# TGTS Tetrahedral Geometry/Topology Seminar

Sponsored by Elizabethtown College, Franklin and Marshall College,
Lebanon Valley College, and Millersville University

### Speakers Fall 2016

16 September: Ziva Myer, Bryn Mawr College
14 October: Vince Coll, Lehigh University
4 November: Carl Droms, James Madison University
2 December: Evan Folkestad, Franklin and Marshall College

TGTS is a regional mathematics seminar/colloquium. We meet at 4:30
p.m. on the first Friday of each month during the academic year (with
some exceptions, as noted in the schedule above). The public is
cordially invited to attend.
### Next Talk

**Date:** 14 October 2016, 4:30pm
**Location:** Hempfield High School, Room 213
**Speaker:** Vincent E. Coll
**Title:** Seaweed and poset algebras -- synergies and cohomology
**Abstract.** Part I, Seaweeds. In my previous talk, I introduced
seaweed algebras as subalgebras of An = sl(n) and examined certain
newly discovered spectral invariants. We have extended the work to
the symplectic Type-C case, Cn = sp(2n), and have strong indications
of what is true in all other cases – these cases corresponding to the
simple Lie algebras in the grand classification. One finds,
curiously, that these spectral properties are not unique to
Frobenious seaweed subalgebras of the simple Lie algebras. It seems
that these properties are shared by certain Lie poset algebras
recently introduced by myself and Gerstenhaber in the J. Lie Theory
article: Cohomology of Lie semidirect products and poset algebras
(2016).
Part II, Posets. These Lie poset algebras are concrete matrix
algebras and they stand at the nexus of three great cohomology
theories: simplicial, the algebraic cohomology of Hochshild, and the
Lie algebraic cohomology of Chevalley-Eilenberg. More explicitly, now
classic results of Gerstenhaber and Schack elegantly established that
simplicial cohomology is a special case of algebraic cohomology. That
is, associated to each triangulable space, there is an associative
matrix algebra whose algebraic cohomology is the same as the
simplicial cohomology of the original space. These matrix algebras
are also Lie algebras and therefore have a Lie algebra cohomology
which controls their deformations as Lie algebras. We can establish
that the latter cohomology is also essentially simplicial and that
the deformation theory of these Lie poset algebras is analogous to
that of complex analytic manifolds for which this theory is a small model.

### Past Seminars

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