METU Mathematics Seminars
Spring 2011


Previous Seminars: Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011.


February 17
Alexander Pott
Universitat Magdeburg
On the equivalence of certain functions that occur in cryptography and in finite geometries
The talk will be concerned with the equivalence of functions that occur in cryptography and in finite geometries. Difference type constructions are very common in discrete mathematics. They include: Semifields (projective planes), almost perfect nonlinear functions, bent functions. The speaker will describe some constructions and discuss the problem as to how to distinguish these combinatorial objects.

March 3
Burak Aksoylu
TOBB University
Louisiana State University
Robust multilevel preconditioners for highly heterogeneous media
The application of interest comes from flow in highly heterogeneous porous media which involves the solution of diffusion equation with rough coefficients. Roughness of PDE coefficients causes loss of robustness of preconditioners. The main goal is to recover robustness and obtain rigorous structural understanding of the involved process. A qualitative understanding of the PDE operators and their dependence on the coefficients is essential for designing preconditioners. Controlling the infinite dimensional problem provides a basis for the construction of preconditioners. We use tools from operator theory for this. On the other hand, we control the discretized problem using singular perturbation analysis (SPA) which provides valuable insight to the asymptotic behavior of the solution of the underlying PDE. We construct a preconditioner based on this feedback and justify its effectiveness rigorously. Our numerical experiments, including an example derived from the SPE10 benchmark problem, show that our preconditioning strategy is computationally comparable to algebraic multigrid both in terms of iteration count and CPU-time, but with rigorous justification.

March 7
Marat Akhmet
Middle East Technical University
Synchronization of integrate-and-fire biological oscillators
We survey algorithms to compute with large finite permutation and matrix groups. Particular attention will be given to handling both types of groups with similar methods, using structural properties to answer even basic questions such as the order of the input group.

March 17
Mustafa Kalafat
Middle East Technical University
Analysis and Group Theory on Gravitational Instantons
We give a brief survey of conjectural classification of the gravitational instantons, which are exact solutions to the Einstein field equation in general relativity. Then we show that a complete simply-connected hyperkahlerian 4-manifold with an isometric triholomorphic circle action is obtained from the Gibbons-Hawking ansatz with some suitable harmonic function. This comes as an application of classification of positive harmonic functions. This is joint work with Justin Sawon.

March 24
Turker Biyikoglu
Isik University
Extremal eigenvalues of graphs and their applications
The fundamental graph properties e.g. coloring, diameter, isomorphism and connectivity are closely related to the eigenvalues of matrix representations of these graphs (e.g. adjacency matrix or Laplacian matrix of the graph). The sharp eigenvalue bounds for such graph invariants depend on the extremal eigenvalues. Extremal graph eigenvalue problem is finding a graph in a given graph class that has the minimum (or maximum) eigenvalue for a given matrix representation. I shall talk about these connections between graph properties and eigenvalues of graphs. I shall present results, methods, difficulties and possible further research topics on extremal graph eigenvalue problems. I shall present some applications of extremal eigenvalues, especially on the synchronization of dynamical systems. This talk is intended for a general audience. No specialist knowledge is required.

March 31
Ergun Yalcin
Bilkent University
Fusion systems and constructions of finite group actions on products of spheres.
Some of the most interesting problems in group action theory are about finite group actions on products of spheres. I will first give an overview of problems and conjectures in this area and explain some of the tools that are used for constructing group actions on products of spheres. Then, I will describe a recent construction that we have done with Ozgun Unlu using fusion systems. Fusion systems are abstract models for the p-local structure of a finite group and recently have been studied intensively. Using fusion systems in the constructions of finite group actions is one of the few explicit applications of abstract fusion systems.

April 7
Ferit Ozturk
Bogazici University
Topology, in contact, in real
On every 3-manifold there is a completely non-integrable 2-plane distribution called a contact structure. Some 3-manifolds have an orientation preserving, nontrivial Z/2 action called a real structure. If the real structure sends the contact structure to its negative, such a pair on the manifold is called a real contact structure. The natural examples of real contact 3-manifolds are links of algebraic surface singularities given by polynomials with real coefficients. In this talk I am going to present some recent results with Nermin Salepci, including uniqueness of real tight contact 3-ball and the Giroux correspondence in real setting. The talk will be elementary and will be a mixture of mathematics and the impressions of Mexican mathematical life that I acquired during my short stay in Cuernavaca.

April 21
Sinan Sertoz
Bilkent University
Counting lines on algebraic surfaces
This is mostly a survey of what is known on the problem of counting the number of lines on a complex algebraic surface. The problem probably became of interest when Segre showed in 1943 that the maximal number of lines on a quartic surface is 64. To motivate the contemporary student on this problem it may suffice to say that the maximal number of lines on a quintic is yet to be found. Moreover, the proof of Segre uses hea- vily the tools of classical algebraic geometry. Reproducing the same result using the lattice theoretic properties of a quartic is also an open problem on which Alexander Degtyarev and I started a joint project some details of which I may reveal during the talk!

April 28
Aurelian Gheondea
Bilkent University
When are the products of normal operators normal?
The products of normal operators on a Hilbert space are not normal in general. Commutation is a sufficient condition but this is not necessary. Motivated by some questions in quantum optics we present a few historical results on this question and some recent progress in the case of non-compact operators.

May 5
Bayram Tekin
Department of Physics, Middle East Technical University
Some extensions of general relativity
I will talk about some modifications and extensions of general theory of relativity (GR). Since GR does not work at extremely small and large distances as well as it does in the solar system scale, physicists search for consistent extensions of the theory. I hope to give some basic introduction to these theories.

May 12
Serkan Eryilmaz
Department of Industrial Engineering, Atilim University
Computing the system reliability by combinatorial methods
Reliability is defined to be the probability that a system will perform satisfactorily for at least a given period of time when used under stated conditions. One of the main problems in reliability theory is the derivation of system reliability formula as a function of component reliabilities. Combinatorial methods have been effectively used for computing the system reliability whenever the system consists of independent and identical components. In this talk, we present the use of traditional combinatorial methods for computing the reliability of well-known systems such as k-out-of-n, consecutive-k-out-of-n and their generalizations.

May 26
Akos Seress
Ohio State University
University of Western Australia
A unified approach to computations with permutation groups and matrix groups
We survey algorithms to compute with large finite permutation and matrix groups. Particular attention will be given to handling both types of groups with similar methods, using structural properties to answer even basic questions such as the order of the input group.