 Info
Four Cohomological Methods from 18931957 in Topology
Seth Arnold, SLU
What 

When 
Mon, Apr 23, 2018
from
10:00 AM
to
10:50 AM

Where 
204 Ritter Hall

Contact Name 
Dr. Khan

Attendees 
PhD Candidacy Committee:
B Clair, K Druschel, J Kalliongis, Q Khan (chair), A Srivastava

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Explanation of four 6000level graduate exercises:
 Represent the isomorphism classes of group extensions 1 ⟶ Z^{n} ⟶ Γ ⟶ C_{2} ⟶ 1. First step in this algebra problem is a paper of I Reiner (1957). Second step is calculation of the group cohomology H^{2}(C_{2};Z^{n}), whose origin is O Hölder's factorset (1893). Third step is construction of models.
 Compute the rational cohomology ring of the Eilenberg–Maclane space K(Z,n). First done by J P Serre (1951) with spectral sequences. Applied to show the famous result: the stable homotopy groups of spheres are finite.
 Compute the homotopy set [X,S^{n}] and for n odd [X,RP^{n}] in terms of basic invariants, where X is an ndimensional CW complex. Application of 1940s and 1950s obstruction theory, respectively.
 Define the obstructions to lifting a map X ⟶ B to X ⟶ E, where X is a CW complex and E ⟶ B is a fibration with simple fiber F. Standard extension of 1950s obstruction theory with the use of twisted coefficients.


PhD Oral Exam
Mon, Apr 23, 2018
Four Cohomological Methods from 18931957 in Topology
Seth Arnold, SLU

Geometry/ Topology Seminar
Tue, Apr 24, 2018
Necessary and Sufficient Conditions for a Triangle Comparison Theorem, I
James Hebda, SLU

PhD Oral Defense
Thu, Apr 26, 2018
Finite, fiberpreserving group actions on orientable Seifert manifolds
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PhD Oral Exam
Fri, Apr 27, 2018
Leavitt Path Superalgebras
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Annual Awards Ceremony
Fri, Apr 27, 2018
The 2018 Math & Statistics Department Award Ceremony
Featuring Sarah Greenwald, Appalachian State University
