Topology Seminar
Tuesdays 11:10
am-12 pm
Surge 268
(Fall and Spring)
Surge 284
(Winter)
Spring
2011
March 29: Michael Williams, On nonhyperbolic handle number one links
Abstract:
The handle number of a link in the three sphere is the least number of disjoint
proper arcs needed to be attached to the link so that resulting (possibly
disconnected) graph is unknotted. In particular, the exteriors of handle number
one links admit genus 2 Heegaard splittings. In this talk, some results on
nonhyperbolic handle number links will be presented. This is joint work with
Abby
Thompson
(UC Davis).
April 5: Ilesanmi Adeboye (UC Santa Barbara), Volumes of Hyperbolic Orbifolds
Abstract: In this talk, a result due to H. C. Wang, and some comparison geometry, are used to construct an explicit lower bound for the volume of a hyperbolic orbifold, dependent only on dimension. We then show how these techniques lead to similar results in the context of the complex, quaternionic and octonionic hyperbolic spaces. This is joint work with Guofang Wei.
April 12:
Philip Hackney, Drinfeld’s formula for geometric realization
April 19: Ettore Aldovandi (Florida State), Mapping spaces of group-like stacks
Abstract: Stacks
with a group law (gr-stacks, for short) arise, for example, as automorphisms of
algebraic or topological stacks. Morphisms between them are essentially
derived mapping space between two complexes (of length 2) of non-necessarily
abelian groups. I will show how they can be computed by certain diagrams called
butterflies. In the abelian case this reproduces a previous result by
Deligne characterizing the derived category in terms of morphisms of Picard
stacks. The main applications are to the long exact sequence and to the
change of coefficient map in nonabelian cohomology. This is based on
joint work with Behrang Noohi.
April 26: Dave
Bachman (Pitzer College), Topological, PL, and geometric minimal surfaces
Abstract: We discuss a program to show that a
topologically minimal surface (of arbitrary index) in a compact 3-manifold can
be isotoped to meet a triangulation so that it meets each tetrahedron in
precisely the same way that a geometrically minimal surface (of at most the
same index) can meet a ball. We will then discuss the immediate applications to
topology, as well as potential applications to geometry.
May 3: Julie
Bergner, Homotopy theories and higher categories
May 10:
Michael Williams, A survey of Freedman’s Classification Theorem for simply
connected closed 4-manifolds
May 17: Liam
Watson (UCLA), Turaev
torsion, definite 4-manifolds, and quasi-alternating knots.
Abstract: Quasi-alternating knots -- providing a natural
extension of the class of alternating knots -- first arose in the context of
Heegaard Floer homology for two-fold branched covers. Like alternating knots,
quasi-alternating knots have particularly simple homological invariants: the
various knot homologies (Khovanov, Floer, etc.) for this class of knots is
supported in a single diagonal and are essentially determined by the relevant
polynomial invariant. The converse, however, does not hold. It is possible to
exhibit infinite families of so-called thin knots that are non-quasi-alternating.
The proof, which is arguably more interesting than the result itself, draws on
a surprising range of results to combine Heegaard Floer invariants, Turaev
torsion, and the Casson invariant (among others), in order to study the
two-fold branched covers of an infinite family of knots. This is joint work
with Josh Greene.
May 24:
Michael Williams, Examples of closed, smooth, simply connected 4-manifolds:
hypersurfaces in CP^3
May 31:
Michael Menke, The Arnold Conjecture
Winter
2011
January 4: Philip Hackney, Operations from E-infinity chain algebras
January 11:
Stefano Vidussi, Minimal genus in dimension 4
January 18: Stefano
Vidussi, Minimal genus in dimension 4, part 2
January 25:
Stefano Vidussi, Minimal genus in dimension 4, part 3
February 1:
Julie Bergner, Algebraic theories
February 8:
Julie Bergner, Algebraic theories, part 2
February 15:
Jim Hoste (Pitzer College), The Ohtsuki-Riley-Sakuma partial order on 2-bridge knots
February 22:
Ko Honda (USC), HF=ECH via open book decompositions
Abstract: The goal of this talk is to sketch a proof
of the equivalence of Heegaard Floer homology (due to Ozsvath-Szabo) and
embedded contact homology (due to Hutchings). This is joint work with
Vincent Colin and Paolo Ghiggini.
March 1: Chris
Carlson, Contact structures, foliations, and group actions on 3-manifolds
March 8:
Azadeh Rafizadeh, Reidemeister-Schreier algorithm and some of its
applications to low-dimensional topology
Fall
2010
September 28:
Julie Bergner, Introduction to simplicial methods
October 5:
Julie Bergner, Introduction to simplicial methods 2
October 12:
Chris Carlson, Spectral sequences
October 19:
Azadeh Rafizadeh, Twisted Alexander polynomials and fiberability
October 26: Michael Williams, Background Talk 1: Some topics in 3-dimensional topologyNovember 2: Michael Williams, Background Talk 2: Dehn surgery on knots and linksNovember 9: Michael Williams, Handle number one links and Generalized Property R
November 16: Philip Hackney, Operads and operations
November 23:
Philip Hackney, Operads and operations 2
November 30:
Dennis Gumaer, TBA
http://www.math.ucr.edu/~jbergner/topologysem1011.htm Last updated:
27 May 2011