Boston College G.I.S.T Seminar
(Getting Into Some Theorems!)
Spring 2016
Mondays at 4pm in Maloney 560
This is the homepage of the BC math department's graduate student seminar. Interested in speaking? Email Siddhi!

Sept 192016
Matt Grimes
Moduli spaces and the fundamental theorem of algebra
It is one of life's funny ironies that the fundamental theorem of algebra is usually not proved with algebra. In this talk, we will develop some of the language of moduli spaces and use tools from geometry and topology to prove the fundamental theorem of algebra. We will place heavy emphasis on accessibility and motivation.

Sept 262016
Spencer Leslie
Intersection Homology, Poincare Duality and Perverse Sheaves
In the context of closed, orientable manifolds, Poincare duality is a beautiful and important relationship between the singular homology and cohomology of the space which also has connections to intersection pairing of cycles. In the context of singular spaces, however, this relationship breaks down.
In this talk, we will discuss the theory of intersection homology, a theory developed to extend Poincare duality and intersection pairings to singular spaces. It is from this very topological construction that the theory of perverse sheaves emerges.

Oct 32016
Ian Banfield
Constructions of fibered knots
A knot K is fibered if it bounds a surface S, such that the knot exterior fibers over the circle with S a fiber. This is a very strong geometric condition; it implies for example that S is minimal genus amongst all surfaces bounding the knot. We’ll review constructions by Stallings, Milnor and Rudolph to construct fibered knots. It turns out that these constructions are all related to braid theory (and complex geometry), and we’ll explain why. If time permits, we may talk about homological invariants.

Oct 172016
Scott Mullane
Moduli spaces, geometric interpretations of residues and orbit closures of null ngon surfaces
I plan on providing many different ways of thinking about Riemann surfaces, holomorphic and meromorphic differentials on Riemann surfaces and geometric ways to consider the residue at a pole of a meromorphic differential. Providing an upper bound for the number of irreducible components of the strata of zero residue differentials in general genus can be reduced to the question of the SL(2,R) orbit closures of null ngon surfaces in genus one. I'll explain this question and give examples.

Oct 242016
Mustafa Cengiz

Oct 312016
Shucheng Yu

Nov 72016
Cristina Mullican

Nov 142016
Tom Crawford

Nov 212016
Ross Goluboff

Nov 282016
Siddhi Krishna

Dec 52016
Tom Cremaschi