METU Mathematics Seminars
Spring 2017

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

The seminars will be held in Gündüz İkeda Room at 15:40 unless otherwise stated.

March 2
Recent Advances in Sphere Packing Problems
The aim of this talk will be to report on some recent advances in the sphere packing problem in n-dimensional Euclidean space. After an exposition of the problem, M. Viazovska's result shoving that the E8 lattice packing is optimal among all sphere packings in 8-dimensions will be outlined. The follow-up work in 24 dimensions will also be discussed.

March 9
Hacettepe University
Contact Surgery
After a brief introduction on contact 3-manifolds and knots in contact 3-manifolds, we will focus on an operation called topological Dehn surgery and its contact analogue, contact surgery. Then, we will discuss exciting work that is going on in this area.

March 16
Mimar Sinan Fine Arts University
Residually finite groups with finite centralizers
A group is called residually finite if for every non-identity element there is a normal subgroup of finite index which does not contain that element. One can easily show that residually finite groups embed in their profinite completion as dense subgroups. In this talk we will discuss the following problem: Does there exists an infinite residually finite group in which every centralizer is finite? We will present recent results of this ongoing study joint with Maria Tota and Antonio Tortora.

March 23
Bilkent University Department of Physics
Topological Effects in Non-relativistic Quantum Mechanics:An overview of the 2016 Nobel Prize

March 30
Digital Signatures and KamuSM Certificate Setup Tutorial
Digital signature schemes are protocols that are used sign documents and messages electronically. Main requirement for such scheme is to satisfy that messages should only be signed by the one in possession of a secret, yet anyone should be able to verify the authenticity of a signed message. In this talk, first we are going to give a introduction to digital signatures, security requirements such as confidentiality, integrity, message authentication, nonrepudiation. Then we are going to delve into digital signature schemes and the underlying computational problems. In the second part of the talk, we are going to present a step by step how to on KamuSM certificate setup procedures.

April 6
Bilkent University
Singular Integral Operators Induced by Bergman-Besov Kernels on Weighted Lebesgue Classes on the Ball
We analyze weighted Bergman-Besov projection operators as singular integral operators between different weighted Lebesgue classes of the unit ball of C^n, where we use standard weights throughout. Unlike earlier limited attempts, we exhaust all Lebesgue classes and all Bergman-Besov kernels, and treat the widest possible ranges of the parameters in a unified and systematic way. Our main tools are various forms of the Schur test on integral operators, growth estimates of the integrals of Bergman-Besov kernels, representation of radial fractional derivaties as integral operators, and precise inclusion relations among Bergman-Besov spaces and also bounded holomorphic functions. (This is joint work with A. Ersin Üreyen of Anadolu University, Eskişehir.)

April 13
METU Department of Philosophy
The Rhind Mathematical Papyrus (RMP) is one of the surviving and major sources to illustrate the level and scope of the mathematical knowledge of ancient Egyptians. Two particular problems stated in the RMP, that is, Problems 48 and 50, are often uttered as the main sources of information about the way in which ancient Egyptians obtained a value for \pi. But a question naturally arises: how did they do it? Cantor (1907) and Vogel (1958) are said to remark that we do not know. Likewise, Peet (1931) writes that “we have no idea how this result was obtained. The expression of the area as a square suggests a graphic solution”. Among some conjectures offered to answer the question of how ancient Egyptian might have discovered that value, the ones by Vogel (1958) and Gillings (1982) have interesting elements; but they all established only how the scribe might have obtained the reckoning only in the case of Problem 50. It is possible that the procedures they suggested may not work in the cases of the circles other than the one with diameter 9 units. This is because they did not establish in their treatments that there was a solid reason for the scribe to utter the rule for all circles as the rule at all. This reason would basically boil down to the fact that there is an invariant relationship between the areas of the square and the circle, and that there is a secure way of transferring this invariant relationship into the one between the length of the diameter of the circle, and of the side of the square. In this talk, I would like to offer a conjecture that ancient Egyptians had that solid reason.

April 20
Boğaziçi University
Constructing and obstructing Stein cobordisms between singularity links
It is well known that any pair of closed and oriented 3-manifolds cobound a 4-manifold. In this talk, we will explore a refined problem of whether a pair of contact 3-manifolds cobound a compatible Stein 4-manifold. To get some partial answers, we utilize powerful tools from symplectic geometry, Floer homology and singularity theory.

April 27
Bilkent University
Manifolds in the homotopy type of Z/n homology spheres
We will discuss a method which allows us to estimate the diffeomorphism types of smooth manifolds in the homotopy type of a Z/n homology m-sphere, where n is a number depending on m greater than or equal to 5 (m is odd). Our method relies on comparing the set of diffeomorphism classes in the homotopy type of a Z/n homology m-sphere X, with the orbit space of the K-theory group KO(X), under the action of the group of self homotopy equivalences of X. We use cobordism calculations via James spectral sequence for certain bundles over X.

May 4
Sabancı University
Comparison of solutions of nonlocal wave equations
I will talk about some recent results concerning the comparison of solutions of two different equations in asymptotic regimes. There are many works in literature on such comparisons, investigating how solutions of a model equation approximate those of a parent equation. In the scope of fluid dynamics, typical model equations are Camassa-Holm (CH) type equations. These are derived from a parent equation, typically the Euler equations, the Boussinesq system, or a similar system. With H. A. Erbay and S. Erbay, we have considered the same question within the scope of nonlocal elasticity. Our parent equation is the Improved Boussinesq (IB) or more generally a nonlocal equation, representing bidirectional wave propagation, while the model equations are again CH type unidirectional equations. In that respect I will concentrate on three types of results that we have obtained: 1. Derivation of the unidirectional equations from the model equation. 2. Estimates between solutions of unidirectional (CH type) equations and the IB (and the general nonlocal wave) equation. 3. Comparison of two parent equations: Estimates between solutions of two nonlocal wave equations.

May 11
Atılım University
Artin’s Primitive Root Conjecture
In the talk we introduce Artin’s primitive root conjecture. Firstly, historical background of the problem will be given, then heuristic ideas behind the conjecture will be discussed. If time permits the proof of Hooley assuming GRH will be outlined and some variations of Artin’s primitive root conjecture will be discussed.

May 18
İstanbul University
Slant geometry on spacelike submanifolds of codimension two

May 25