Recent Advances in Algebraic Topology
Special Session at an AMS Sectional Meeting
Southeastern Section, Fall 2007
- Job Seekers
- Here's a brief paragraph for those who wanted to post their
information:
- Scott Bailey, Northwestern University
- Scott is a student at Northwestern University under the guidance
of Paul Goerss, planning to receive his PhD in the spring of 2008.
The aim of his thesis, currently in production, is to demonstrate the
topological splitting of the Tate cohomology spectrum of tmf at the
prime 2. As a key step, Scott studied the connective K-theory of tmf,
topologically splitting the representing spectrum into suspensions of
integral Brown-Gitler spectra, imitating earlier work of Davis and
of Mahowald. He has also done work with v_n self maps of finite
p-local spectra lying in the center of their endomorphism rings.
Scott will be applying to postdoctoral positions across the U.S.
in algebraic topology throughout the fall of 2007.
- Julia Bergner, Kansas State University
- Julie's thesis work, under the direction of Bill Dwyer at the University
of Notre Dame, involved better understanding and comparing different
models for the homotopy theory of homotopy theories. This work has been
of interest from a higher-categorical viewpoint as well, as homotopy
theories can be viewed as (infinity, 1)-categories. It has also led to
new results about diagrams describing algebraic structures on spaces. Her
current work involves using the complete Segal space model to answer
questions that arise in the model category setting, and has applications
to both topology and representation theory. Julie will be applying for
positions in fall 2007.
- Sunil Chebolu, University of Western Ontario
- A student of John Palmieri who graduated in 2005 from the University of Washington, Sunil is interested in the interactions between Algebraic Topology, modular representation theory, and Galois cohomology. In his thesis he studied refinements of chromatic towers and Krull-Schmidt decompositions in stable homotopy theory. In recent projects with his collaborators he has solved the Generating Hypothesis in modular representation theory, and is currently working on a refinement of the Bloch-Kato conjecture. In the fall of 2007 he will be applying for tenure-track positions.
- Christopher Dwyer, Binghamton University (SUNY)
- Chris Dwyer's thesis, under Alejandro Adem at the University of
Wisconsin-Madison, involved a constuction of twisted K-theory for proper
actions of discrete groups. It has led to many interesting applications
involving extending classical results about equivariant K-theory and
connections with the Baum-Connes conjecture. His current work involves using
group cohomology and equivariant topology techniques to study properties of
orbifolds. Chris will be applying for tenure-track positions of all kinds
in the fall of 2007.
- Thomas Fiore,
University of Chicago
- Fiore's research can be broadly characterized as topological applications of category theory. In his thesis, under the direction of Igor Kriz at the University of Michigan, he worked out the categorical foundations of conformal field theory. He has applied these results to the factorization of certain field theories through a Jacobian map with Kriz. After detailed comparisons of this approach to others, he has developed the homotopy theory of double categories with collaborators.
- Daniel Ramras, Vanderbilt University
- Daniel Ramras's thesis, directed by Gunnar Carlsson at Stanford University, involved applying K-theoretical techniques to study representation spaces of infinite discrete groups. In particular, using Yang-Mills theory, he related deformation K-theory of the fundamental group of a surface to the topological K-theory of the surface itself. Deformation K-theory serves as the homotopy theoretical analogue of the representation ring, and this result is an analogue of the classical Atiyah-Segal theorem for compact groups. Daniel has also studied the behavior of deformation K-theory on amalgamated products, obtaining excision results in certain settings. Combined with work of Tyler Lawson, these results provide homotopical information about stabilized representation spaces of infinite discrete groups. Daniel is currently in the first year of a three-year post-doctoral fellowship.
- Leticia Zárate, CINESTAV
-
Leticia's Ph.D. thesis, under the direction of Jesús Gonzalez at Cinvestav,
is based on the computation of the BP<n>-homology, of the classifying space of the
group Z2e × Z2e.
She also studied the BP-cohomology of finite dimensional 4-torsion lens spaces Ln(4) and
knowledge of the annihilator ideal of the toral class in this particular case alowed her to obtain lower bounds for the topological complexity for particular values of n.
For the general case, she obtained a family of elements annihilating the toral class in
BP*(Z2e × Z2e), which is conjectured to describe the entire annihilator ideal.
Leticia will be applying for postdoctoral positions in Algebraic Topology and/or Commutative ring theory worldwide in fall of 2007.
- Speakers and Participants
- A listing of confirmed speakers for the session and those
who intend to participate, updated fairly regularly.
- Tentative Schedule
- This is our tentative schedule of speakers, along with titles
and links to abstracts.
-
AMS meeting website
- This link will direct you to the AMS meeting wesite.
The invited addresses
for this meeting are also available.
- Organizers
-