METU Mathematics Seminars
Fall 2014
Previous Seminars: Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011.
October 2
University of Leeds
Study of Unsolvability
Recursion Theory is a branch of mathematical logic which originates from the study of recursive (i.e. computable) functions. One of its main aims is to investigate the algorithmic relationship between undecidable sets, uncomputable functions and relations. In this seminar, we will talk about what recursion theorists do and give some current research topics in this field.
October 9
Middle East Technical University
Symplectic and nonsymplectic 6-manifolds
A topological construction of simply connected smooth six manifolds with
$w_2=0, b_2=1$ and $b_3=0$ will be explained. This construction may
result with symplectic manifolds as well as nonsymplectic manifolds. The
reason for unsimilar outcomes will be explored.
October 23
University of Ljubljana
Gropes and their fundamental groups
Recent results on gropes and their fundamental groups are presented.
Gropes are an important construction in geometric and algebraic topology,
introduced by Sta'nko and Cannon. Open infinite gropes are nice
2-dimensional CW complexes and Eilenberg-MacLane spaces of their
fundamental groups, but they are on the one hand closely related to wild
spaces and on the other hand their fundamental groups are in some sense
wild.
October 30
Middle East Technical University
Impressions from ICM 2014
November 6
Middle East Technical University
Conjectures on modules of constant Jordan type and Betti numbers of fixed point sets
Let A be an abelian p-group of exponent p^t,
and k be an algebraically closed field of characteristic p. Since there is no classification for indecomposable modules over k[A] except for cyclic groups, and the group Z_2 x Z_2, these modules are studied via restrictions to subalgebras corresponding to the cyclic subgroups of the unit group of k[A]. This approach became useful especially after the definition of modules of constant Jordan type. We define the class of restricted k[A]-modules of constant p^t-Jordan type, generalize several theorems by Benson, and verify a generalization of conjectures by Suslin and Rickard.
November 13
Middle East Technical University
An Axiomatization of Euclidean Geometry by means of the Cayley-Menger
Determinants
The purpose of this talk is to present an observation by C. Soland that it is possible to characterize the Euclidean plane as
a metric space which obeys three further and natural axioms employing the Cayley-Menger determinants.
November 20
Ali Ulaş Özgür Kişisel
Middle East Technical University
Linear Tropicalizations
Studying tropicalizations of algebraic varieties proved to be useful for
answering several questions in algebraic geometry. The tropicalization
construction is extrinsic, namely it depends on the ambient space that the
variety lies in. An intrinsic tropicalization for a variety was defined by
S. Payne and was shown to be homeomorphic to another natural object, the
Berkovich space of X. After describing these results I will present a
variant of this construction and show some applications. This is joint
work with Hakan Güntürkün.
November 27
Southern Illinois University
Analytical routes of periodic motions to chaos
In this talk, analytical solutions for period-m flows and chaos in nonlinear dynamical systems are presented through the generalized harmonic
balance method. The nonlinear damping, periodically forced, Quadratic
nonlinear oscillator was investigated as an example to demonstrate the
analytical solutions of periodic motions and chaos. Through this
investigation, the mechanism for a period-m motion jumping to another
period-n motion in numerical computation is found. In this problem, the
Hopf bifurcation of periodic motions is equivalent to the period-doubling
bifurcation via Poincare mappings of dynamical systems. The stable and
unstable period-m motions can be obtained analytically. Even more, the
stable and unstable chaotic motions can be achieved analytically. The
methodology presented in this paper can be applied to other nonlinear
vibration systems, which is independent of small parameters.
December 4
Düzce University
Leavitt path algebras: a taste for all?
First decade of research is done in this newly defined structure, yet surprising connections have flourished with C*-algebras, symbolic dynamics, noncommutative geometry and algebra. We will introduce the
structure and report on the research done in the last 10 years.
December 11
Tülin Sertöz
Bilimin Kıyısında
December 18
Middle East Technical University
Action of a Frobenius-Like Group
December 25
Middle East Technical University
R. Thompson's Groups