements in the stable homotopy groups of spheres. This is joint work with Carlos Dominguez.
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Boston College
Thu 25 Mar 2021, 3:00pm SPECIAL
Topology and related seminars
Zoom
TBA
Zoom
Thu 25 Mar 2021, 3:00pm-4:00pm

Abstract

 TBA
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