Cannon Seminar: Fall 2017/Winter 2018
Seminars will be on Wednesdays at 2:00 - 2:50 pm in
294 TMCB, unless otherwise noted.
Wednesday, Sept 18, 2018 at 4pm
Nick
Callor (Brigham Young University)
Title:
Persistent Homology
Abstract:
Wednesday, Sept 26, 2018
Curtis
Kent (Brigham Young University)
Title:
Splittings of the first homology of Peano continua.
Abstract:
We will give examples of path connected and non-path connected fibrations. We will
show how to endow the fundamental group of a Peano continuum with a topology
such that the closure of the commutator subgroup, the infinite commutator
subgroup, corresponds to a path connected upl fibration and induces a splitting of the first homology.
Wednesday, Oct 3, 2018
Nathan
Sunukjian (Calvin College)
Title:
Exotic 4-manifolds and equivalence classes of smoothly embedded surfaces.
Abstract:
The field of smooth 4-manifolds contains one of the great longstanding
mysteries in the history of geometric topology -- that although many four
manifolds seem to have an infinite number of smooth structures (something that
is not true in any other dimension), no one has managed to propose a way to
categorize or classify these smooth structures. On the other hand, smooth
structures on 4-manifolds are closely related to surfaces embedded in
4-manifolds, and there are various schemes for trying to understand such
surfaces. The purpose of this talk will be to explore this relationship between
smooth structures and embedded surfaces. We'll survey examples of embedded
surfaces, and look at equivalence classes of embedded surfaces, in particular
the equivalence classes of concordance and 0-concordance. Specifically, we'll
describe the usefulness of these equivalence classes for understanding smooth
structures, and describe various cases where we can actually say something
about the structure of these equivalence classes.
Friday, Oct 12, 2018
Jingyin Huang (The
Ohio State University)
Title:
Two-dimensional Artin groups and metric systolicity
Abstract: We show that every 2-dimensional Artin group is non-positively curved in an appropriate
sense. Then it follows that any finitely presented subgroup of a 2-dimensional Artin group has quadratic Dehn
function and solvable conjugacy problem. If time premits,
I will also discuss a sub-class of these Artin group
where we can prove biautomaticity. No previous
knowledge on Artin group is required. This is joint
work with D. Osajda.
Wednesday, Oct 17, 2018
Eric
Swenson (Brigham Young University)
Title:
Abstract:
Wednesday, Oct 24, 2018
Steve
Humphries (Brigham Young University)
Title:
Schur rings, Random walks on groups and cogrowth series
Abstract: We explain some connections between these
three topics
Wednesday, Nov 7, 2018
Michael
Andersen (Brigham Young University)
Title:
Abstract:
Wednesday, Nov 14, 2018
Maggie Miller (Princeton University)
Title:
Fibering ribbon disk complements
Abstract:
I will construct singular fibrations on $3$-manifolds
with boundary, and discuss when they may trace smooth fibrations
(over $S^1$) of a $4$-manifold $X^4$ with boundary, with particular emphasis on
when $X^4$ is the complement of a ribbon disk in $B^4$ whose boundary is a
fibered knot in $S^3$. This is related to a question of Casson
and Gordon.
Wednesday, Dec 5, 2018
Mark Hughes (Brigham Young University)
Title:
Abstract:
Winter 2019
Seminars will be on Wednesdays at 2:00 - 2:50 pm in
294 TMCB, unless otherwise noted.
Wednesday, Jan 16, 2019
Nick
Callor (Brigham Young University)
Title:
Persistent Homology
Abstract:
Wednesday, Jan 30, 2019
Curt Kent
(Brigham Young University)
Title:
Homotopy type and homology of Peano
continua
Abstract:
We will discuss how to extend traditional machinery from topology and geometric
group theory to spaces without universal covers. Specifically we will
discuss homotopy type of low-dimensional continua and
metrics on fundamental groups which lead to splittings
for their abelianization.
Wednesday, Feb 6, 2019
Mark
Hughes (Brigham Young University)
Title:
Categorification, matrix factorization, and link homology
Abstract:
Categorification is a relatively recent viewpoint, in which simple invariants
(often numerical or polynomial) are strengthened to "categorical"
invariants. In this talk I will describe what this means, with examples
from basic topology. I will then describe instances of categorification in knot theory, and its applications.
Wednesday, Feb 13, 2019
Greg
Conner (Brigham Young University)
Title:
Abstract:
Wednesday, Feb 20, 2019
Eric
Swenson (Brigham Young University)
Title:
Abstract:
Wednesday, Feb 27, 2019
Stewart
McGinnis (Brigham Young University)
Title:
Path-connectedness
of Fibrations over the Hawaiian Earring
Abstract:
We present a
class of UPL fibrations that are inverse limits of
towers of regular covering spaces over the Hawaiian Earring and give a
characterization of when they are path-connected.
Wednesday, Mar 6, 2019
Tyler
Hills (Brigham Young
University)
Title:
Abstract:
Tuesday, May 7, 2019
Seungwon Kim (National
Institute for Mathematical Sciences)
Title: Trisections of surface complements and the Price twist
Abstract:
In this talk, we will discuss a method to produce a trisection of a surface
complement in a 4-manifold. If the time remains, we will discuss how to obtain
a Price twist, which changes the manifold by removing a neighborhood of an
embedded real projective plane in a 4-manifold and regluing it in a different
way. This is joint work with Maggie
Miller.