http://home.gwu.edu/~harizanv/Logic%20Seminar%20F09.html

3:00–4:00p.m.

Speaker: Jacob Learned, GWU

Place: Corcoran Hall
(725 21^{st} Street), Room 106

Title: *Quantum neural networks*

2:30–330p.m.

Speaker: Mariel Supina,
GWU

Place: Bell Hall (2029
G Street), Room 108

Title: *GroverŐs search algorithm: quantum speed-up*

5:30–6:30p.m.

Speaker: Valentina
Harizanov, GWU

http://home.gwu.edu/~harizanv/

Place: Corcoran Hall
(725 21^{st} Street), Room 101

Title: *Transforming structures*

Abstract: Often, interesting computability-theoretic phenomena
are first obtained on structures of special kind, which result from specific
complicated constructions and may not come from natural classes. It is often
desirable to find such phenomena on structures in other, well-known classes. We
will present algorithmic ways of transforming certain countable structures and
their isomorphisms into other types of algebraic
structures and their isomorphisms in such a way that
relevant computability-theoretic properties are transferred.

5:30–6:30p.m.

Speaker: Johanna Franklin, Hofstra University, NY

https://people.hofstra.edu/Johanna_N_Franklin/

Place: Funger Hall (2201 G Street), Room 108

Title: *Category and lowness for isomorphism*

Abstract:**
**A Turing
degree **d** is said to be low for
isomorphism if, whenever two structures are **d**-isomorphic, they are already computably isomorphic. Solomon and I
proved that every 2-generic Turing degree was low for isomorphism and
hypothesized that no weaker level of genericity would
suffice. However, Turetsky and I constructed a
properly 1-generic real that is low for isomorphism. In this talk, I will
present proofs of both of these results.

**Wednesday, February 3, 2016**

5:30–6:30p.m.

Speaker: Valentina Harizanov, GWU

http://home.gwu.edu/~harizanv/

Place: Phillips Hall (801 22nd Street), Room 110

Title: *The tree method in priority arguments*

5:30–6:30p.m.

Speaker: Russell Miller, City University of New York

http://qcpages.qc.cuny.edu/~rmiller/

Place: Phillips Hall (801 22nd Street), Room 110

Title: *Computable functors and effective interpretations*

Abstract:**
**We draw connections between two related
notions. An *effective interpretation*
of a countable structure *A* in another
countable structure *B* uses exactly
the notion of interpretation from model theory, except that now the domain of
the interpretation is allowed to use tuples from *B* of arbitrary finite length, and that
the formulas to be used must be computable infinitary
Sigma_1 formulas, rather than finitary formulas of
arbitrary complexity. A *computable functor*, from the category Iso(*B*) of all structures with domain omega isomorphic to *B* to the corresponding category Iso(*A*), is given
by two Turing functionals, one mapping objects from Iso(*B*) to objects
in Iso(*A*) and
the other mapping isomorphisms between objects in Iso(*B*) to isomorphisms between the corresponding objects in Iso(*A*). Recent
work by Harrison-Trainor, Melnikov,
Montalb‡n and the speaker has shown these two
concepts to very tightly related. An effective interpretation of *A* in *B*
clearly yields a computable functor from Iso(*B*) to Iso(*A*). We will describe the converse and
consider how these notions may be extended to continuous functors and interpretations by L_omega_1,omega formulas
in general.

5:30–6:30p.m.

Speaker: Tslil
Clingman, GWU

Place: Monroe Hall
(2115 G Street), Room 267

Title: *An exploration of the category of relations*

Abstract:**
**The category of relations, Rel, has a rich
structure and serves as an important example of many concepts in the general
theory. We will begin by understanding morphisms, limits and self-duality in
this category, observing that one may take the external axiom of choice (as
this is not always possible), before moving to understand any of the several
important structural notions present in Rel. Depending on audience interest, we
will see how Rel is a (closed) monoidal category, an enriched category (in two
important ways) and even a strict 2-category. Finally, time permitting,
we will explore a very important generalisation of Rel which leads to the
general theory of weak 2-categories. Only elementary knowledge of category
theory will be assumed.

6:00–7:00p.m.

Speaker: Valentina Harizanov, GWU

Place: Monroe Hall
(2115 G Street), Room 110

Title: *Coding sets into orders*

5:30–6:30p.m.

Speaker: Ajit Iqbal Singh, Indian National Science Academy

http://insaindia.org/detail.php?id=N99-1262

Place: Monroe Hall
(2115 G Street), Room 267

Title: *Roping more by ringing less in topology*

6:00–7:00p.m.

Speaker: Rumen Dimitrov, Western Illinois University

http://www.wiu.edu/users/rdd104/home.htm

Place: Monroe Hall
(2115 G Street), Room 110

5:30–6:30p.m.

Speaker: Tslil
Clingman, GWU

Place: Monroe Hall
(2115 G Street), Room 267

Title: *A gentle introduction to monoidal categories*

Abstract:**
**While
general categories provide a rich and deep theory, more focused inquiry may be
achieved by requiring of the categories a certain additional structure. Perhaps
one of simplest starting points is requiring the objects of the category to
form a monoid in an appropriate sense. We shall work
our way up from elementary definitions in the general theory to such Ňmonoidal categoriesÓ, examine their natural manifestations,
explore what Ňgeneralised elementsÓ of such
categories may be and, time allowing, further directions and motivations. No
prior understanding of category theory will be assumed.

**Wednesday, October 7, 2015**

5:30–6:30p.m.

Speaker: Dr. Fredrick Nelson

Place: Monroe Hall
(2115 G Street), Room 267

Title: *The group of rational points on the Holm curve is torsion-free*

Abstract:**
**The Holm
curve is the elliptic curve given by the equation *k,,y-^3.*–*y. = l,,x^-3.*–*x.* where
*k* and *l* are distinct, relatively prime, square-free, positive integers. It is isomorphic to the
elliptic curve in Weierstrass form. By MordellŐs
theorem, the group of rational points on the Holm curve is a finitely-generated
abelian group. I will prove that this group is
torsion-free, thus establishing a previous conjecture. The proof uses McKeeŐs algorithm
for computing division polynomials of elliptic curves.

5:30–6:30p.m.

Speaker: Hakim Walker, GWU

Place: Monroe Hall
(2115 G Street), Room 267

Title: *Computable isomorphisms between *(2,1):1* structures*

Abstract: A (2,1):1 structure consists
of a countable set *A *(usually the
natural numbers) and a function *f* that
maps, to each element of *A*, either
exactly one element of *A* or exactly two
elements of *A*. Similar structures
have been studied recently by Harizanov, Cenzer, Remmel, and Marshall,
particularly the complexity of isomorphisms between
such structures. In this talk, we will begin by presenting some of the basic
properties of these structures, particularly the types of orbits under *f*, which can be interpreted as directed
graphs. Then we will discuss some computability-theoretic results, including
two classes of (2,1):1 structures that are computably
categorical, i.e., every two computable copies of the structure have a
computable isomorphism between them. Finally, we will conclude with an
application to the Collatz conjecture.

5:30–6:30p.m.

Speaker: Jozef
Przytycki, GWU

http://home.gwu.edu/~przytyck/

Place: Monroe Hall
(2115 G Street), Room 267

Abstract: We show a simple
visualization that allows us to construct homology theory for a Yang-Baxter operator.
The linear map $R: V\otimes V \to V\otimes V$ is called by Fadeev
school of theoretical physics the Yang-Baxter operator if it is invertible and
satisfies the following equation:

$(R\otimes Id) (Id \otimes
R)(R\otimes Id) = (Id \otimes
R)(R\otimes Id)(Id \otimes
R)$.

We show that the quandle homology, in its cubic form,
can be presented graphically using a diagram (curtain diagram). This in turn
gives rise to homology of Yang-Baxter operator. We speculate that this homology
is related to Khovanov homology of links and gives a
deep connection between Knot Theory and Statistical Physics.