11:00am–12:00noon
Speaker: Jennifer Chubb,
University of San Francisco and GWU
http://www.cs.usfca.edu/~jcchubb/
Place: Phillip Hall
(801 22nd Street), Room 736
11:00am–12:00noon
Speaker: Valentina
Harizanov, GWU
http://home.gwu.edu/~harizanv/
Place:
Phillip Hall (801 22nd Street), Room
736
11:00am–12:00noon
Speaker: Rumen Dimitrov,
Western Illinois University
http://www.wiu.edu/users/rdd104/home.htm
Place: Rome Hall (801 22nd
Street), Room 351
Title: Cohesive Powers, Definability,
and Automorphisms
2:30–3:30p.m.
Speaker: Tslil Clingman,
Johns Hopkins University
Place:
Rome Hall (801 22nd Street), Room 771
2:30–3:30p.m.
Speaker: Valentina Harizanov,
GWU
http://home.gwu.edu/~harizanv/
Place:
Rome Hall (801 22nd Street), Room 771
Abstract:
For a
computable structure, we define its index set to be the set of all Goedel codes
for computable isomorphic copies. We will show how to calculate precisely the
complexity of the index sets for some familiar algebraic structures. We will
further discuss the most recent results in this area.
3:00–4:00p.m.
Speaker: Russell Miller, City University of New York
http://qcpages.qc.cuny.edu/~rmiller/
Place:
Rome Hall (801 22nd Street), Room 771
Title: Classification
and measure for algebraic fields
Abstract:
The
algebraic fields of characteristic 0 are precisely the subfields of the
algebraic closure of the rationals, up to isomorphism. We describe a way
to classify them effectively, via a computable homeomorphism onto Cantor
space. This homeomorphism makes it natural to transfer Lebesgue measure
from Cantor space onto the class of these fields, although there is
another probability measure on the same class, which seems in some ways more
natural than Lebesgue measure. We will discuss how certain properties of
these fields – notably, relative computable categoricity – interact with these
measures: the basic result is that only measure-0-many of these fields
fail to be relatively computably categorical. (The work on computable
categoricity is joint with Johanna Franklin.)
2:30–3:30p.m.
Speaker: Valentina Harizanov,
GWU
http://home.gwu.edu/~harizanv/
Place:
Rome Hall (801 22nd Street), Room 771
Abstract:
The
Scott Isomorphism Theorem says that for any countable structure M there is a sentence, in countable
infinitary language, the countable models of which are exactly the isomorphic
copies of M. Here, we consider a
computable structure A and define its
index set to be the set of all Gdel codes for computable isomorphic copies of A. We will present evidence
for the following thesis. To calculate the precise complexity of the index set
of A, we need a good description of A, using computable infinitary language,
and once we have an optimal description, the exact complexity within a computability-theoretic
hierarchy will match that of the description.
4:15–5:15p.m.
Speaker: Jennifer Chubb, University
of San Francisco and GWU
http://www.cs.usfca.edu/~jcchubb/
Place:
Rome Hall (801 22nd Street), Room 771
Abstract: An ordering of an algebraic structure with identity can
often be identified with the corresponding set of positive elements. For
a given algebraic structure, we can organize the cones of all the admitted
orderings on a tree. When the structure is computable, the tree can be
constructed in an effective way. Topological properties of this space of
orderings can provide insight into algorithmic properties of the orderings, and
vice versa. In this talk, we will see how to construct these trees and
what they can tell us.
2:30–3:30p.m.
Speaker: Jennifer Chubb, GWU
http://www.cs.usfca.edu/~jcchubb/
Place:
Rome Hall (801 22nd Street), Room 771
Abstract: A left- or bi- partial ordering of an algebraic
structure is a partial ordering of the elements of the structure that is
invariant under the structure acting on itself on the left or, respectively,
both on the left and on the right. I will discuss algorithmic properties of the
orderings admitted by computable structures and their general properties, and
describe some open problems.
2:30–3:30p.m.
Speaker: Jozef Przytycki,
GWU
http://home.gwu.edu/~przytyck/
Place:
Rome Hall (801 22nd Street), Room 771
Abstract: We will describe the work of our Mathathon group
(Sujoy Mukherjee, Marithania Silvero, Xiao Wang, Seung
Yeop Yang), December 2016–January 2017, on torsion in
Khovanov homology different from Z_2. Khovanov homology, one of the most
important constructions at the end of XX century, has been computed for
many links. However, computation is NP-hard and we are limited to generic knots
of up to 35 crossings with only some families with larger number of
crossings.
The
experimental data suggest that there is abundance of Z_2-torsion but other
torsion seems to be rather rear phenomenon. The first Z_4 torsion appears
in 15 crossing torus knot T(4,5), and the first Z_3 and Z_5 torsion in the
torus knot T(5,6). Generally, calculations by Bar-Nathan, Shumakovitch, and Lewark suggest Z_p^k torsion in the torus knot T(p^k,p^k+1), p^k >3, but this has not yet been proven. We show, with Mathathoners, the existence of Z_n-torsion,
n>3, for some infinite family of knots. The simplest of them is obtained
by deforming the torus knot T(5,7) by a t_2k-moves. We
also prove the existence of knots with other torsion, the largest being Z_2^23,
so the cyclic group of over 8 millions elements. We combine computer
calculations (and struggle with NP hardness) with homological algebra
technique.
The
talk will be elementary and all needed notions will be defined.