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BEGIN:VEVENT
SUMMARY:Zeinab Akhlaghi (Amirkabir University of technology (Iran))
DTSTART:20210226T143000Z
DTEND:20210226T151500Z
DTSTAMP:20260404T094531Z
UID:FGV/1
DESCRIPTION:Title: Character degree graph and Huppert’s ρ-σ- conjecture\nby Zeinab
Akhlaghi (Amirkabir University of technology (Iran)) as part of Finite Gr
oups in Valencia\n\n\nAbstract\nCharacter Theory is one of the strong tool
s in the theory of finite groups\, and\, given a finite group $G$ the stud
y of the set $\\mathrm {cd}(G)=\\{\\\,\\theta(1)\\\,|\\\,\\theta\\in \\mat
hrm{ Irr}(G)\\}$\, of all degrees of the irreducible complex characters of
$G$\, has an important role in finite group theory. Associating a graph
to the degree-set is one of the method to approach this set. The characte
r degree graph $\\Delta(G)$ is defined as the graph whose vertex set is t
he set of all the prime numbers that divide some $\\theta(1)\\in \\mathrm{
cd}(G)$\, while a pair $(p\,q)$ of distinct vertices $p$ and $q$ belongs t
o the edge set if and only if $pq$ divides an element in $\\mathrm{cd}(G)$
. So far\, many studies have been done on this graph. In this talk\, we wi
ll discuss the recent development obtained on this graph and finally focus
on a new result on Huppert’s $\\rho-\\sigma$ conjecture\, which is der
ived from the recent development on this graph.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Álvaro L. Martínez (Columbia University (USA))
DTSTART:20210226T152000Z
DTEND:20210226T154500Z
DTSTAMP:20260404T094531Z
UID:FGV/2
DESCRIPTION:Title: Symmetric groups and the Heisenberg category\nby Álvaro L. Martín
ez (Columbia University (USA)) as part of Finite Groups in Valencia\n\n\nA
bstract\nWe will see how induction and restriction give an action of the H
eisenberg algebra on the category of representations of symmetric groups.
We will discuss how this inspired Khovanov’s definition of the Heisenber
g category\, as well as some recent developments.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Vallejo (Universidad Carlos III de Madrid-ICMAT (Spain))
DTSTART:20210226T155000Z
DTEND:20210226T163500Z
DTSTAMP:20260404T094531Z
UID:FGV/3
DESCRIPTION:Title: Problems on characters involving two primes\nby Carolina Vallejo (U
niversidad Carlos III de Madrid-ICMAT (Spain)) as part of Finite Groups in
Valencia\n\n\nAbstract\nIn the first part of the talk we will see that if
$G$ is a nontrivial finite group\, then for every pair of primes $\\{p\,q
\\}$ there is some nontrivial irreducible character of $G$ whose degree is
not divisible by $p$ nor $q$. This result will allow us to characterize g
roups in which all irreducible characters of degree not divisible by $p$ n
or $q$ are linear. In the second part of my talk\, I will discuss on what
can be said about the field of values of such a character of $\\{p\, q\\}$
'-degree. This talk is based in joint works with E Giannelli\, N. Hung and
M. Schaeffer Fry.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio Marchi (University of Manchester (UK))
DTSTART:20210226T164000Z
DTEND:20210226T170500Z
DTSTAMP:20260404T094531Z
UID:FGV/4
DESCRIPTION:Title: Picard groups for blocks with normal defect groups\nby Claudio Marc
hi (University of Manchester (UK)) as part of Finite Groups in Valencia\n\
n\nAbstract\nLet $G$ be a finite group\, $B$ a $p$-block of $OG$\, $O$ a c
omplete DVR. The Picard group of $B$ is the group of auto-Morita equivalen
ces of $B$ and it revealed itself to be a useful tool\, for example for de
aling with Donovan conjecture. However\, it is also interesting in its own
right\, since it has the structure of a finite group\, when $O$ has char
0.\n\nIn this talk we will give an introduction to Picard groups for block
s and then present joint work with Livesey on blocks with normal defect gr
oups\, providing evidence to a conjecture on basic Morita equivalences.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changguo Shao (University of Jinan (China))
DTSTART:20210305T143000Z
DTEND:20210305T151500Z
DTSTAMP:20260404T094531Z
UID:FGV/5
DESCRIPTION:Title: Groups in which the centralizer of any non-central primary element is m
aximal\nby Changguo Shao (University of Jinan (China)) as part of Fini
te Groups in Valencia\n\n\nAbstract\nIn this talk\, we investigate the str
ucture of a finite group $G$ whose centralizer of each primary element is
maximal in $G$. This is a question raised by Zhao\, Chen and Guo in "Zhao\
, Xianhe\; Chen\, Ruifang\; Guo\, Xiuyun Groups in which the centralizer
of any non-central element is maximal. J. Group Theory 23 (2020)\, no. 5\,
871–878". \n\nIn this talk\, we also provide an independent result focu
sed on the centralizers of primary elements in finite simple groups.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pietro Gheri (Università degli Studi di Firenze (Italy))
DTSTART:20210305T152000Z
DTEND:20210305T154500Z
DTSTAMP:20260404T094531Z
UID:FGV/6
DESCRIPTION:Title: On the number of $p$-elements in finite groups\nby Pietro Gheri (Un
iversità degli Studi di Firenze (Italy)) as part of Finite Groups in Vale
ncia\n\n\nAbstract\nGiven a finite group $G$ and a prime $p$ dividing its
order\, we consider the ratio between the number of $p$-elements and the o
rder of a Sylow $p$-subgroup of $G$. Frobenius proved that this ratio is a
lways an integer\, but no combinatorial interpretation of this number seem
s to be known.\n\nWe will talk about the search for a lower bound on this
ratio in terms of the number of Sylow $p$-subgroups of $G$.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damiano Rossi (Bergische Universität Wuppertal (Germany))
DTSTART:20210305T155000Z
DTEND:20210305T161500Z
DTSTAMP:20260404T094531Z
UID:FGV/7
DESCRIPTION:Title: Character Triple Conjecture for Groups of Lie Type\nby Damiano Ross
i (Bergische Universität Wuppertal (Germany)) as part of Finite Groups in
Valencia\n\n\nAbstract\nDade’s Conjecture is an important conjecture in
representation theory of finite groups. It implies most of the\, so calle
d\, global-local conjectures. In 2017\, Späth introduced a strengthening
of Dade’s Conjecture\, called the Character Triple Conjecture\, which de
scribes the Clifford theory of corresponding characters. Moreover\, she pr
oved a reduction theorem\, namely that if her conjecture holds for every q
uasisimple group\, then Dade’s Conjecture holds for every finite group.
Extending ideas of Broué\, Fong and Srinivasan we provide a strategy to
prove the Character Triple Conjecture for quasisimple groups of Lie type i
n the nondefining characteristic.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mandi Schaeffer Fry (Metropolitan State University of Denver (USA)
)
DTSTART:20210305T162000Z
DTEND:20210305T170500Z
DTSTAMP:20260404T094531Z
UID:FGV/8
DESCRIPTION:Title: The McKay-Navarro Conjecture: the Conjecture That Keeps on Giving!\
nby Mandi Schaeffer Fry (Metropolitan State University of Denver (USA)) as
part of Finite Groups in Valencia\n\n\nAbstract\nThe McKay conjecture is
one of the main open conjectures in the realm of the local-global philosop
hy in character theory. It posits a bijection between the set of irreduci
ble characters of a group with $p'$-degree and the corresponding set in th
e normalizer of a Sylow p-subgroup. In this talk\, I’ll give an overview
of a refinement of the McKay conjecture due to Gabriel Navarro\, which br
ings the action of Galois automorphisms into the picture. A lot of recent
work has been done on this conjecture\, but possibly even more interestin
g is the amount of information it yields about the character table of a fi
nite group. I’ll discuss some recent results on the McKay—Navarro con
jecture\, as well as some of the implications the conjecture has had for o
ther interesting character-theoretic problems.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Miquel Martínez (Universitat de València (Spain))
DTSTART:20210312T155000Z
DTEND:20210312T161500Z
DTSTAMP:20260404T094531Z
UID:FGV/9
DESCRIPTION:Title: Degrees of characters in the principal block\nby J. Miquel Martíne
z (Universitat de València (Spain)) as part of Finite Groups in Valencia\
n\n\nAbstract\nLet $G$ be a finite group and let $p$ be a prime. The set o
f complex irreducible characters in the principal $p$-block of $G$ is rich
enough that their degrees encode information of the structure of the grou
p $G$. We study the case where the set of degrees of characters in the pri
ncipal $p$-block of $G$ has size at most $2$\, finding information about t
he structure of $G$ and its Sylow $p$-subgroups. We will also show some re
lated results on similar problems for arbitrary $p$-blocks.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Grittini (Università degli Studi di Firenze (Italy))
DTSTART:20210312T152000Z
DTEND:20210312T154500Z
DTSTAMP:20260404T094531Z
UID:FGV/10
DESCRIPTION:Title: The generalization of a theorem on real valued characters\nby Nico
la Grittini (Università degli Studi di Firenze (Italy)) as part of Finit
e Groups in Valencia\n\n\nAbstract\nThe Theorem of Ito-Michler\, one of th
e most celebrated results in character theory of finite groups\, states th
at a group has a normal abelian Sylow $p$-subgroup if and only if the prim
e number $p$ does not divide the degree of any irreducible character of th
e group.\n\nAmong the many variants of the theorem\, there exists one\, du
e to Dolfi\, Navarro and Tiep\, which involves only the real valued irredu
cible characters of the group\, and the prime number $p = 2$.\n\nThis vari
ant\, however\, fails if we consider a prime number different from 2\, and
any generalization in this direction seems hard\, due to some specific pr
operties of real valued characters.\n\nThis talk proposes a new way to app
roach the problem\, which takes into account a different subset of the irr
educible characters\, however related with real valued characters. This ne
w approach has already been partially successful and it may suggest a way
to generalize also other similar results.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nguyen Ngoc Hung (University of Akron (USA))
DTSTART:20210312T162000Z
DTEND:20210312T170500Z
DTSTAMP:20260404T094531Z
UID:FGV/11
DESCRIPTION:Title: Bounding $p$-regular conjugacy classes and $p$-Brauer characters in fi
nite groups\nby Nguyen Ngoc Hung (University of Akron (USA)) as part o
f Finite Groups in Valencia\n\n\nAbstract\nWe discuss two closely related
problems on bounding the number of $p$-regular conjugacy classes of a fini
te group $G$ and bounding the number of irreducible $p$-Brauer characters
of $G$ or a block of $G$. Among other results we will show that the number
of $p$-regular classes of a finite group $G$ is bounded below by $2\\sqrt
{p−1}+1−k_p(G)$\, where $k_p(G)$ is the number of classes of $p$-eleme
nts of $G$. This and the celebrated Alperin weight conjecture imply the sa
me bound for the number of irreducible $p$-Brauer characters in the princi
pal $p$-block of $G$. We also discuss the bounds in the minimal situation
when $G$ has a unique class of nontrivial $p$-elements\, which have applic
ations to the study of principal blocks with few characters. The talk is b
ased on joint works with A. Moretó\, with A. Maroti\, and with B. Sambale
and P.H. Tiep.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zinovy Reichstein (University of British Columbia (Canada))
DTSTART:20210312T171000Z
DTEND:20210312T175500Z
DTSTAMP:20260404T094531Z
UID:FGV/12
DESCRIPTION:Title: Fields of definition for linear representations\nby Zinovy Reichst
ein (University of British Columbia (Canada)) as part of Finite Groups in
Valencia\n\n\nAbstract\nA classical theorem of Richard Brauer asserts that
every finite-dimensional non-modular representation $\\rho$ of a finite g
roup $G$ defined over a field $K$\, whose character takes values in $k$\,
descends to $k$\, provided that $k$ has suitable roots of unity. If $k$ do
es not contain these roots of unity\, it is natural to ask how far $\\rho$
is from being definable over $k$. The classical answer to this question i
s given by the Schur index of $\\rho$\, which is the smallest degree of a
finite field extension $l/k$ such that $\\rho$ can be defined over $l$. In
this talk\, based on joint work with Nikita Karpenko\, Julia Pevtsova and
Dave Benson\, I will discuss another invariant\, the essential dimension
of $\\rho$\, which measures ''how far'' $\\rho$ is from being definable ov
er $k$ in a different way by using transcendental\, rather than algebraic
field extensions. I will also talk about recent results of Federico Scavia
on essential dimension of representations of algebras.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvio Dolfi (Università degli Studi di Firenze (Italy))
DTSTART:20210316T144000Z
DTEND:20210316T151500Z
DTSTAMP:20260404T094531Z
UID:FGV/16
DESCRIPTION:Title: $p$-constant characters in finite groups\nby Silvio Dolfi (Univers
ità degli Studi di Firenze (Italy)) as part of Finite Groups in Valencia\
n\n\nAbstract\nLet $p$ be a prime number\; an irreducible character of a f
inite group $G$ is called $p$-constant if it takes a constant value on all
the elements of G whose order is divisible by $p$ ($p$-singular elements)
. Irreducible characters of $p$-defect zero are\, by a classical result or
R. Brauer\, an important instance of this class of characters: they take
value zero on every $p$-singular element. I will present some results on
faithful $p$-constant characters of 'positive defect'\; in particular\, a
characterization of the finite $p$-solvable groups having a character of
this type (joint work with E. Pacifici and L. Sanus).\n
LOCATION:https://stable.researchseminars.org/talk/FGV/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noelia Rizo (Universitat de València (Spain))
DTSTART:20210316T152000Z
DTEND:20210316T154500Z
DTSTAMP:20260404T094531Z
UID:FGV/17
DESCRIPTION:Title: Counting characters in blocks\nby Noelia Rizo (Universitat de Val
ència (Spain)) as part of Finite Groups in Valencia\n\n\nAbstract\nLet $G
$ be a finite group\, let $p$ be a prime number and let $B$ be a $p$-block
of $G$ with defect group $D$. Studying the structure of $D$ by means of t
he knowledge of some aspects of $B$ is a main area in character theory of
finite groups. Let $k(B)$ be the number of irreducible characters in the $
p$-block $B$. It is well-known that $k(B)=1$ if\, and only if\, $D$ is tri
vial. It is also true that $k(B)=2$ if\, and only if\, $|D|=2$. For blocks
$B$ with $k(B)=3$ it is conjectured that $|D|=3$. \n\nIn this talk we res
trict our attention to the principal $p$-block of $G$\, $B_0(G)$\, that is
\, the $p$-block containing the trivial character of $G$. In this case\, b
y work of Belonogov\, Koshitani and Sakurai we know the structure of $D$ w
hen $k(B_0(G))=3$ or $4$. In this work\, we go one step further and analyz
e the structure of D when $k(B_0(G))=5$. \n\nThis is a joint work with Man
di Schaeffer Fry and Carolina Vallejo.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Camina (University of Cambridge (UK))
DTSTART:20210316T155000Z
DTEND:20210316T163500Z
DTSTAMP:20260404T094531Z
UID:FGV/18
DESCRIPTION:Title: Word problems for finite nilpotent groups\nby Rachel Camina (Unive
rsity of Cambridge (UK)) as part of Finite Groups in Valencia\n\n\nAbstrac
t\nWe consider word maps on finite nilpotent groups and count the sizes of
the fibres for elements in the image. We consider Amit’s conjecture and
its generalisation\, which say that these fibres should have size at leas
t $|G^{(k−1)}|$ where the word is on $k$ variables. This is joint work w
ith Ainhoa Iñiguez and Anitha Thillaisundaram.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carmen Melchor (Universitat de València)
DTSTART:20210316T164000Z
DTEND:20210316T170500Z
DTSTAMP:20260404T094531Z
UID:FGV/19
DESCRIPTION:Title: An Arad and Fisman's theorem on products of conjugacy classes revisite
d\nby Carmen Melchor (Universitat de València) as part of Finite Grou
ps in Valencia\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/FGV/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuele Pacifici (Università degli Studi di Milano (Italy))
DTSTART:20210330T133000Z
DTEND:20210330T141500Z
DTSTAMP:20260404T094531Z
UID:FGV/22
DESCRIPTION:Title: On Huppert’s $\\rho-\\sigma$ conjecture\nby Emanuele Pacifici (U
niversità degli Studi di Milano (Italy)) as part of Finite Groups in Vale
ncia\n\n\nAbstract\nThe set of the degrees of the irreducible complex char
acters of a finite group $G$ has been an object of considerable interest s
ince the second part of the 20th century\, and the study of the arithmetic
al structure of this set is a particularly intriguing aspect of Character
Theory of finite groups. A remarkable question in this research area was p
osed by B. Huppert in the 80’s: is it true that at least one of the char
acter degrees is divisible by a ”large” portion of the entire set of p
rimes that appear as divisors of some character degree? More precisely\, d
enoting by $\\rho(G)$ the set of primes that divide some character degree\
, and by $\\sigma(G)$ the largest number of primes that divide a single ch
aracter degree\, Huppert’s $\\rho-\\sigma$ conjecture predicts that $|\\
rho(G)| ≤ 3\\sigma(G)$ holds for every finite group G\, and that $|\\rho
(G)| ≤ 2\\sigma(G)$ if $G$ is solvable. In this talk we will discuss som
e recent developments in the study of Huppert’s conjecture\, obtained in
a joint work with Z. Akhlaghi and S. Dolfi.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Martínez (Universitat de València (Spain))
DTSTART:20210330T142000Z
DTEND:20210330T144500Z
DTSTAMP:20260404T094531Z
UID:FGV/23
DESCRIPTION:Title: On the order of products of elements in finite groups\nby Juan Mar
tínez (Universitat de València (Spain)) as part of Finite Groups in Val
encia\n\n\nAbstract\nIt was proved by B. Baumslag and J. Wiegold that a fi
nite group $G$ is nilpotent if and only if $o(x)o(y)=o(xy)$ for every pair
of elements $x\,y$ of coprime order. In this talk\, we will present sever
al theorems that generalize this result.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenio Giannelli (Università degli Studi di Firenze (Italy))
DTSTART:20210330T145000Z
DTEND:20210330T153500Z
DTSTAMP:20260404T094531Z
UID:FGV/24
DESCRIPTION:Title: On a Conjecture of Malle and Navarro\nby Eugenio Giannelli (Univer
sità degli Studi di Firenze (Italy)) as part of Finite Groups in Valencia
\n\n\nAbstract\nLet $G$ be a finite group and let $P$ be a Sylow subgroup
of $G$. In 2012 Malle and Navarro conjectured that $P$ is normal in $G$ if
and only if the permutation character associated to the natural action of
$G$ on the cosets of $P$ has some specific structural properties. In rece
nt joint work with Law\, Long and Vallejo we prove this conjecture. In thi
s talk we will explain the main ideas involved in the proof. In particular
we will discuss the importance of studying Sylow Branching Coefficients i
n this context.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Martínez-Pastor (Universitat Politècnica de València (Spain
))
DTSTART:20210330T154000Z
DTEND:20210330T162500Z
DTSTAMP:20260404T094531Z
UID:FGV/25
DESCRIPTION:Title: Hall-like theorems in products of $\\pi$-decomposable groups\nby A
na Martínez-Pastor (Universitat Politècnica de València (Spain)) as par
t of Finite Groups in Valencia\n\n\nAbstract\nWe discuss in this talk some
Hall-like results for a finite group $G=AB$ which is the product of two $
\\pi$-decomposable subgroups $A = A_{\\pi}\\times A_{\\pi'}$ and $B=B_\\pi
\\times B_{\\pi'}$\, being $\\pi$ a set of odd primes. More concretely\, w
e show that such a group $G$ has a unique conjugacy class of Hall $\\pi$-s
ubgroups\, and any $\\pi$-subgroup is contained in a Hall $\\pi$-subgroup
(i.e. $G$ satisfies property $D_\\pi$).\n\n(Joint work with Lev S. Kazarin
and M. Dolores Pérez-Ramos.)\n
LOCATION:https://stable.researchseminars.org/talk/FGV/25/
END:VEVENT
END:VCALENDAR