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BEGIN:VEVENT
SUMMARY:Ergün Yalçın (Bilkent University)
DTSTART;VALUE=DATE-TIME:20201009T100000Z
DTEND;VALUE=DATE-TIME:20201009T110000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/1
DESCRIPTION:Title: The Dade Group of a Finite Group and Dimension Functions\nby
Ergün Yalçın (Bilkent University) as part of Yeditepe Mathematics Semi
nars\n\n\nAbstract\nLet $G$ be a finite group and $k$ an algebraically clo
sed field of characteristic\n$p > 0$. We define the notion of a Dade $kG$-
module as a generalization of endopermutation modules for $p$-groups. We s
how that under a suitable equivalence relation\, the set of equivalence cl
asses of Dade $kG$-modules forms a group under tensor product\, and the gr
oup obtained this way is isomorphic to the Dade group $D(G)$ defined by La
ssueur $[2]$.\n\nWe also consider the subgroup $D^\\Omega (G)$ of $D(G)$
generated by relative syzygies\n$\\Omega X$\, where $X$ is a finite $G$-se
t. Let $C(G\; p)$ denote the group of superclass\nfunctions defined on the
p-subgroups of G. There are natural generators $\\omega_X$\nof $C(G\; p)$
. We prove that there is a well-defined group homomorphism $\\psi_G :\nC(G
\; p) \\to D^\\Omega (G)$ that sends $\\omega_X$ to $ \\Omega_X$.\n\nThe
main theorem is the verification that the subgroup of $C(G\; p)$ consistin
g\nof the dimension functions of $k$-orientable real representations of $G
$ lies in the\nkernel of $\\psi_G$. In the proof we consider Moore $G$-spa
ces which are the equivariant\nversions of spaces which have nonzero reduc
ed homology in only one dimension.\n\nThis talk is about a theorem in modu
lar representation theory whose proof is\ntopological using equivariant ho
motopy theory and homological algebra over\norbit category. I will give al
l necessary definitions to make it possible to follow\nthe talk and provid
e examples to motivate the theorems.\n\nThis is a joint work with Matthew
Gelvin $[1]$.\n\n$\\mathbf{References}$\n\n$[1]$ M. Gelvin and E. Yalçın
\, Dade Groups for Finite Groups and Dimension Functions\, preprint\, 2020
(arXiv:2007.05322v2).\n\n$[2]$ C. Lassueur\, The Dade group of a finite g
roup\, J. Pure Appl. Algebra\, 217 (2013)\,\n97-113.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aslı Güçlükan İlhan (Dokuz Eylül University)
DTSTART;VALUE=DATE-TIME:20201016T100000Z
DTEND;VALUE=DATE-TIME:20201016T110000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/2
DESCRIPTION:Title: $\\omega$-Weighted Digraphs and Local Complementations\nby A
slı Güçlükan İlhan (Dokuz Eylül University) as part of Yeditepe Math
ematics Seminars\n\n\nAbstract\nIn this talk\, we introduce $\\omega$-weig
hted digraphs for a given dimension function $\\omega$. We generalize the
notion of a local complementation to $\\omega$-weighted digraphs. Then we
establish a bijection between isomorphism classes of $\\omega$-weighted di
graphs up to local complementations and the isomorphism classes of weakly
$\\mathbb{Z}_2^n$-equivariant small covers over a product of simplices.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazım İlhan İkeda (Boğaziçi University)
DTSTART;VALUE=DATE-TIME:20201030T100000Z
DTEND;VALUE=DATE-TIME:20201030T110000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/3
DESCRIPTION:Title: On the Langlands reciprocity and functoriality principles\nb
y Kazım İlhan İkeda (Boğaziçi University) as part of Yeditepe Mathema
tics Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atabey Kaygun (İstanbul Technical University)
DTSTART;VALUE=DATE-TIME:20201106T140000Z
DTEND;VALUE=DATE-TIME:20201106T150000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/4
DESCRIPTION:Title: Generalized Weyl Algebras\, Birational Equivalences and Gelfand
Kirillov Conjecture\nby Atabey Kaygun (İstanbul Technical University)
as part of Yeditepe Mathematics Seminars\n\n\nAbstract\nRank $1$ generali
zed Weyl algebras (GWAs) form an interesting class of algebras that includ
e (quantum) enveloping algebra of $sl(2)$ and some interesting quantum gro
ups of rank $1$ and $2$. In this talk I will define GWAs and then explain
how these examples fit into the framework of GWAs. Birational equivalence\
, on the other hand\, is a tool (commutative) algebraic geometers use quit
e extensively. Interestingly\, GWAs are birationally equivalent to a smash
product with a torus of rank $1$. Time permitting\, I will talk about how
all of these relate to Gelfand-Kirillov conjecture.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özgün Ünlü (Bilkent University)
DTSTART;VALUE=DATE-TIME:20210108T100000Z
DTEND;VALUE=DATE-TIME:20210108T110000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/5
DESCRIPTION:Title: Free Group Actions on Products of Two Equidimensional Spheres\nby Özgün Ünlü (Bilkent University) as part of Yeditepe Mathematics
Seminars\n\n\nAbstract\nWe will first review some known restrictions on fi
nite groups\nthat can act freely on products of two equidimensional sphere
s. Then we\nwill discuss some constructions of free actions of finite p-g
roups on\nproducts of two equidimensional spheres. Finally\, we will discu
ss some\nopen problems about free p-group actions on two equidimensional s
pheres.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Turgut Önder (Middle East Techinal University)
DTSTART;VALUE=DATE-TIME:20201204T140000Z
DTEND;VALUE=DATE-TIME:20201204T150000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/6
DESCRIPTION:Title: Existence of Almost Complex Foliations on Spheres\nby Turgut
Önder (Middle East Techinal University) as part of Yeditepe Mathematics
Seminars\n\n\nAbstract\nIntuitively\, a foliation on a manifold correspond
s to a partition of the manifold into connected\, immersed submanifolds of
the same dimension\, called leaves which form locally layers of a Euclide
an space. An almost complex foliation is a foliation whose tangent bundle
admits a complex structure. The existence problem of foliations on closed
manifolds is reduced to the existence problem of plane fields in 1970’s
by W. Thurston which can be attacked by algebraic topological methods. How
ever\, not much has been written about the existence problem of almost com
plex foliations. On spheres\, İ. Dibağ’s results provide concrete nece
ssary conditions in terms of the dimension of the sphere and the dimension
of the foliation. In this talk\, after reviewing some basic notions about
the foliations\, we will present some results in the other direction\, i.
e. about the sufficient conditions for the existence of almost complex fol
iations on spheres.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özgür Kişisel (Middle East Techinal University)
DTSTART;VALUE=DATE-TIME:20201211T140000Z
DTEND;VALUE=DATE-TIME:20201211T150000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/7
DESCRIPTION:Title: On complex 4-nets\nby Özgür Kişisel (Middle East Techinal
University) as part of Yeditepe Mathematics Seminars\n\n\nAbstract\nNets
are certain special line arrangements in the plane and they occur in vario
us contexts related to algebraic geometry\, such as resonance varieties\,
homology of Milnor fibers and fundamental groups of curve complements. We
will investigate nets in the complex projective plane $\\mathbb{CP}^2$. Le
t $m\\geq 3$ and $d\\geq 2$ be integers. An $(m\,d)$-net is a pencil of de
gree $d$ algebraic curves in $\\mathbb{CP}^2$ with a base locus of exactly
$d^2$ points\, which degenerates into a union of $d$ lines $m$ times. It
was conjectured that the only $4$-net is a $(4\,3)$-net called the Hessian
arrangement. I will outline our proof together with A. Bassa of this conj
ecture.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatih Erman (İzmir İnstitute of Technology)
DTSTART;VALUE=DATE-TIME:20201218T100000Z
DTEND;VALUE=DATE-TIME:20201218T110000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/8
DESCRIPTION:Title: On the Existence of a Self-Adjoint Hamiltonian for a Singular In
teraction on Manifolds\nby Fatih Erman (İzmir İnstitute of Technolog
y) as part of Yeditepe Mathematics Seminars\n\n\nAbstract\nAccording to th
e postulates of Quantum Mechanics\, the dynamics of quantum systems are ge
nerated by a self-adjoint operator\, namely Hamiltonian operator associate
d with the energy of the system. Dirac delta potentials are known as one c
lass of singular interactions\, which have many applications in various ar
eas of physics. There are different mathematically rigorous approaches for
the description of such systems by some self-adjoint Hamiltonian operator
in $L^2(\\mathbb{R}^n)$. In this talk\, I would like to introduce the sub
ject in a rather elementary way and briefly discuss such interactions in o
ne dimension heuristically and from the Von Neumann's self-adjoint extensi
on point of view. Then\, I shall extend the same model onto the two and th
ree dimensional Cartan-Hadamard manifolds with Ricci curvature bounded bel
ow by describing the system in terms of "limit" of resolvent of the regula
rized version of the initial singular Hamiltonian. This will be accomplish
ed by the heat kernel defined on manifolds and its Li-Yau type of estimate
s.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noyan Er (Dokuz Eylül University)
DTSTART;VALUE=DATE-TIME:20201225T100000Z
DTEND;VALUE=DATE-TIME:20201225T110000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/9
DESCRIPTION:Title: Pure Things\nby Noyan Er (Dokuz Eylül University) as part o
f Yeditepe Mathematics Seminars\n\n\nAbstract\nThis will be a down-to-eart
h that talk aims to spark interest\, especially among young researchers\,
in a notion at the crossroads of several fields of algebra\, including rep
resentation theory of algebras\, abelian group theory and ring theory\, na
mely purity. However\, whatever the path it may have followed historically
\, we will derive our motivation from a subject accessible to pretty much
every one with a basic understanding of linear algebra: systems of linear
equations.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Serdar Ay (Bilkent University)
DTSTART;VALUE=DATE-TIME:20200508T100000Z
DTEND;VALUE=DATE-TIME:20200508T110000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/12
DESCRIPTION:Title: Dilations of positive semidefinite kernels valued in operators
of barrelled VH-spaces\nby Serdar Ay (Bilkent University) as part of Y
editepe Mathematics Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Akif Erdal (Yeditepe University)
DTSTART;VALUE=DATE-TIME:20200306T100000Z
DTEND;VALUE=DATE-TIME:20200306T110000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/13
DESCRIPTION:Title: Brown Fibration Categories and Enrichments in Monoidal Model Ca
tegories\nby Mehmet Akif Erdal (Yeditepe University) as part of Yedite
pe Mathematics Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuna Bayraktar (Yeditepe University)
DTSTART;VALUE=DATE-TIME:20200417T100000Z
DTEND;VALUE=DATE-TIME:20200417T110000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/14
DESCRIPTION:Title: Minimal surfaces and smooth autonomous dynamical systems in 2D<
/a>\nby Tuna Bayraktar (Yeditepe University) as part of Yeditepe Mathemati
cs Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent University)
DTSTART;VALUE=DATE-TIME:20210507T100000Z
DTEND;VALUE=DATE-TIME:20210507T110000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/16
DESCRIPTION:Title: Counting lines\, curves\, planes… in algebraic varieties\
nby Alexander Degtyarev (Bilkent University) as part of Yeditepe Mathemati
cs Seminars\n\n\nAbstract\nI will start from several classical but very si
mple\, almost high school level\, examples of algebraic varieties containi
ng many lines\, planes\, etc. These varieties are very special\, as a typi
cal one from the same family would have no lines at all. This brings up a
natural problem of finding the *maximal* possible number of lines\, planes
\, etc. that can be contained in a member of a fixed family (say\, hypersu
rfaces of a given dimension and degree). In general\, this problem is wide
open\, but I will describe an approach that lets one attack it for a wide
variety of seemingly unrelated families. Finally\, if time permits\, I wi
ll cite a few recent results.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selçuk Demir (Dokuz Eylül University)
DTSTART;VALUE=DATE-TIME:20210521T130000Z
DTEND;VALUE=DATE-TIME:20210521T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/17
DESCRIPTION:Title: On Some Entropy Inequalities\nby Selçuk Demir (Dokuz Eylü
l University) as part of Yeditepe Mathematics Seminars\n\n\nAbstract\nI pl
an to give a survey of an approach of Besenyei and Petz to some entropy in
equalities related to the so-called strong subadditivity. I will discuss a
related conjecture and give a\nreport on its current status. Most of the
talk will be an introduction to this area for mathematicians and will hope
fully be accessible to graduate students of mathematics.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semra Pamuk (Middle East Technical University)
DTSTART;VALUE=DATE-TIME:20210312T130000Z
DTEND;VALUE=DATE-TIME:20210312T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/18
DESCRIPTION:Title: Rank conditions for finite group actions on $4$-manifolds\n
by Semra Pamuk (Middle East Technical University) as part of Yeditepe Math
ematics Seminars\n\n\nAbstract\nIn this talk\, I will give some old and ne
w information about the existence of finite group actions on closed\, conn
ected\, orientable $4$-manifolds. In this dimension\, the comparison betwe
en smooth and topological group actions are interesting but our focus will
be on locally linear topological actions. In particular\, we will talk ab
out the following question: Given a closed orientable $4$-manifold $M$\, w
hat is the maximum value of $\\mathrm{rk}(G)$ over all the finite groups $
G$ which act effectively\, locally linearly\, and homologically trivially
on $M$? This is a joint work with Ian Hambleton.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatma Altunbulak Aksu (Mimar Sinan Fine Arts University)
DTSTART;VALUE=DATE-TIME:20210604T130000Z
DTEND;VALUE=DATE-TIME:20210604T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/19
DESCRIPTION:Title: Group codes: an application of group algebras to coding theory<
/a>\nby Fatma Altunbulak Aksu (Mimar Sinan Fine Arts University) as part o
f Yeditepe Mathematics Seminars\n\n\nAbstract\nBerman and MacWilliams inde
pendently define group codes as ideals in finite group algebras. Many line
ar codes can be viewed as group codes. For example\, cyclic codes can be c
onsidered as ideals in finite group algebras of cyclic groups and Reed Mul
ler codes over $\\mathbb{F}_p$ can be viewed as ideals in modular group al
gebra of an elementary abelian $p$-group. Group codes have richer algebra
ic structures than linear codes\, for that reason\, considering codes as g
roup codes have many advantages. Algebraic tools in ring theory and charac
ter theory can be used to understand codes via group codes. In this talk I
will give a gentle introduction for group codes and state some problems
and results in the literature. If time permits\, I will state some recent
contributions which are joint work with İpek Tuvay.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Engin Büyükaşık (İzmir Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210528T130000Z
DTEND;VALUE=DATE-TIME:20210528T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/20
DESCRIPTION:Title: Dual Baer Criterion and R-projectivity of injective modules
\nby Engin Büyükaşık (İzmir Institute of Technology) as part of Yedit
epe Mathematics Seminars\n\n\nAbstract\nLet $R$ be a ring with unity and M
od-$R$ be the category of right $R$-modules. The Baer's Criterion for inje
ctivity states that a right module $M$ is injective iff it is $R$-injectiv
e\, that is for each right ideal $I$ of $R$\, any homomorphism from $I$ i
nto $M$ extends to $R$. Dually\, a right module $P$ is $R$-projective if f
or each right ideal $I$ of $R$ any homomorphism from $M$ into $R/I$ lifts
to $R$. Unlike the case for injectivity\, $R$-projective modules need not
be projective. That is\, the Dual Baer Criterion (DBC\, for short) does n
ot hold over every ring. The rings $R$ for which the DBC holds in Mod-$R$
are called right testing. From [4]\, it is known that right perfect rings
are right testing. In [3]\, Faith stated the characterization of all ri
ght testing rings as an open problem. Recently in [6]\, Trlifaj proved tha
t the problem of characterizing right testing rings is undecidable in ZFC.
\n\nIn this talk\, after summarizing the aforementioned results\, I will m
ention an extend of the notion of $R$-projectivity\, and discuss some pro
blems related to the rings whose injective right modules are $R$-projectiv
e which are partially solved in [1].\n\nReferences\n\n[1] Y. Alagöz and E
. Büyükaşık\, Max-projective modules\, J. Algebra Appl. 20 (2021)\, no
. 6. 2150095.\n\n[2] H. Alhilali\, Y. Ibrahim\, G. Puninski\, and M. Yousi
f\, When R is a testing module for projectivity? J. Algebra 484 (2017)\, 1
98-206.\n\n[3] C. Faith\, Algebra. II\, Springer-Verlag\, Berlin-New York\
, 1976. Ring theory\, Grundlehren der Mathematischen Wissenschaften\, No.
191.\n[4] F .L. Sandomierski\, Relative injectivity and projectivity\, 196
4. Thesis (Ph.D.) The Pennsylvania\nState University.\n\n[5] J. Trlifaj\,
Whitehead test modules\, Trans. Amer. Math. Soc. 348 (1996)\, no. 4\, 1521
-1554.\n\n[6] J. Trlifaj\, Faith’s problem on R-projectivity is undecida
ble\, Proc. Amer. Math. Soc. 147 (2019)\,\nno. 2\, 497-504.\n\n[7] J. Trli
faj\, The dual Baer Criterion for non-perfect rings\, Forum Math. 32 (2020
)\, no. 3\, 663-672.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alp Bassa (Boğaziçi University)
DTSTART;VALUE=DATE-TIME:20210409T130000Z
DTEND;VALUE=DATE-TIME:20210409T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/21
DESCRIPTION:Title: Rational points on curves over finite fields and their asymptot
ic\nby Alp Bassa (Boğaziçi University) as part of Yeditepe Mathemati
cs Seminars\n\n\nAbstract\nCurves over finite fields with many rational po
ints have been of interest for both theoretical reasons and for applicatio
ns. To obtain such curves with large genus various methods have been emplo
yed in the past. One such method is by means of explicit recursive equatio
ns and will be the emphasis of this talk. The recursive nature of these to
wers makes them very special and in fact all good examples have been shown
to have a modular interpretation of some sort. In this talk I will try to
give an overview of the landscape of explicit recursive towers and their
modularity.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Müge Kanuni Er (Düzce University)
DTSTART;VALUE=DATE-TIME:20210416T100000Z
DTEND;VALUE=DATE-TIME:20210416T110000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/22
DESCRIPTION:Title: Socle of Incidence Rings\nby Müge Kanuni Er (Düzce Univer
sity) as part of Yeditepe Mathematics Seminars\n\n\nAbstract\nIn his semin
al paper of 1964\, "On the foundations of combinatorial theory I: Theory o
f Möbius Functions" Gian-Carlo Rota defined an incidence ring as a tool f
or solving combinatorial problems. Incidence ring is a specific ring of fu
nctions defined on the ordered pairs of a given partially ordered set to a
given ring. Möbius function is an element of an incidence ring\, besides
with the appropriate choice of the partially ordered set\, Möbius functi
on of this incidence algebra coincides with the well-known Möbius functio
n of number theory. A product of copies of a ring and upper triangular mat
rices are typical examples of incidence algebras. \n\nThe investigation of
a ring is usually enriched by understanding specialtypes of ideals of it\
, such as the Jacobson radical\, the prime radical\, the socle\,the singul
ar ideal\, the center\, etc. Although incidence rings have been an object
of study for a few decades\, there does not seem to be any results in the
literature on the socle of incidence rings.\n\nIn this talk\, we will be r
estricting the left socle of an incidence ring between two sets.More expli
citly\, we compute the socle of an incidence ring I(X\,R) under some assu
mptions on the ring R and/or the partially ordered set X. \n\n(This joint
work with Özkay Özkan- https://doi.org/10.15672/hujms.684042 )\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Matschke (Boston University)
DTSTART;VALUE=DATE-TIME:20210319T150000Z
DTEND;VALUE=DATE-TIME:20210319T160000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/23
DESCRIPTION:Title: Proofs by example\nby Benjamin Matschke (Boston University)
as part of Yeditepe Mathematics Seminars\n\n\nAbstract\nWe study the proo
f method "proof by example" in which a general statement can be proved by
verifying it for a single example. This strategy can indeed work if the st
atement in question is an algebraic identity and the example is "generic".
This talk addresses the problem of constructing a practical example\, whi
ch is sufficiently generic\, for which the statement can be verified effic
iently\, and which allows for a numerical margin of error.\n\nOur method i
s based on diophantine geometry\, in particular an arithmetic Bezout theor
em\, an arithmetic Nullstellensatz\, and a new effective Liouville-Lojasie
wicz type inequality for algebraic varieties. As an application we discuss
theorems from plane geometry and how to\nprove them by example.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oğuz Şavk (Boğaziçi University)
DTSTART;VALUE=DATE-TIME:20210305T130000Z
DTEND;VALUE=DATE-TIME:20210305T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/24
DESCRIPTION:Title: Classical and New Plumbings Bounding Contractible Manifolds and
Homology Balls\nby Oğuz Şavk (Boğaziçi University) as part of Yed
itepe Mathematics Seminars\n\n\nAbstract\nA central problem in low-dimensi
onal topology asks which\nhomology 3-spheres bound contractible 4-manifold
s and homology 4-balls.\nIn this talk\, we address this problem for plumbe
d 3-manifolds and we\npresent the classical and new results together. Our
approach is based on\nMazur’s famous argument which provides a unificati
on of all results in a\nfairly simple way.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Berrin Şentürk (TED University)
DTSTART;VALUE=DATE-TIME:20210430T130000Z
DTEND;VALUE=DATE-TIME:20210430T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/25
DESCRIPTION:Title: Free Group Actions on Product of 3 Spheres\nby Berrin Şent
ürk (TED University) as part of Yeditepe Mathematics Seminars\n\n\nAbstra
ct\nA long-standing Rank Conjecture states that if an elementary abelian $
p$-group acts freely on a product of spheres\, then the rank of the group
is at most the number of spheres in the product. We will discuss the algeb
raic version of the Rank Conjecture given by Carlsson for a differential g
raded module $M$ over a polynomial ring. We will state a stronger conjectu
re concerning varieties of square-zero upper triangular matrices correspon
ding to the differentials of certain modules. By the work on free flags in
$M$ introduced by Avramov\, Buchweitz\, and Iyengar\, we will obtain some
restriction on the rank of submodules of these matrices. By this argument
we will show that $(\\mathbb{Z}/2\\mathbb{Z})^4$ cannot act freely on pro
duct of $3$ spheres of any dimensions.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uğur Yiğit (İstanbul Medeniyet University)
DTSTART;VALUE=DATE-TIME:20210402T130000Z
DTEND;VALUE=DATE-TIME:20210402T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/26
DESCRIPTION:Title: $C_2$-Equivariant EHP Sequences\nby Uğur Yiğit (İstanbul
Medeniyet University) as part of Yeditepe Mathematics Seminars\n\n\nAbstr
act\nTo determine the homotopy groups $\\pi_n(S^k)$ of spheres is a centra
l problem in homotopy\ntheory. One of the main tools for calculations in t
he classical unstable homotopy theory is\nthe EHP sequence. In this talk\,
we give the generalizations of the EHP sequence in the classical homotopy
theory to the $C_2$-equivariant case.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayhan Günaydin (Boğaziçi University)
DTSTART;VALUE=DATE-TIME:20210611T130000Z
DTEND;VALUE=DATE-TIME:20210611T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/27
DESCRIPTION:Title: Model Theory of Beatty Sequences\nby Ayhan Günaydin (Boğa
ziçi University) as part of Yeditepe Mathematics Seminars\n\n\nAbstract\n
The Beatty Sequence generated by an irrational r>1 is ([nr] : n>0)\, where
[c] denotes the integer part of a real number c. A well-known property of
this sequence is that "any pattern that appears once has to appear infini
tely many times\; moreover we may determine when a pattern appears next ti
me with a small error". After explaining what this means\, we will present
the proof of a strengthening of it. Our proof depends on the model theore
tic study of the sequence and all the necessary background will be overvie
wed. (This is a joint work with Melissa Özsahakyan.)\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuf Ünlü (Yeditepe University)
DTSTART;VALUE=DATE-TIME:20211001T130000Z
DTEND;VALUE=DATE-TIME:20211001T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/28
DESCRIPTION:Title: The impossibility of the angle trisection by straightedge and c
ompass revisited\nby Yusuf Ünlü (Yeditepe University) as part of Yed
itepe Mathematics Seminars\n\n\nAbstract\nIt is well known that the angle
trisection or doubling the cube is impossible by using only ruler and comp
ass. The usual algebraic proof uses the fact that if a real number $\\xi$
is constructible using only ruler and compass then there is a tower of fie
lds\n$$\\mathbb Q= F_0 \\subset F_1 \\subset \\cdots \\subset F_n$$\nsu
ch that if $n \\geq 1$\, then $F_i = F_{i-1}(u_i)$ where $u_i\\notin F_{i-
1}$ but $u_i^2\\in F_{i-1}$ and $\\xi \\in F_n$. Hence $2^m = [F_n : \\ma
thbb Q]$ for some $m \\in \\mathbb N$. This shows that $$2^m = [F_n : \\ma
thbb Q]= [F_n : \\mathbb Q(\\xi)][\\mathbb Q(\\xi) : \\mathbb Q]$$ \nSo\,
if the minimal polynomial of $\\xi$ in $\\mathbb Q(x)$ is of odd degree\,
then $\\xi$ is\nnot constructible by only ruler and compass. Moreover\, t
he minimal\npolynomial of $\\cos 20^\\circ$ has degree $3$. So it is impos
sible to trisect $60^\\circ$ by\nusing only ruler and compass.\n\nHowever\
, this proof requires the fundamentals of vector spaces. In this talk\, we
wíll tweak the last part of the proof to avoid vector spaces.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cihan Okay (Bilkent University)
DTSTART;VALUE=DATE-TIME:20211105T130000Z
DTEND;VALUE=DATE-TIME:20211105T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/29
DESCRIPTION:Title: Homotopy classification of operator solutions of linear systems
\nby Cihan Okay (Bilkent University) as part of Yeditepe Mathematics S
eminars\n\n\nAbstract\nLinear systems of equations over a finite field pla
y an important role in quantum information theory. Instead of looking for
solutions over the base field one can look for solutions (in a certain sen
se) over the unitary group\, which are called operator solutions. The data
of this system of equations can be expressed using a hypergraph and the o
perator solutions can be studied from a topological point of view by consi
dering certain topological realizations of these hypergraphs. In this talk
I will describe how homotopical methods provide a way to classify operato
r solutions of linear systems. Our basic approach is to interpret operator
solutions as maps from a topological realization of the hypergraph to a c
ertain classifying space first introduced by Adem-Cohen-Torres Giese.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oktay Pashaev (İzmir Institute of Technology)
DTSTART;VALUE=DATE-TIME:20211008T130000Z
DTEND;VALUE=DATE-TIME:20211008T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/30
DESCRIPTION:Title: Quantum Calculus of Fibonacci Divisors applied to Classical Met
hod of Images and Quantum Computational States\nby Oktay Pashaev (İz
mir Institute of Technology) as part of Yeditepe Mathematics Seminars\n\n\
nAbstract\nStarting from divisibility problem for Fibonacci numbers\, we i
ntroduce integer Fibonacci divisors\, conjugate to $F_k$\, related hierarc
hy of Golden derivatives in powers of the Golden Ratio and develop corresp
onding quantum calculus. By the set of translation operators\, we find the
hierarchy of Golden binomials and related Golden analytic functions. In t
he limit $k \\to 0\,$ these functions reduce to classical holomorphic func
tions and quantum calculus of Fibonacci divisors to the usual one. The hie
rarchy of Golden periodic functions appearing in this calculus\, we relate
with classical method of images in planar hydrodynamics (electrostatics).
Several applications of the calculus to quantum deformed algebras and qua
ntum computation and information theory are discussed. In particular\, we
show that for repeated consecutive duplicated qubit states\, probabilities
are determined by Fibonacci numbers. We generalize these results for dire
ct product of multiple qubit states and arbitrary position of repeated sta
tes. The calculations are based on structure of Fibonacci trees in space o
f qubit states\, growing in the left and in the right directions\, number
of branches and allowed paths on the trees.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sefa Feza Arslan (Mimar Sinan Fine Arts University)
DTSTART;VALUE=DATE-TIME:20211210T130000Z
DTEND;VALUE=DATE-TIME:20211210T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/32
DESCRIPTION:by Sefa Feza Arslan (Mimar Sinan Fine Arts University) as part
of Yeditepe Mathematics Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Postponed
DTSTART;VALUE=DATE-TIME:20211112T150000Z
DTEND;VALUE=DATE-TIME:20211112T160000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/33
DESCRIPTION:by Postponed as part of Yeditepe Mathematics Seminars\n\nAbstr
act: TBA\n\nThis talk has been postponed\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gülin Ercan (Middle East Technical University)
DTSTART;VALUE=DATE-TIME:20211217T130000Z
DTEND;VALUE=DATE-TIME:20211217T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/34
DESCRIPTION:by Gülin Ercan (Middle East Technical University) as part of
Yeditepe Mathematics Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sibel Şahin (Mimar Sinan Fine Arts University)
DTSTART;VALUE=DATE-TIME:20211015T130000Z
DTEND;VALUE=DATE-TIME:20211015T140000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/35
DESCRIPTION:Title: de Branges-Rovnyak spaces $H(b)$ from unit disc to unit ball of
$\\mathbb C^n$\nby Sibel Şahin (Mimar Sinan Fine Arts University) as
part of Yeditepe Mathematics Seminars\n\n\nAbstract\nIn this talk we will
consider a special subclass of the Hardy-Hilbert space $H^2$ namely de Br
anges-Rovnyak spaces $H(b)$\, first with an introduction of model spaces i
n the unit disc and then in the setting of the unit ball of $\\mathbb C^n$
. One of the main problems in the study of $H(b)$ functions is their integ
ral representation and in this talk we will see how we can represent these
classes through the Clark measure on $S^n$ associated with $b$. In the se
cond part we will give a characterization of admissible boundary limits in
relation with finite angular derivatives and we will see the interplay be
tween Clark measures and angular derivatives showing that Clark measure as
sociated with $b$ has an atom at a boundary point if and only if $b$ has f
inite angular derivative at the same point. More detailed analysis of the
concepts mentioned in this talk can be found in the following study.\n\n\
n[1] Şahin\, S.\, Angular Derivatives and Boundary Values of $H(b)$ Space
s of Unit Ball of $\\mathbb C^n$\, Complex Variables and Elliptic Equation
s\, Volume 66\, Issue 2\, pp:226-237\, (2021).\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadia Romero (Universidad de Guanajuato)
DTSTART;VALUE=DATE-TIME:20211119T150000Z
DTEND;VALUE=DATE-TIME:20211119T160000Z
DTSTAMP;VALUE=DATE-TIME:20211128T092012Z
UID:7tepemathseminars/36
DESCRIPTION:Title: Operations on the Frobenius-Wielandt morphism\nby Nadia Rom
ero (Universidad de Guanajuato) as part of Yeditepe Mathematics Seminars\n
\n\nAbstract\nIn 1992\, Dress\, Siebeneicher and Yoshida introduced the Fr
obenius-Wielandt morphism (FW morphism)\, defined from the Burnside ring o
f a cyclic group C to the Burnside ring of a finite group G of order |C|.
A remark in their article indicates that their intention was "to give a pr
ecise conceptual interpretation of the observation that many elementary gr
oup-theoretic results can be derived from the fact that various invariants
of an arbitrary group are closely related to the same invariant evaluated
for the cyclic group C". Among other properties\, they investigated the r
elation of the FW morphism with the operations of restriction\, induction\
, inflation and fixed points. In this talk we will see what can be said ab
out the relation of the FW morphism with other operations related to the B
urnside ring\, especifically: tensor induction and deflation.\n
LOCATION:https://researchseminars.org/talk/7tepemathseminars/36/
END:VEVENT
END:VCALENDAR