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BEGIN:VEVENT
SUMMARY:Zeinab Akhlaghi (Amirkabir University of technology (Iran))
DTSTART;VALUE=DATE-TIME:20210226T143000Z
DTEND;VALUE=DATE-TIME:20210226T151500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/1
DESCRIPTION:Title: Char
acter degree graph and Huppert’s ρ-σ- conjecture\nby Zeinab Akhlag
hi (Amirkabir University of technology (Iran)) as part of Finite Groups in
Valencia\n\n\nAbstract\nCharacter Theory is one of the strong tools in th
e theory of finite groups\, and\, given a finite group $G$ the study of th
e set $\\mathrm {cd}(G)=\\{\\\,\\theta(1)\\\,|\\\,\\theta\\in \\mathrm{ Ir
r}(G)\\}$\, 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 character degre
e graph $\\Delta(G)$ is defined as the graph whose vertex set is the 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 to the e
dge set if and only if $pq$ divides an element in $\\mathrm{cd}(G)$. So fa
r\, many studies have been done on this graph. In this talk\, we will disc
uss the recent development obtained on this graph and finally focus on a n
ew result on Huppert’s $\\rho-\\sigma$ conjecture\, which is derived fr
om the recent development on this graph.\n
LOCATION:https://researchseminars.org/talk/FGV/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Álvaro L. Martínez (Columbia University (USA))
DTSTART;VALUE=DATE-TIME:20210226T152000Z
DTEND;VALUE=DATE-TIME:20210226T154500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/2
DESCRIPTION:Title: Symm
etric groups and the Heisenberg category\nby Álvaro L. Martínez (Col
umbia University (USA)) as part of Finite Groups in Valencia\n\n\nAbstract
\nWe will see how induction and restriction give an action of the Heisenbe
rg algebra on the category of representations of symmetric groups. We will
discuss how this inspired Khovanov’s definition of the Heisenberg categ
ory\, as well as some recent developments.\n
LOCATION:https://researchseminars.org/talk/FGV/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Vallejo (Universidad Carlos III de Madrid-ICMAT (Spain))
DTSTART;VALUE=DATE-TIME:20210226T155000Z
DTEND;VALUE=DATE-TIME:20210226T163500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/3
DESCRIPTION:Title: Prob
lems on characters involving two primes\nby Carolina Vallejo (Universi
dad Carlos III de Madrid-ICMAT (Spain)) as part of Finite Groups in Valenc
ia\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 $\\{p\,q\\}$ th
ere is some nontrivial irreducible character of $G$ whose degree is not di
visible by $p$ nor $q$. This result will allow us to characterize groups i
n which all irreducible characters of degree not divisible by $p$ nor $q$
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 $\\{p\, q\\}$'-degre
e. This talk is based in joint works with E Giannelli\, N. Hung and M. Sch
aeffer Fry.\n
LOCATION:https://researchseminars.org/talk/FGV/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio Marchi (University of Manchester (UK))
DTSTART;VALUE=DATE-TIME:20210226T164000Z
DTEND;VALUE=DATE-TIME:20210226T170500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/4
DESCRIPTION:Title: Pica
rd groups for blocks with normal defect groups\nby Claudio Marchi (Uni
versity of Manchester (UK)) as part of Finite Groups in Valencia\n\n\nAbst
ract\nLet $G$ be a finite group\, $B$ a $p$-block of $OG$\, $O$ a complete
DVR. The Picard group of $B$ is the group of auto-Morita equivalences of
$B$ and it revealed itself to be a useful tool\, for example for dealing w
ith 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\nI
n this talk we will give an introduction to Picard groups for blocks and t
hen present joint work with Livesey on blocks with normal defect groups\,
providing evidence to a conjecture on basic Morita equivalences.\n
LOCATION:https://researchseminars.org/talk/FGV/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changguo Shao (University of Jinan (China))
DTSTART;VALUE=DATE-TIME:20210305T143000Z
DTEND;VALUE=DATE-TIME:20210305T151500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/5
DESCRIPTION:Title: Grou
ps in which the centralizer of any non-central primary element is maximal<
/a>\nby Changguo Shao (University of Jinan (China)) as part of Finite Grou
ps in Valencia\n\n\nAbstract\nIn this talk\, we investigate the structure
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\, Xianh
e\; 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 focused on
the centralizers of primary elements in finite simple groups.\n
LOCATION:https://researchseminars.org/talk/FGV/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pietro Gheri (Università degli Studi di Firenze (Italy))
DTSTART;VALUE=DATE-TIME:20210305T152000Z
DTEND;VALUE=DATE-TIME:20210305T154500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/6
DESCRIPTION:Title: On t
he number of $p$-elements in finite groups\nby Pietro Gheri (Universit
à degli Studi di Firenze (Italy)) as part of Finite Groups in Valencia\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 order of
a Sylow $p$-subgroup of $G$. Frobenius proved that this ratio is always a
n integer\, but no combinatorial interpretation of this number seems to be
known.\n\nWe will talk about the search for a lower bound on this ratio i
n terms of the number of Sylow $p$-subgroups of $G$.\n
LOCATION:https://researchseminars.org/talk/FGV/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damiano Rossi (Bergische Universität Wuppertal (Germany))
DTSTART;VALUE=DATE-TIME:20210305T155000Z
DTEND;VALUE=DATE-TIME:20210305T161500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/7
DESCRIPTION:Title: Char
acter Triple Conjecture for Groups of Lie Type\nby Damiano Rossi (Berg
ische Universität Wuppertal (Germany)) as part of Finite Groups in Valenc
ia\n\n\nAbstract\nDade’s Conjecture is an important conjecture in repres
entation theory of finite groups. It implies most of the\, so called\, glo
bal-local conjectures. In 2017\, Späth introduced a strengthening of Dade
’s Conjecture\, called the Character Triple Conjecture\, which describes
the Clifford theory of corresponding characters. Moreover\, she proved a
reduction theorem\, namely that if her conjecture holds for every quasisim
ple group\, then Dade’s Conjecture holds for every finite group. Extend
ing ideas of Broué\, Fong and Srinivasan we provide a strategy to prove t
he Character Triple Conjecture for quasisimple groups of Lie type in the n
ondefining characteristic.\n
LOCATION:https://researchseminars.org/talk/FGV/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mandi Schaeffer Fry (Metropolitan State University of Denver (USA)
)
DTSTART;VALUE=DATE-TIME:20210305T162000Z
DTEND;VALUE=DATE-TIME:20210305T170500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/8
DESCRIPTION:Title: The
McKay-Navarro Conjecture: the Conjecture That Keeps on Giving!\nby Man
di Schaeffer Fry (Metropolitan State University of Denver (USA)) as part o
f Finite Groups in Valencia\n\n\nAbstract\nThe McKay conjecture is one of
the main open conjectures in the realm of the local-global philosophy in c
haracter theory. It posits a bijection between the set of irreducible cha
racters of a group with $p'$-degree and the corresponding set in the norma
lizer of a Sylow p-subgroup. In this talk\, I’ll give an overview of a r
efinement of the McKay conjecture due to Gabriel Navarro\, which brings th
e action of Galois automorphisms into the picture. A lot of recent work h
as been done on this conjecture\, but possibly even more interesting is th
e amount of information it yields about the character table of a finite gr
oup. I’ll discuss some recent results on the McKay—Navarro conjecture
\, as well as some of the implications the conjecture has had for other in
teresting character-theoretic problems.\n
LOCATION:https://researchseminars.org/talk/FGV/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Miquel Martínez (Universitat de València (Spain))
DTSTART;VALUE=DATE-TIME:20210312T155000Z
DTEND;VALUE=DATE-TIME:20210312T161500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/9
DESCRIPTION:Title: Degr
ees of characters in the principal block\nby J. Miquel Martínez (Univ
ersitat de València (Spain)) as part of Finite Groups in Valencia\n\n\nAb
stract\nLet $G$ be a finite group and let $p$ be a prime. The set of compl
ex irreducible characters in the principal $p$-block of $G$ is rich enough
that their degrees encode information of the structure of the group $G$.
We study the case where the set of degrees of characters in the principal
$p$-block of $G$ has size at most $2$\, finding information about the stru
cture of $G$ and its Sylow $p$-subgroups. We will also show some related r
esults on similar problems for arbitrary $p$-blocks.\n
LOCATION:https://researchseminars.org/talk/FGV/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Grittini (Università degli Studi di Firenze (Italy))
DTSTART;VALUE=DATE-TIME:20210312T152000Z
DTEND;VALUE=DATE-TIME:20210312T154500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/10
DESCRIPTION:Title: The
generalization of a theorem on real valued characters\nby Nicola Grit
tini (Università degli Studi di Firenze (Italy)) as part of Finite Group
s in Valencia\n\n\nAbstract\nThe Theorem of Ito-Michler\, one of the most
celebrated results in character theory of finite groups\, states that a gr
oup has a normal abelian Sylow $p$-subgroup if and only if the prime numbe
r $p$ does not divide the degree of any irreducible character of the group
.\n\nAmong the many variants of the theorem\, there exists one\, due to Do
lfi\, Navarro and Tiep\, which involves only the real valued irreducible c
haracters of the group\, and the prime number $p = 2$.\n\nThis variant\, h
owever\, fails if we consider a prime number different from 2\, and any ge
neralization in this direction seems hard\, due to some specific propertie
s of real valued characters.\n\nThis talk proposes a new way to approach t
he problem\, which takes into account a different subset of the irreducibl
e characters\, however related with real valued characters. This new appro
ach has already been partially successful and it may suggest a way to gene
ralize also other similar results.\n
LOCATION:https://researchseminars.org/talk/FGV/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nguyen Ngoc Hung (University of Akron (USA))
DTSTART;VALUE=DATE-TIME:20210312T162000Z
DTEND;VALUE=DATE-TIME:20210312T170500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/11
DESCRIPTION:Title: Bou
nding $p$-regular conjugacy classes and $p$-Brauer characters in finite gr
oups\nby Nguyen Ngoc Hung (University of Akron (USA)) as part of Finit
e Groups in Valencia\n\n\nAbstract\nWe discuss two closely related problem
s on bounding the number of $p$-regular conjugacy classes of a finite grou
p $G$ 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 $p$-elements of
$G$. This and the celebrated Alperin weight conjecture imply the same boun
d for the number of irreducible $p$-Brauer characters in the principal $p$
-block of $G$. We also discuss the bounds in the minimal situation when $G
$ has a unique class of nontrivial $p$-elements\, which have applications
to the study of principal blocks with few characters. The talk is based on
joint works with A. Moretó\, with A. Maroti\, and with B. Sambale and P.
H. Tiep.\n
LOCATION:https://researchseminars.org/talk/FGV/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zinovy Reichstein (University of British Columbia (Canada))
DTSTART;VALUE=DATE-TIME:20210312T171000Z
DTEND;VALUE=DATE-TIME:20210312T175500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/12
DESCRIPTION:Title: Fie
lds of definition for linear representations\nby Zinovy Reichstein (Un
iversity of British Columbia (Canada)) as part of Finite Groups in Valenci
a\n\n\nAbstract\nA classical theorem of Richard Brauer asserts that every
finite-dimensional non-modular representation $\\rho$ of a finite group $G
$ defined over a field $K$\, whose character takes values in $k$\, descend
s to $k$\, provided that $k$ has suitable roots of unity. If $k$ does not
contain these roots of unity\, it is natural to ask how far $\\rho$ is fro
m being definable over $k$. The classical answer to this question is 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 t
alk\, based on joint work with Nikita Karpenko\, Julia Pevtsova and Dave B
enson\, I will discuss another invariant\, the essential dimension of $\\r
ho$\, which measures ''how far'' $\\rho$ is from being definable over $k$
in a different way by using transcendental\, rather than algebraic field e
xtensions. I will also talk about recent results of Federico Scavia on ess
ential dimension of representations of algebras.\n
LOCATION:https://researchseminars.org/talk/FGV/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvio Dolfi (Università degli Studi di Firenze (Italy))
DTSTART;VALUE=DATE-TIME:20210316T144000Z
DTEND;VALUE=DATE-TIME:20210316T151500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/16
DESCRIPTION:Title: $p$
-constant characters in finite groups\nby Silvio Dolfi (Università de
gli Studi di Firenze (Italy)) as part of Finite Groups in Valencia\n\n\nAb
stract\nLet $p$ be a prime number\; an irreducible character of a finite g
roup $G$ is called $p$-constant if it takes a constant value on all the el
ements of G whose order is divisible by $p$ ($p$-singular elements). Irred
ucible characters of $p$-defect zero are\, by a classical result or R. Bra
uer\, an important instance of this class of characters: they take value z
ero on every $p$-singular element. I will present some results on faithfu
l $p$-constant characters of 'positive defect'\; in particular\, a charact
erization of the finite $p$-solvable groups having a character of this ty
pe (joint work with E. Pacifici and L. Sanus).\n
LOCATION:https://researchseminars.org/talk/FGV/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noelia Rizo (Universitat de València (Spain))
DTSTART;VALUE=DATE-TIME:20210316T152000Z
DTEND;VALUE=DATE-TIME:20210316T154500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/17
DESCRIPTION:Title: Cou
nting characters in blocks\nby Noelia Rizo (Universitat de València (
Spain)) as part of Finite Groups in Valencia\n\n\nAbstract\nLet $G$ be a f
inite 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 the knowl
edge of some aspects of $B$ is a main area in character theory of finite g
roups. 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 trivial. It
is also true that $k(B)=2$ if\, and only if\, $|D|=2$. For blocks $B$ wit
h $k(B)=3$ it is conjectured that $|D|=3$. \n\nIn this talk we restrict ou
r 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\, by work o
f Belonogov\, Koshitani and Sakurai we know the structure of $D$ when $k(B
_0(G))=3$ or $4$. In this work\, we go one step further and analyze the st
ructure of D when $k(B_0(G))=5$. \n\nThis is a joint work with Mandi Schae
ffer Fry and Carolina Vallejo.\n
LOCATION:https://researchseminars.org/talk/FGV/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Camina (University of Cambridge (UK))
DTSTART;VALUE=DATE-TIME:20210316T155000Z
DTEND;VALUE=DATE-TIME:20210316T163500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/18
DESCRIPTION:Title: Wor
d problems for finite nilpotent groups\nby Rachel Camina (University o
f Cambridge (UK)) as part of Finite Groups in Valencia\n\n\nAbstract\nWe c
onsider word maps on finite nilpotent groups and count the sizes of the fi
bres for elements in the image. We consider Amit’s conjecture and its ge
neralisation\, which say that these fibres should have size at least $|G^{
(k−1)}|$ where the word is on $k$ variables. This is joint work with Ain
hoa Iñiguez and Anitha Thillaisundaram.\n
LOCATION:https://researchseminars.org/talk/FGV/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carmen Melchor (Universitat de València)
DTSTART;VALUE=DATE-TIME:20210316T164000Z
DTEND;VALUE=DATE-TIME:20210316T170500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/19
DESCRIPTION:Title: An
Arad and Fisman's theorem on products of conjugacy classes revisited\n
by Carmen Melchor (Universitat de València) as part of Finite Groups in V
alencia\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FGV/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuele Pacifici (Università degli Studi di Milano (Italy))
DTSTART;VALUE=DATE-TIME:20210330T133000Z
DTEND;VALUE=DATE-TIME:20210330T141500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/22
DESCRIPTION:Title: On
Huppert’s $\\rho-\\sigma$ conjecture\nby Emanuele Pacifici (Universi
tà degli Studi di Milano (Italy)) as part of Finite Groups in Valencia\n\
n\nAbstract\nThe set of the degrees of the irreducible complex characters
of a finite group $G$ has been an object of considerable interest since th
e second part of the 20th century\, and the study of the arithmetical stru
cture of this set is a particularly intriguing aspect of Character Theory
of finite groups. A remarkable question in this research area was posed by
B. Huppert in the 80’s: is it true that at least one of the character d
egrees is divisible by a ”large” portion of the entire set of primes t
hat appear as divisors of some character degree? More precisely\, denoting
by $\\rho(G)$ the set of primes that divide some character degree\, and b
y $\\sigma(G)$ the largest number of primes that divide a single character
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 some rec
ent developments in the study of Huppert’s conjecture\, obtained in a jo
int work with Z. Akhlaghi and S. Dolfi.\n
LOCATION:https://researchseminars.org/talk/FGV/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Martínez (Universitat de València (Spain))
DTSTART;VALUE=DATE-TIME:20210330T142000Z
DTEND;VALUE=DATE-TIME:20210330T144500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/23
DESCRIPTION:Title: On
the order of products of elements in finite groups\nby Juan Martínez
(Universitat de València (Spain)) as part of Finite Groups in Valencia\n
\n\nAbstract\nIt was proved by B. Baumslag and J. Wiegold that a finite gr
oup $G$ is nilpotent if and only if $o(x)o(y)=o(xy)$ for every pair of ele
ments $x\,y$ of coprime order. In this talk\, we will present several theo
rems that generalize this result.\n
LOCATION:https://researchseminars.org/talk/FGV/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenio Giannelli (Università degli Studi di Firenze (Italy))
DTSTART;VALUE=DATE-TIME:20210330T145000Z
DTEND;VALUE=DATE-TIME:20210330T153500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/24
DESCRIPTION:Title: On
a Conjecture of Malle and Navarro\nby Eugenio Giannelli (Università d
egli Studi di Firenze (Italy)) as part of Finite Groups in Valencia\n\n\nA
bstract\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 on
ly if the permutation character associated to the natural action of $G$ on
the cosets of $P$ has some specific structural properties. In recent join
t work with Law\, Long and Vallejo we prove this conjecture. In this talk
we will explain the main ideas involved in the proof. In particular we wil
l discuss the importance of studying Sylow Branching Coefficients in this
context.\n
LOCATION:https://researchseminars.org/talk/FGV/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Martínez-Pastor (Universitat Politècnica de València (Spain
))
DTSTART;VALUE=DATE-TIME:20210330T154000Z
DTEND;VALUE=DATE-TIME:20210330T162500Z
DTSTAMP;VALUE=DATE-TIME:20240522T215334Z
UID:FGV/25
DESCRIPTION:Title: Hal
l-like theorems in products of $\\pi$-decomposable groups\nby Ana Mart
ínez-Pastor (Universitat Politècnica de València (Spain)) as part of Fi
nite Groups in Valencia\n\n\nAbstract\nWe discuss in this talk some Hall-l
ike results for a finite group $G=AB$ which is the product of two $\\pi$-d
ecomposable subgroups $A = A_{\\pi}\\times A_{\\pi'}$ and $B=B_\\pi\\times
B_{\\pi'}$\, being $\\pi$ a set of odd primes. More concretely\, we show
that such a group $G$ has a unique conjugacy class of Hall $\\pi$-subgroup
s\, 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://researchseminars.org/talk/FGV/25/
END:VEVENT
END:VCALENDAR