IEU - Department of Mathematics

General Seminars of
Department of Mathematics

Announcements

This site is to announce General Seminars of our department in this academic year. Below is a list of speakers in reverse chronological order. Our seminars are open to anyone interested to listen and/or give a talk. If you need any assistance, please get in touch with the organizer.

June 11, 2013
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Hakan Gündüz
- Title: Local Bifurcation Analysis In Discreet and Continuous Case with Applications
- Place: M403
- Time: 10:30-11:30
- Abstract:
  In this seminar, I talk about Bifurcation theory, which is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behaviour. Bifurcations occur in both continuous systems, and discrete systems.
  
  After that, I talk about local bifurcations, which can be analysed entirely through changes in the local stability properties of equilibria, periodic orbits or other invariant sets as parameters cross through critical thresholds and give the examples that are saddle-node (fold) bifurcation, transcritical bifurcation, pitchfork bifurcation, period-doubling (flip) bifurcation, hopf bifurcation in one dimeonsional and two dimensional systems with discreet and continuous cases.
May 31, 2013
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: H. Can Koyuncuoğlu
- Title: A new periodicity concept on time scales
- Place: M403
- Time: 16:30-17:30
- Abstract:
  In this talk, we introduce the backward and the forward shift operators $\delta_{\pm}$ on time scales by means of which we construct a new periodicity concept on time scales. This approach enables the investigation of periodic solutions of dynamic equations on time scales that are not periodic with respect to conventional periodicity definition. Hence, we establish the periodicty notion on a large class of time scales such as; $\overline{q^{\mathbb{Z}}}:=\left\{ q^{n}:n\in\mathbb{Z}\right\} \cup\left\{0\right\}$ , $q>1$ and $\cup_{k=1}^{\infty}\left[ 3^{\pm k},2.3^{\pm k}\right] \cup\left\{ 0\right\}$ which may not satisfy the $t \pm P \in T for all t \in T,$ $t\pm P\in\mathbb{T}\text{ for all }t\in\mathbb{T}\text{,}%$ for a fixed $P>0$ . Moreover, based on the new periodicity notion, we propose the possible future research directions regarding Floquet theory on time scales.
May 28, 2013
- Poster: As a pdf document.
- Speaker: Caner Kazancı (University of Georgia)
- Title: Modeling an ecosystem from the point of view of a Carbon atom
- Place: C308
- Time: 16:30-17:30
- Abstract:
  Ecosystems are often modeled using weighted digraphs, representing flow of energy or nutrients among compartments. Depending on the model, what a compartment represents may range from dissolved organic matter in a lake, to multiple species with common properties living in a specific area. Flows among compartments may represent predation, uptake, excretion, etc. Ecological networks can be fairly large and complex. Decomposing an ecosystem model into smaller sub networks for easier analysis is often tempting. However, essential ecosystem behavior may be lost by breaking connections, or excluding compartments. Neither flows, nor compartments can function by themselves. Therefore we propose two new alternative mathematical representations, that preserve system wide behavior of ecosystems: (1) Pathways (2) Fluxes. A pathway represents the ecosystem from the point of view of a single Carbon atom, or a single energy quantum. A flux represents the smallest process within the ecosystem that can theoretically sustain itself. This can be a material cycle within the ecosystem, or a simple food chain in a complex ecosystem. In this talk, we'll discuss how these two representations can be useful for ecological studies.
May 16, 2013
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Müfit Sezer (İ.D.Bilkent University)
- Title: Monomial Gotzmann sets
- Place: M301
- Time: 13:30-14:20
- Abstract:
  A homogeneous set of monomials in a quotient of the polynomial ring $S:=F[x_1,…,x_n]$ is called Gotzmann if the size of this set grows minimally when multiplied with the variables. These sets arise naturally in computation of the Hilbert functions of graded ideals. We give some back ground on them and then note that Gotzmann sets in the quotient arise from certain Gotzmann sets in $S$ . Secondly, we prove a combinatorial result about the deletion of a variable in a Gotzmann set in $S$ .
May 9, 2013
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Uğur Madran
- Title: Generalized Invariants of Cyclic Groups
- Place: M301
- Time: 13:30-14:20
- Abstract:
  Let $G$ be finite groups acting on a polynomial algebra $\mathbb{F}[x_1,\ldots,x_n]$ by homogenous linear substitutions. In this talk, we will first briefly summarize properties of invariant ring and related structures. Generalized invariants have been introduced for (pesudo)reflection groups by Kac and Peterson in 1985 and have nice properties. We will extend this definition for cyclic groups.
April 26, 2013
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Güven Yücetürk (TÜBİTAK BİLGEM)
- Title: Gregarious Path Decompositions of Some Graphs
- Place: M403
- Time: 16:30-17:30
- Abstract:
  Let $G$ be a simple graph and $f(v)$ a positive integer for each vertex $v$ of $G$ . Form $G^f$ by replacing each $v$ by a set $F(v)$ of $f(v)$ vertices, and each edge $uv$ by complete bipartite graph on bipartition $(F(u), F(v)).$ Can we partition $G^f$ into paths of length 2 which are gregarious, that is, meet three different $F(u)$ 's?
December 26, 2012
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Deniz Erdemirci Erkuş
- Title: Generators of Hilbert Ideal of Cyclic Groups in Modular Invariant Theory
- Place: M301
- Time: 16:30-17:30
- Abstract:
  The Hilbert ideal is the ideal generated by polynomial invariants of positive degree. We deal with a conjecture of Harm Derksen and Gregor Kemper which is given with the following statement:
  
  Let $V$ be a representation of a finite group $G$ . The Hilbert ideal $\mathfrak{h}$ is generated by homogeneous elements of degree at most the order of $G$ .
  
  In this talk, our studies on this conjecture will be mentioned.
December 12, 2012
- Poster: As a pdf document
- Speaker: Nikolai Valtchev Kolev (Sao Paulo University)
- Title: Nonexchangebility and Radial Asymmetry Identification via Bivariate Quantiles
- Place: M301
- Time: 16:30-17:30
- Abstract:
  In the talk will be discussed the folloing topics: Kendall distribution, bivariate quantile curves, central and lateral regions, new measures of asymmetry and related hypothesis test.
November 7, 2012
- Speaker: Nikolai Valtchev Kolev (Sao Paulo University)
- Title: Extended Marshall Olkin Model and Finance Applications
- Place: M301
- Time: 16:30-17:30
- Abstract:
  In the classical Marshall Olkin model it is assumed that the variables involved are independent and exponentıally distributed. We offer an extension relaxing independence assumption between variables which not necessarily are identical. Finance aplications will be discussed as well.
October 10, 2012
- Speaker: Nikolai Valtchev Kolev (Sao Paulo University)
- Title: T(q)-maximum Likelihood Estimation and Applications
- Place: M301
- Time: 16:30-17:30
- Abstract:
  An extension of the classical maximum likelihood estimation will be introduced by incorporating an additional parameter q (playing the role of distortion parameter). Relations to q-entropy and classical Box-Cox transformation will be discussed. The new methodology will be applied to extreme value analysis and will be shown its priority in comparison with classical methods.

Previous Seminars: