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BEGIN:VEVENT
SUMMARY:Florian Eisele (University of Manchester)
DTSTART;VALUE=DATE-TIME:20220117T140000Z
DTEND;VALUE=DATE-TIME:20220117T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/1
DESCRIPTION:Title: Bij
ections of silting complexes and derived Picard groups\nby Florian Eis
ele (University of Manchester) as part of Greek Algebra & Number Theory Se
minar\n\n\nAbstract\nI will start with an introduction to derived categori
es and derived equivalences of finite-dimensional algebras\, and the notio
n of silting complexes. I will then talk about results on two large classe
s of finite-dimensional algebras\, namely Brauer graph algebras and the we
ighted surface algebras introduced by Erdmann and Skowronski\, which show
that these algebras have multiplicity-independent sets of silting complexe
s. The key ingredient for this is the existence of lifts of these algebras
to orders over formal power series rings\, which are remarkably similar t
o orders over p-adic rings encountered in the modular representation theor
y of finite groups.\n
LOCATION:https://researchseminars.org/talk/GANT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Céline Maistret (University of Bristol)
DTSTART;VALUE=DATE-TIME:20220124T140000Z
DTEND;VALUE=DATE-TIME:20220124T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/2
DESCRIPTION:Title: Par
ity of ranks of abelian surfaces\nby Céline Maistret (University of B
ristol) as part of Greek Algebra & Number Theory Seminar\n\n\nAbstract\nLe
t $K$ be a number field and $A/K$ an abelian surface. By the Mordell-Weil
theorem\, the group of $K$-rational points on $A$ is finitely generated an
d as for elliptic curves\, its rank is predicted by the Birch and Swinnert
on-Dyer conjecture. A basic consequence of this conjecture is the parity c
onjecture: the sign of the functional equation of the L-series determines
the parity of the rank of $A/K$. \n\nAssuming finiteness of the Shafarevic
h-Tate group\, we prove the parity conjecture for principally polarized ab
elian surfaces under suitable local constraints. Using a similar approach
we show that for two elliptic curves $E_1$ and $E_2$ over $K$ with isomor
phic $2$-torsion\, the parity conjecture is true for $E_1$ if and only if
it is true for $E_2$. In both cases\, we prove analogous unconditional res
ults for Selmer groups.\n
LOCATION:https://researchseminars.org/talk/GANT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioannis Emmanouil (National and Kapodistrian University of Athens)
DTSTART;VALUE=DATE-TIME:20220207T140000Z
DTEND;VALUE=DATE-TIME:20220207T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/3
DESCRIPTION:Title: Hom
ological and homotopical properties of unbounded complexes\nby Ioannis
Emmanouil (National and Kapodistrian University of Athens) as part of Gre
ek Algebra & Number Theory Seminar\n\n\nAbstract\nBousfield localizing pai
rs in the homotopy category of a ring are non-linear analogues of cotorsio
n pairs in the module category. We shall present several examples of Bousf
ield localizing pairs that are related to acyclicity\, flatness and purity
.\n
LOCATION:https://researchseminars.org/talk/GANT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angelos Koutsianas (Aristotle University of Thessaloniki)
DTSTART;VALUE=DATE-TIME:20220221T140000Z
DTEND;VALUE=DATE-TIME:20220221T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/4
DESCRIPTION:Title: Sol
ving generalized Fermat equations with Frey hyperelliptic curves\nby A
ngelos Koutsianas (Aristotle University of Thessaloniki) as part of Greek
Algebra & Number Theory Seminar\n\n\nAbstract\nIn this talk\, I will talk
about Darmon's program and the resolution of the generalized Fermat equat
ion of signature $(p\,p\,5)$ using Frey hyperelliptic curves. This is join
t work with Imin Chen (Simon Fraser University).\n
LOCATION:https://researchseminars.org/talk/GANT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Tziolas (University of Cyprus)
DTSTART;VALUE=DATE-TIME:20220314T140000Z
DTEND;VALUE=DATE-TIME:20220314T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/5
DESCRIPTION:Title: The
role of automorphisms in the classification of surfaces of general type i
n characteristic $p>0$.\nby Nikolaos Tziolas (University of Cyprus) as
part of Greek Algebra & Number Theory Seminar\n\n\nAbstract\nThe classifi
cation of varieties of general type is one of the fundamental problems of
algebraic geometry. In characteristic zero it is known that varieties of g
eneral type with fixed volume have a coarse moduli space of finite type ov
er the base field and the corresponding moduli stack is Deligne-Mumford. I
n positive characteristic the first property is at the moment unknown if i
t holds in dimensions at least $3$ and the second fails in general in dime
nsion at least $2$.\n\nIn this talk I will explain how the failure of the
second property is related to the existence of varieties of general type
with non reduced automorphism scheme. I will present explicit examples of
such surfaces and present results regarding their geometry and the structu
re of their automorphism scheme.\n
LOCATION:https://researchseminars.org/talk/GANT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicole Raulf (University of Lille)
DTSTART;VALUE=DATE-TIME:20220321T140000Z
DTEND;VALUE=DATE-TIME:20220321T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/6
DESCRIPTION:Title: Asy
mptotics of class numbers\nby Nicole Raulf (University of Lille) as pa
rt of Greek Algebra & Number Theory Seminar\n\n\nAbstract\nIn this talk we
present results on the asymptotic behaviour of class numbers in the situa
tion that the class numbers are ordered by the size of the regulator. We a
lso will discuss the methods that can be used to obtain these results.\n
LOCATION:https://researchseminars.org/talk/GANT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasiliki Petrotou (University of Ioannina)
DTSTART;VALUE=DATE-TIME:20220404T130000Z
DTEND;VALUE=DATE-TIME:20220404T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/7
DESCRIPTION:Title: Tom
& Jerry Unprojection triples\nby Vasiliki Petrotou (University of Ioa
nnina) as part of Greek Algebra & Number Theory Seminar\n\n\nAbstract\nUnp
rojection is a theory in Commutative Algebra due to Miles \nReid which con
structs and analyses more complicated rings from simpler \nones.\n\nThe ta
lk will be about a new format of unprojection which we call Tom \n& Jerry
triples. The motivation is to construct codimension $6$ Gorenstein\nrings
starting from codimension $3$. As an application we will construct \ntwo f
amilies of codimension $6$ Fano $3$-folds in weighted projective space.\n
LOCATION:https://researchseminars.org/talk/GANT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Masdeu (Universitat Autònoma de Barcelona)
DTSTART;VALUE=DATE-TIME:20220418T130000Z
DTEND;VALUE=DATE-TIME:20220418T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/8
DESCRIPTION:Title: Num
erical experiments with plectic Darmon points\nby Marc Masdeu (Univers
itat Autònoma de Barcelona) as part of Greek Algebra & Number Theory Semi
nar\n\n\nAbstract\nLet $E/F$ be an elliptic curve defined over a number fi
eld $F$\, and let $K/F$ be a quadratic extension. If the analytic rank of
$E(K)$ is one\, one can often use Heegner points (or the more general Darm
on points) to produce (at least conjecturally) a nontorsion generator of $
E(K)$. If the analytic rank of $E(K)$ is larger than one\, the problem of
constructing algebraic points is still very open. In recent work\, Michele
Fornea and Lennart Gehrmann have introduced certain $p$-adic quantities t
hat may be conjecturally related to the existence of these points. In this
talk I will explain their construction\, and illustrate with some numeric
al experiments some support for their conjecture. This is joint work with
Michele Fornea and Xevi Guitart.\n
LOCATION:https://researchseminars.org/talk/GANT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sofia Lambropoulou (National Technical University of Athens)
DTSTART;VALUE=DATE-TIME:20220502T130000Z
DTEND;VALUE=DATE-TIME:20220502T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/9
DESCRIPTION:Title: Bra
idings\, braid equivalences and Jones-type invariants\nby Sofia Lambro
poulou (National Technical University of Athens) as part of Greek Algebra
& Number Theory Seminar\n\n\nAbstract\nWe will present algorithms for turn
ing knots and links into braids in various diagrammatic settings. Then we
will explain the construction of Jones-type knot and link invariants via M
arkov traces onappropriate quotient algebras of braid groups\n
LOCATION:https://researchseminars.org/talk/GANT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Morten Risager (University of Copenhagen)
DTSTART;VALUE=DATE-TIME:20220516T130000Z
DTEND;VALUE=DATE-TIME:20220516T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/10
DESCRIPTION:Title: Di
stributions of twists of multiple L-series of modular forms.\nby Morte
n Risager (University of Copenhagen) as part of Greek Algebra & Number The
ory Seminar\n\n\nAbstract\nStarting with a historical introduction involvi
ng Menogoli\, Goldbach\, Euler and Zagier we introduce certain additive tw
ists of multiple L-series. These turn out to be expressible through Manin
’s iterated integrals. We then go on to describe our recent work on the
distribution of the central values of these additive twists.\n
LOCATION:https://researchseminars.org/talk/GANT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Frot (Alfréd Rényi Institute of Mathematics)
DTSTART;VALUE=DATE-TIME:20220606T130000Z
DTEND;VALUE=DATE-TIME:20220606T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/11
DESCRIPTION:Title: Ex
plicit bounds for prime gaps and graphic sequence\nby Robin Frot (Alfr
éd Rényi Institute of Mathematics) as part of Greek Algebra & Number The
ory Seminar\n\n\nAbstract\nA prime gap graph is defined to be a graph on $
n$ vertices with respective degrees $1$ and the $n-1$ first prime gaps. I
n a recent paper of P. Erdős\, G. Harcos\, S. Kharel\, P. Maga\, T. Mezei
\, Z. Toroczkai\, they proved that under RH\, prime gap graphs exist for e
very $n$. Also they exist unconditionally for $n$ large enough. Moreover\,
it is possible to give an iterative construction of these graphs. \n\nThe
ideas in this result lie between elementary number theory\, graph theory
and combinatorics. In this talk\, I will explain how to obtain this result
in its unconditional form\, while trying to find explicitly how large $n$
should be to get a graphic sequence.\n\nThis talk is based on the aforeme
ntioned paper\, and a joint work with Keshav Aggarwal.\n
LOCATION:https://researchseminars.org/talk/GANT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Cruz (Universität Stuttgart)
DTSTART;VALUE=DATE-TIME:20220523T130000Z
DTEND;VALUE=DATE-TIME:20220523T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/12
DESCRIPTION:Title: Ri
ngel self-duality via relative dominant dimension\nby Tiago Cruz (Univ
ersität Stuttgart) as part of Greek Algebra & Number Theory Seminar\n\n\n
Abstract\nQuasi-hereditary algebras provide an abstract framework for the
homological structure of Schur algebras and the BGG category $O$ of a semi
-simple Lie algebra and they always appear in pairs via Ringel duality.\n\
nIn this talk\, we discuss a generalisation of dominant dimension using re
lative homological algebra. This homological invariant is compatible with
the tools from integral representation theory and it increases our underst
anding of classical dominant dimension.\n\nIn particular\, this homologica
l invariant provides tools to deduce that quasi-hereditary covers formed b
y quasi-hereditary algebras with a simple preserving duality with large en
ough dominant dimension also appear in pairs. As an application\, we give
a new proof of Ringel self-duality of the blocks of the BGG category $O$ o
f a complex semi-simple Lie algebra.\n
LOCATION:https://researchseminars.org/talk/GANT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stevan Gajovic (Max Planck Institute for Mathematics\, Bonn)
DTSTART;VALUE=DATE-TIME:20221003T130000Z
DTEND;VALUE=DATE-TIME:20221003T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/13
DESCRIPTION:Title: Qu
adratic Chabauty for integral points and p-adic heights on even degree hyp
erelliptic curves\nby Stevan Gajovic (Max Planck Institute for Mathema
tics\, Bonn) as part of Greek Algebra & Number Theory Seminar\n\n\nAbstrac
t\nThe method of Chabauty and Coleman is a powerful method to determine ra
tional points on curves whose Jacobian has the Mordell-Weil rank over $\\m
athbb{Q}$ (denoted by $r$) less than its genus (denoted by $g$). In this t
alk\, we show how to construct a locally analytic function\, using $p$-adi
c (Coleman-Gross) heights\, that we use to compute integral points on cert
ain even degree hyperelliptic curves when $r=g$. This is joint work with S
teffen Müller.\n
LOCATION:https://researchseminars.org/talk/GANT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Chlouveraki (National and Kapodistrian University of Athens)
DTSTART;VALUE=DATE-TIME:20221017T130000Z
DTEND;VALUE=DATE-TIME:20221017T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/14
DESCRIPTION:Title: Th
e defect of blocks in Hecke algebras\nby Maria Chlouveraki (National a
nd Kapodistrian University of Athens) as part of Greek Algebra & Number Th
eory Seminar\n\n\nAbstract\nWhen an algebra is not semisimple\, a good way
to understand its representation theory is through the study of its block
s. To each simple module in a block we can attach a numerical datum\, whic
h measures the complexity of the block: the defect. This is true for the s
ymmetric group algebra\, as well as its generalisations\, the Iwahori-Heck
e algebra of type A and the Ariki-Koike algebra. In a joint work with Nic
olas Jacon we have proved\, using algebraic combinatorics\, that the defec
t is a block invariant for Ariki-Koike algebras\, thus proving a conjectur
e formulated by Geck 30 years ago. In this talk we will present our proof\
, as well as our data indicating that this fact is true for all Hecke alge
bras associated with complex reflection groups.\n
LOCATION:https://researchseminars.org/talk/GANT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioannis Tsokanos (The University of Manchester)
DTSTART;VALUE=DATE-TIME:20221031T140000Z
DTEND;VALUE=DATE-TIME:20221031T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/15
DESCRIPTION:Title: De
nsity of oscillating sequences in the real line\nby Ioannis Tsokanos (
The University of Manchester) as part of Greek Algebra & Number Theory Sem
inar\n\n\nAbstract\nIn this talk\, we study the density properties in the
real line of oscillating sequences of the form $( g(k) \\cdot F(ka) )_{k \
\in \\mathbb{N}}$\, where $g$ is a positive increasing function and $F$ a
real continuous $1$-periodic function. This extends work by Berend\, Bosh
ernitzan and Kolesnik who established differential properties on the funct
ion $F$ ensuring that the oscillating sequence is dense modulo $1$. More p
recisely\, when F has finitely many roots in $[0\,1)$\, we provide necessa
ry and sufficient conditions for the oscillating sequence under considerat
ion to be dense in $\\mathbb{R}$. All the related results are stated in te
rms of the Diophantine properties of $a$\, with the help of the theory of
continued fractions.\n
LOCATION:https://researchseminars.org/talk/GANT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleni Tzanaki (University of Crete)
DTSTART;VALUE=DATE-TIME:20221128T140000Z
DTEND;VALUE=DATE-TIME:20221128T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/16
DESCRIPTION:Title: Sy
mmetric decompositions\, triangulations and real-rootedness\nby Eleni
Tzanaki (University of Crete) as part of Greek Algebra & Number Theory Sem
inar\n\n\nAbstract\nA triangulation of a simplicial complex $Δ$ is said t
o be uniform if the $f$-vector of its restriction to a face of $Δ$ depend
s only on the dimension of that face. The notion of uniform triangulation
was introduced by Christos Athanasiadis in order to conveniently unify man
y well known types of triangulations such as barycentric\, $r$-colored bar
ycentric\, $r$-fold edgewise etc. These triangulations have the common fea
ture that\, for certain "nice" classes of simplicial complexes $Δ$\, the
$h$-polynomial of the triangulation $Δ^′$ of $Δ$\, is real rooted with
nonnegative coefficients. Athanasiadis proved that\, uniform triangulatio
ns having the so called stong interlacing property\, have real rooted $h$-
polynomials with nonnegative coefficients.\n\nWe continue this line of res
earch and we study under which conditions the $h$-polynomial of a uniform
triangulation $Δ^′$ of $Δ$ has a nonnegative real rooted symmetric dec
omposition. We also provide conditions under which this decomposition is a
lso interlacing. Applications yield new classes of polynomials in geometri
c combinatorics which afford nonnegative\, real-rooted symmetric decomposi
tions. Some interesting questions in $h$-vector theory arise from this wor
k.\n\nThis is joint work with Christos Athanasiadis.\n
LOCATION:https://researchseminars.org/talk/GANT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantinos Tsouvalas (IHÉS)
DTSTART;VALUE=DATE-TIME:20221114T140000Z
DTEND;VALUE=DATE-TIME:20221114T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/17
DESCRIPTION:Title: An
osov groups that are indiscrete in rank one\nby Konstantinos Tsouvalas
(IHÉS) as part of Greek Algebra & Number Theory Seminar\n\n\nAbstract\nH
yperbolic groups is a rich and well-studied class of finitely presented gr
oups introduced by Gromov in the 80's. It is an open question on whether t
here exist examples of linear hyperbolic groups which do not admit discret
e faithful representation into any real semisimple Lie group. In this talk
\, we are going to provide linear examples of hyperbolic groups which\, on
the one hand admit Anosov representations into higher rank Lie groups\, b
ut fail to admit discrete faithful representation into any product of (fin
itely many) rank one Lie groups. This is joint work with Sami Douba.\n
LOCATION:https://researchseminars.org/talk/GANT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stelios Sachpazis (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20221212T140000Z
DTEND;VALUE=DATE-TIME:20221212T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/18
DESCRIPTION:Title: A
different proof of Linnik's estimate for primes in arithmetic progressions
\nby Stelios Sachpazis (Université de Montréal) as part of Greek Alg
ebra & Number Theory Seminar\n\n\nAbstract\nLet $a$ and $q$ be two coprime
positive integers. In 1944\, Linnik\nproved his celebrated theorem concer
ning the size of the smallest prime\n$p(q\,a)$ in the arithmetic progressi
on $a(\\mod q)$. In his attempt to prove\nhis result\, Linnik established
an estimate for the sums of the von Mangoldt\nfunction $\\Lambda$ on arith
metic progressions. His work on $p(q\,a)$ was later\nsimplified\, but the
simplified proofs relied in one form or another on the\nsame advanced tool
s that Linnik originally used. The last two decades\, some\nmore elementar
y approaches for Linnik's theorem have appeared. Nonetheless\,\nnone of th
em furnishes an estimate of the same quantitative strength as the\none tha
t Linnik obtained for $\\Lambda$. In this talk\, we will see how one can s
eal\nthis gap and recover Linnik’s estimate by largely elementary means.
The\nideas that I will describe build on methods from the treatment of\nK
oukoulopoulos on multiplicative functions with small partial sums and his\
npretentious proof for the prime number theorem in arithmetic progressions
.\n
LOCATION:https://researchseminars.org/talk/GANT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Hadjievangelou (University of Bath)
DTSTART;VALUE=DATE-TIME:20230130T140000Z
DTEND;VALUE=DATE-TIME:20230130T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/19
DESCRIPTION:Title: Le
ft 3-Engel Elements in Locally Finite p-groups\nby Anastasia Hadjievan
gelou (University of Bath) as part of Greek Algebra & Number Theory Semina
r\n\n\nAbstract\nEngel Theory is of significant interest in group theory a
s there\nis an unmistakable correlation between Engel and Burnside problem
s. In\nthis talk we first introduce Engel elements and Engel groups and in
\nparticular we expand our knowledge on locally finite Engel groups. It is
\nimportant to know that M. Newell proved that if $x$ is a right $3$-Engel
\nelement in a group $G$ then $x$ lies in $HP(G)$ (Hirsch-Plotkin radical)
and in\nfact he proved the stronger result that the normal closure of $x$
is\nnilpotent of class at most $3$. The natural question arises whether t
he\nanalogous result holds for left $3$-Engel elements. We will give vario
us\nexamples of locally finite p-groups $G$ containing a left $3$-Engel el
ement $x$\nwhose normal closure is not nilpotent. Lastly\, we will discuss
the open\nproblem of whether or not a left $3$-Engel element always lies
in the $HP(G)$.\n(This is joint work with Gunnar Traustason and Marialaura
Noce)\n
LOCATION:https://researchseminars.org/talk/GANT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Vasilakopoulou (National Technical University of Athens)
DTSTART;VALUE=DATE-TIME:20230116T140000Z
DTEND;VALUE=DATE-TIME:20230116T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/20
DESCRIPTION:Title: Du
al algebraic structures and enrichment\nby Christina Vasilakopoulou (N
ational Technical University of Athens) as part of Greek Algebra & Number
Theory Seminar\n\n\nAbstract\nIn this talk\, we will provide an overview o
f the sometimes called “Sweedler theory” for algebras and modules. Thi
s begins by establishing an enrichment of the category of algebras in the
category of coalgebras\, as well as an enrichment of a global category of
modules in a global category of comodules\, giving rise to a structure des
cribed as an enriched fibration. Moreover\, by investigating a many-object
generalization involving categories and modules\, we will discuss further
directions and applications of this framework to operadic structures.\n
LOCATION:https://researchseminars.org/talk/GANT/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Loukaki (University of Crete)
DTSTART;VALUE=DATE-TIME:20230220T140000Z
DTEND;VALUE=DATE-TIME:20230220T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/21
DESCRIPTION:Title: Co
ngruences in finite $p$-groups\nby Maria Loukaki (University of Crete)
as part of Greek Algebra & Number Theory Seminar\n\n\nAbstract\nLet $G$ b
e a finite $p$-group. How many abelian subgroups of a\ngiven order does $G
$ have $\\pmod p$? Elementary abelian? What about normal\nabelian or norma
l elementary abelian? This type of questions we will try to\nanswer\, for
any subgroup-closed class $\\mathfrak{X}$ of finite groups\, in\nthis join
t work with S. Aivazidis. Relations to known results\, a sharpened\nversio
n of a celebrated theorem of Burnside and some open questions are\nalso pr
esented.\n
LOCATION:https://researchseminars.org/talk/GANT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Myrto Mavraki (Harvard University)
DTSTART;VALUE=DATE-TIME:20230327T130000Z
DTEND;VALUE=DATE-TIME:20230327T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/22
DESCRIPTION:Title: Dy
namics\, number theory and unlikely intersections\nby Myrto Mavraki (H
arvard University) as part of Greek Algebra & Number Theory Seminar\n\n\nA
bstract\nFruitful interactions between arithmetic geometry and dynamical s
ystems have emerged in recent years. In this talk I will illustrate how in
sights from complex dynamics can be employed to study problems from arithm
etic geometry. And conversely how arithmetic geometry can be used in the s
tudy of dynamical systems. The motivating questions are inspired by a recu
rring phenomenon in arithmetic geometry known as `unlikely intersections'
and conjectures of Pink and Zilber therein. More specifically\, I will dis
cuss work toward understanding the distribution of preperiodic points in s
ubvarieties of families of rational maps.\n
LOCATION:https://researchseminars.org/talk/GANT/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Birkbeck (University of East Anglia)
DTSTART;VALUE=DATE-TIME:20230213T140000Z
DTEND;VALUE=DATE-TIME:20230213T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/23
DESCRIPTION:Title: Ov
erconvergent Hilbert modular forms via perfectoid methods\nby Chris Bi
rkbeck (University of East Anglia) as part of Greek Algebra & Number Theor
y Seminar\n\n\nAbstract\nFollowing a construction of Chojecki-Hansen-Johan
sson\, we show how to use Scholze's infinite level modular varieties and t
he Hodge-Tate period map to define overconvergent elliptic and Hilbert mod
ular forms in a way analogous to the standard construction of modular form
s. As an application we show that this is one way of constructing overconv
ergent Eichler-Shimura maps in these settings. This is joint work with Ben
Heuer and Chris Williams.\n
LOCATION:https://researchseminars.org/talk/GANT/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Vlassopoulos (Athena RC)
DTSTART;VALUE=DATE-TIME:20230306T140000Z
DTEND;VALUE=DATE-TIME:20230306T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/24
DESCRIPTION:Title: La
nguage modelling with enriched categories\, the Yoneda embedding and the I
sbell completion\nby Yiannis Vlassopoulos (Athena RC) as part of Greek
Algebra & Number Theory Seminar\n\n\nAbstract\nNeural networks (like Chat
GPT) trained to probabilistically predict the next word to a text\, have r
ecently achieved human like capabilities in language understanding and use
.\n\nWhat is though the underlying mathematical structure that these model
s learn and how is semantic information encoded in the statistics of word
co-occurances?\n\nWe will introduce a category L whose objects are texts i
n the language and a morphism from text x to text y is the probability of
extension from x to y\, in order to propose a partial answer to these ques
tions. The category is enriched over the monoidal closed category whose se
t of objects is [0\, 1] and monoidal structure is multiplication. The Yone
da embedding of L into its category of presheaves naturally encodes co-occ
urance information. Applying −log to morphisms we obtain an equivalent c
ategory which is also a Lawvere metric space and a tropical linear space.
We will then explain the Isbell completion which relates completion by op
co-presheaves (probabilites of extending a text) to completion by presheav
es (probabilities of extending to a text). This is based on joint work wit
h T.D. Bradley\, J. Terilla and S. Gaubert\n
LOCATION:https://researchseminars.org/talk/GANT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgos Kapetanakis (University of Thessaly)
DTSTART;VALUE=DATE-TIME:20230410T130000Z
DTEND;VALUE=DATE-TIME:20230410T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/25
DESCRIPTION:Title: To
wards the Primitive Completely Normal Basis Theorem\nby Giorgos Kapeta
nakis (University of Thessaly) as part of Greek Algebra & Number Theory Se
minar\n\n\nAbstract\nLet GF(q) be the finite field of cardinality q and GF
(q^n) its extension of degree n. A generator of the multiplicative group G
F(q^n)^* is called primitive and some x in GF(q^n) whose GF(q)-conjugates
span a GF(q)-basis is called normal over GF(q). In 1996\, Morgan and Mulle
n conjectured that for every q and n\, there exists some primitive element
of GF(q^n) that is normal over GF(q^d) for every d|n.\nIn this talk\, we
will describe how this conjecture was established when q>n and we will dis
cuss possible improvements. This is joint work with Theodoulos Garefalakis
.\n
LOCATION:https://researchseminars.org/talk/GANT/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ekin Özman (Boğaziçi University)
DTSTART;VALUE=DATE-TIME:20230424T130000Z
DTEND;VALUE=DATE-TIME:20230424T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/26
DESCRIPTION:Title: Mo
dular Curves and Asymptotic Solutions to Fermat-type Equations\nby Eki
n Özman (Boğaziçi University) as part of Greek Algebra & Number Theory
Seminar\n\n\nAbstract\nUnderstanding solutions of Diophantine equations ov
er a number field is one of the main problems of number theory. By the hel
p of the modular techniques used in the proof of Fermat’s last theorem b
y Wiles and its generalizations\, it is possible to solve other Diophantin
e equations too. Understanding quadratic points on the classical modular c
urve also plays a role in this approach. It is also possible to study the
solutions of Fermat type equations over number fields asymptotically. In t
his talk\, I will mention some recent results about these notions for the
classical Fermat equation as well as some other Diophantine equations.\n
LOCATION:https://researchseminars.org/talk/GANT/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Vlassopoulos (Athena RC)
DTSTART;VALUE=DATE-TIME:20230313T140000Z
DTEND;VALUE=DATE-TIME:20230313T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/27
DESCRIPTION:Title: La
nguage modelling with enriched categories\, the Yoneda embedding and the I
sbell completion\nby Yiannis Vlassopoulos (Athena RC) as part of Greek
Algebra & Number Theory Seminar\n\n\nAbstract\nNeural networks (like Chat
GPT) trained to probabilistically predict the next word to a text\, have r
ecently achieved human like capabilities in language understanding and use
.\n\nWhat is though the underlying mathematical structure that these model
s learn and how is semantic information encoded in the statistics of word
co-occurances?\n\nWe will introduce a category L whose objects are texts i
n the language and a morphism from text x to text y is the probability of
extension from x to y\, in order to propose a partial answer to these ques
tions. The category is enriched over the monoidal closed category whose se
t of objects is [0\, 1] and monoidal structure is multiplication. The Yone
da embedding of L into its category of presheaves naturally encodes co-occ
urance information. Applying −log to morphisms we obtain an equivalent c
ategory which is also a Lawvere metric space and a tropical linear space.
We will then explain the Isbell completion which relates completion by op
co-presheaves (probabilites of extending a text) to completion by presheav
es (probabilities of extending to a text). This is based on joint work wit
h T.D. Bradley\, J. Terilla and S. Gaubert.\n
LOCATION:https://researchseminars.org/talk/GANT/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Douvropoulos (University of Massachusetts at Amherst)
DTSTART;VALUE=DATE-TIME:20230508T130000Z
DTEND;VALUE=DATE-TIME:20230508T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/28
DESCRIPTION:Title: Re
cursions and Proofs in Coxeter-Catalan combinatorics\nby Theo Douvropo
ulos (University of Massachusetts at Amherst) as part of Greek Algebra & N
umber Theory Seminar\n\n\nAbstract\nIn a significant --yet absolutely unde
rstandable-- deviation from traditions of logic\, secularism\, and platoni
c dialectic\, combinatorialists the world around have celebrated Catalan o
bjects with a reverence better suited to mystical\, preternatural endeavor
s. Various sects have been formed through the years by mathematicians who
study particular aspects of the Catalan doctrine\, including the Coxeter-C
atalan sect of which the speaker might be a member.\n\nOne of the central
objects in Coxeter-Catalan combinatorics is the noncrossing partition latt
ice $NC(W)$ associated to a finite Coxeter group $W$ and its sibling objec
t\, the cluster complex $Y(W)$. These two objects encode much of the geome
tric group theory\, combinatorics\, and representation theory of $W$\, and
they have fascinating stuctural and enumerative properties\; in particula
r\, the zeta polynomials of certain intervals in $NC(W)$ and the (almost)
colored $f$-vectors of $Y(W)$ all have product formulas given in terms of
invariants of $W$ (generalizing formulas of Kreweras and Loday for the sym
metric group case). A central open problem in the area since at least the
early 2000's has been to give case-free proofs of these product formulas\,
i.e. proofs that do not depend on the classification of finite Coxeter gr
oups. In this talk\, I will present the first such proof\, in collaboratio
n with Matthieu Josuat-Verges\, solving the more general Fuss version of t
he problem\; in our approach\, we develop a collection of recursions that
are shown to be satisfied by both the combinatorial objects and the produc
t formulas.\n
LOCATION:https://researchseminars.org/talk/GANT/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasileios Metaftsis (University of the Aegean)
DTSTART;VALUE=DATE-TIME:20230529T130000Z
DTEND;VALUE=DATE-TIME:20230529T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/29
DESCRIPTION:Title: So
me steps towards understanding the McCool group\nby Vasileios Metaftsi
s (University of the Aegean) as part of Greek Algebra & Number Theory Semi
nar\n\n\nAbstract\nWe give a brief introduction to the group of automorphi
sms of the free group and we give some results concerning the McCool subgr
oup and some subgroups of it.\n
LOCATION:https://researchseminars.org/talk/GANT/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Dalezios (Aristotle University of Thessaloniki)
DTSTART;VALUE=DATE-TIME:20231113T120000Z
DTEND;VALUE=DATE-TIME:20231113T130000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/30
DESCRIPTION:Title: St
able and singular equivalences of finite dimensional algebras I\nby Ge
orge Dalezios (Aristotle University of Thessaloniki) as part of Greek Alge
bra & Number Theory Seminar\n\n\nAbstract\nThe plan is to give two talks o
n homological methods in the representation theory of finite dimensional a
ssociative algebras\, culminating in recent new results on stable and sing
ular equivalences. The first talk will be introductory\, offering a crash
course on concepts such as quiver representations and Morita equivalences
(classical and derived). In the second talk\, we will go beyond the class
of derived equivalences and discuss singularity categories and singular eq
uivalences\, in relation to Gorenstein rings and Cohen-Macaulay modules. E
ffort will be put in making things comprehensive to a broad algebraic audi
ence.\n
LOCATION:https://researchseminars.org/talk/GANT/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Dalezios (Aristotle University of Thessaloniki)
DTSTART;VALUE=DATE-TIME:20231120T120000Z
DTEND;VALUE=DATE-TIME:20231120T130000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/31
DESCRIPTION:Title: St
able and singular equivalences of finite dimensional algebras II\nby G
eorge Dalezios (Aristotle University of Thessaloniki) as part of Greek Alg
ebra & Number Theory Seminar\n\n\nAbstract\nThe plan is to give two talks
on homological methods in the representation theory of finite dimensional
associative algebras\, culminating in recent new results on stable and sin
gular equivalences. The first talk will be introductory\, offering a crash
course on concepts such as quiver representations and Morita equivalences
(classical and derived). In the second talk\, we will go beyond the class
of derived equivalences and discuss singularity categories and singular e
quivalences\, in relation to Gorenstein rings and Cohen-Macaulay modules.
Effort will be put in making things comprehensive to a broad algebraic aud
ience.\n
LOCATION:https://researchseminars.org/talk/GANT/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kostas Psaromiligkos (Université Clermont Auvergne)
DTSTART;VALUE=DATE-TIME:20231204T140000Z
DTEND;VALUE=DATE-TIME:20231204T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/32
DESCRIPTION:Title: De
formation theory of the Lafforgue variety - part 1\nby Kostas Psaromil
igkos (Université Clermont Auvergne) as part of Greek Algebra & Number Th
eory Seminar\n\n\nAbstract\nIn this series of talks we will construct the
Lafforgue variety\, an affine scheme equipped with an open dense subscheme
parametrizing the simple modules of a non-commutative algebra that is a f
inite module over a finitely generated center. Our main applications and s
ource of examples will be in the theory of Hecke algebras. We will also st
udy how the Lafforgue variety varies under deformation of algebras\, and i
n particular we prove in the case the center is regular a conjecture state
d by Aubert\, Baum and Plymen in 2007 on the reducibility loci of affine H
ecke algebras.\n\nIn the first talk\, we will introduce Hecke algebras and
the type of questions we will consider\, as well as relevant algebraic ge
ometric notions for the second talk. In the second talk\, we will construc
t the Lafforgue variety and study its deformation theory (the latter is wo
rk in progress).\n
LOCATION:https://researchseminars.org/talk/GANT/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kostas Psaromiligkos (Université Clermont Auvergne)
DTSTART;VALUE=DATE-TIME:20231211T140000Z
DTEND;VALUE=DATE-TIME:20231211T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T172534Z
UID:GANT/33
DESCRIPTION:Title: De
formation theory of the Lafforgue variety - part 2\nby Kostas Psaromil
igkos (Université Clermont Auvergne) as part of Greek Algebra & Number Th
eory Seminar\n\n\nAbstract\nIn this series of talks we will construct the
Lafforgue variety\, an affine scheme equipped with an open dense subscheme
parametrizing the simple modules of a non-commutative algebra that is a f
inite module over a finitely generated center. Our main applications and s
ource of examples will be in the theory of Hecke algebras. We will also st
udy how the Lafforgue variety varies under deformation of algebras\, and i
n particular we prove in the case the center is regular a conjecture state
d by Aubert\, Baum and Plymen in 2007 on the reducibility loci of affine H
ecke algebras.\n\nIn the first talk\, we will introduce Hecke algebras and
the type of questions we will consider\, as well as relevant algebraic ge
ometric notions for the second talk. In the second talk\, we will construc
t the Lafforgue variety and study its deformation theory (the latter is wo
rk in progress).\n
LOCATION:https://researchseminars.org/talk/GANT/33/
END:VEVENT
END:VCALENDAR