
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, Uğur Madran.
 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: 10:3011:30
 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 saddlenode (fold) bifurcation, transcritical bifurcation, pitchfork bifurcation, perioddoubling (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: 16:3017:30
 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
\[
t\pm P\in\mathbb{T}\text{ for all }t\in\mathbb{T}\text{,}%
\]
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: 16:3017:30
 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: 13:3014:20
 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: 13:3014:20
 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: 16:3017:30
 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: 16:3017:30
 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: 16:3017:30
 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
 October 10, 2012
Previous Seminars:
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