Topology Seminar
2014-2015
Tuesday 11:10-12,
Surge 268
March 31: Julie
Bergner, Modeling homotopical categories
April 7: Julie
Bergner, Modeling homotopical categories, continued
April 14: Akhil
Mathew (UC Berkeley), The Galois group in
stable homotopy theory
Abstract: To a "stable homotopy theory," we naturally
associate a category of finite étale algebra objects and, using Grothendieck's
categorical machine, a profinite group that we call the Galois group. The
Galois group contains a purely algebraic piece coming from the classical
theory, but in general there is an additional (topological) component. This was
first observed by Rognes in the case of periodic real K-theory. We calculate
the Galois groups in several examples. For instance, we show that the Galois
group of the periodic E∞-algebra of topological modular forms
is trivial and that the Galois group of K(n)-local stable homotopy theory is an
extended version of the Morava stabilizer group.
April 21: Julie
Bergner, The model structure for complete Segal spaces
April 28: No seminar
May 5: Eric Peterson
(UC Berkeley), Determinantal K-theory and a few applications
Abstract: Chromatic
homotopy theory is an attempt to divide and conquer algebraic topology by
studying a sequence of what were first assumed to be “easier” categories. These
categories turn out to be very strangely behaved — and furthermore appear to be
equipped with intriguing and exciting connections to number theory. To give an
appreciation for the subject, I’ll describe the most basic of these strange
behaviors, then I’ll describe an ongoing project which addresses a small part
of the “chromatic splitting conjecture”.
May 12: Julie
Bergner, The model structure on simplicial categories
May 19: Angélica
Osorno (Reed College), K-theory for 2-categories
Abstract: We give a
K-theory construction for symmetric monoidal 2-categories, and use it to show
that these model connective spectra, in the sense that the homotopy theories
are equivalent. Our methods require new coherence and strictification
results which are of independent interest, and we will outline these. We
also outline a broader program to give algebraic models for stable 2-types, and
describe how it makes use of this work. This is joint with Nick Gurski
and Niles Johnson.
May 26: Matthew
Barber, An introduction to algebraic theories
June 2: Julie
Bergner, Theories and Segal categories
January 6: Julie Bergner, Overview of abstract homotopy theory
January 13: Matthew Barber – practice oral exam talk
January 20: Julie Bergner, Simplicial objects
January 27: Julie Bergner, Model structures for simplicial spaces
February 3: Greg Chadwick, Cobordism, Thom spectra, and stable
homotopy theory
February 10: Greg Chadwick, Cobordism, Thom spectra, and stable
homotopy theory, part 2
February 17: Julie Bergner, The Reedy model structure for
simplicial spaces
February 24: Sam Nariman (Stanford), On characteristic classes
of flat manifold bundles
Abstract: We prove that group homology of the diffeomorphism group of the
g-fold connect sum of S^n x S^n, as a discrete group is independent of
g in a range, provided that n>2. This was motivated by a
conjecture posed by Morita about discrete surface diffeomorphism
groups. The stable homology is isomorphic to the homology of a
certain infinite loop space related to the Haefliger's classifying space
of foliations. One geometric consequence of this description of the stable
homology is a splitting theorem that implies certain classes called generalized
Mumford-Morita-Miller classes can be detected on a flat #^g S^n
x S^n bundle. If time permits, I will report on the progress about the surface
case.
March 3: Seminar cancelled
March 10: Matthew Barber, Model structure on dendroidal sets
October 7: Greg Chadwick, Nilpotence in stable homotopy theory
October 14: Julie Bergner, Localization of categories
October 21: Julie Bergner, Model categories
October 28: Julie Bergner, Homotopies in a model category
November 4: Marcy Robertson (UCLA), Rational Homotopy Type of
Colored Operads
Abstract: We give a
filtration special pushouts of colored operads that allow us to define a type
of relative left properness and relative change of base theorem for colored
operads. As a consequence, we show how to compute the rational homotopy type of
a colored operad. This is joint work with Philip Hackney and Donald Yau.
November 11: No seminar – Veterans Day
November 18: Julie Bergner, Quillen equivalences of model
categories
November 25: Julie Bergner, Simplicial sets and topological spaces
December 2: Matthew Barber, Dendroidal sets
December 9: Jacob West, An introduction to quasi-categories
http://www.math.ucr.edu/~jbergner/topologysem1415.htm Last updated: 2 June 2015