# 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

METU

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

CANCELLED

March 30

TÜBİTAK BİLGEM

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

A CONJECTURE CONCERNING THE ANCIENT EGYPTIAN WAY OF COMPUTING THE AREA OF A CIRCLE

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

Artins Primitive Root Conjecture

In the talk we introduce Artins 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 Artins
primitive root conjecture will be discussed.

May 18

İstanbul University

Slant geometry on spacelike submanifolds of
codimension two

May 25

Institute

Title

Abstract