BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Priyavrat Deshpande (Chennai Mathematical Institute)
DTSTART:20200715T053000Z
DTEND:20200715T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/1
DESCRIPTION:Title: The Combinatorics of Counting Faces of a Hyperplane Arrangement\n
by Priyavrat Deshpande (Chennai Mathematical Institute) as part of Applica
tions of Combinatorics in Algebra\, Topology and Graph Theory\n\n\nAbstrac
t\nAn arrangement of hyperplanes is a finite collection of hyperplanes in
a vector space. In the case of a Euclidean space the arrangement describes
a stratification where each stratum\, also called a face\, is a convex su
bset. It is a classical problem to determine the number of various-dimensi
onal faces in terms of the combinatorics of intersection of hyperlpanes. I
n this talk I will focus on a class of arrangements called rational arrang
ements and explain the finite field method which helps count the codimensi
on-$0$ strata. With the help of many examples I will demonstrate how vario
us combinatorial techniques play an important role in this counting proble
m. This talk is self-contained and mainly a survey of interesting results
in the field.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sajith P. (Indian Institute of Sciences)
DTSTART:20200722T053000Z
DTEND:20200722T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/2
DESCRIPTION:Title: Distinguishing coloring and its variants\nby Sajith P. (Indian In
stitute of Sciences) as part of Applications of Combinatorics in Algebra\,
Topology and Graph Theory\n\n\nAbstract\nA $k$-coloring of vertices of a
graph $G$ is said to be $k$-distinguishing if no nontrivial automorphism o
f the graph preserves all the color classes. The minimum positive integer
$k$ needed to have a $k$-distinguishing coloring of a graph $G$ is called
distinguishing number of $G$ and is denoted by $D(G)$. This coloring was
introduced by Albertson and Collinns in 1996 (https://www.combinatorics.or
g/ojs/index.php/eljc/article/view/v3i1r18). There are more than 300 resear
ch articles in this area by now. I will discuss about distinguishing color
ing of certain graphs and some of the variants of distinguishing coloring.
\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Biplab Basak (Indian Institute of Technology Delhi)
DTSTART:20200729T053000Z
DTEND:20200729T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/3
DESCRIPTION:Title: Three-dimensional normal pseudomanifolds with relatively few edges\nby Biplab Basak (Indian Institute of Technology Delhi) as part of Appli
cations of Combinatorics in Algebra\, Topology and Graph Theory\n\n\nAbstr
act\nFrom the Lower Bound Theorem\, we know that if $\\Delta$ is a $d$-dim
ensional normal pseudomanifold then $g_2(\\Delta):= f_1(\\Delta)-(d+1)f_0
(\\Delta) + \\binom{d+2}{2}\\geq 0$ and equality holds if and only if $\\D
elta$ is a stacked sphere for $d\\geq 3$. Thus\, Lower Bound Theorem class
ifies normal pseudomanifolds of dimension $d\\geq 3$ with $g_2=0$. Later\,
Nevo and Novinsky have classified homology $d$-spheres with $g_2=1$ for
$d\\geq 3$. Zheng has shown that homology manifolds of dimension $d\\ge
q 3$ with $g_2=2$ are polytopal spheres. From the works of Kalai and Foge
lsanger it follows that $g_2(\\Delta) \\geq g_2({\\rm lk}(v\, \\Delta))$
for any vertex $v$ of $\\Delta$.\n\nIn this talk\, I shall show that the
topological and combinatorial classification of normal $3$-pseudomanifold
s $\\Delta$ when $\\Delta$ has at most two singularity and $g_2(\\Delta) =
g_2({\\rm lk}(v\, \\Delta))$ for some vertex $v$ of $\\Delta$. In particu
lar\, I shall show that normal $3$-pseudomanifolds with $g_2=3$ are eit
her sphere or suspension of $\\mathbb{RP}^2$.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Venkitesh (Indian Institute of Technology Bombay)
DTSTART:20200812T053000Z
DTEND:20200812T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/4
DESCRIPTION:Title: A Tour of Chip-firing Games\nby S. Venkitesh (Indian Institute of
Technology Bombay) as part of Applications of Combinatorics in Algebra\,
Topology and Graph Theory\n\n\nAbstract\nThe term `chip-firing' can now be
used to refer to any among a plethora of variants of a game\, which\, in
its simplest form\, is a discrete dynamical system with chips placed at th
e vertices of a connected graph\, with the vertices being allowed to fire
and send its chips to its neighbouring vertices\, provided some degree con
ditions are met. Originating in the work of Bj{\\"o}rner\, Lov{\\'a}sz an
d Shor (1991) (in the context of graphs) and Bak\, Tang and Weisenfeld (19
87) and Dhar (1999) (in the context of abelian sandpile models)\, there is
now a rich literature on several variants of the game\, spanning both its
algebraic and combinatorial aspects.\n\nWe will have an overview of some
recent work on `chip-firing'\, with a focus on its combinatorial connectio
ns with other ideas.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiranya Kishore Dey (Indian Institute of Technology Bombay)
DTSTART:20200805T053000Z
DTEND:20200805T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/5
DESCRIPTION:Title: On the determining number of Kneser graphs\nby Hiranya Kishore De
y (Indian Institute of Technology Bombay) as part of Applications of Combi
natorics in Algebra\, Topology and Graph Theory\n\n\nAbstract\nThe determi
ning number of a graph $G = (V\,E)$ is the minimum cardinality of a set $S
\\subseteq V$ such that pointwise stabilizer of $S$ under the action of $A
ut(G)$ is trivial. In this talk\, we will discuss on some improved upper a
nd lower bounds on the determining number of Kneser graphs. Moreover\, we
provide the exact value of the determining number for some subfamilies of
Kneser graphs. Finally\, we show that the number of Kneser graphs with a g
iven determining number $r$ is an increasing function of $r$.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dharm Veer (Chennai Mathematical Institute)
DTSTART:20200819T053000Z
DTEND:20200819T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/6
DESCRIPTION:Title: On h-Polynomials of Hibi rings\nby Dharm Veer (Chennai Mathematic
al Institute) as part of Applications of Combinatorics in Algebra\, Topolo
gy and Graph Theory\n\n\nAbstract\nLet $L$ be a finite distributive lattic
e. By a theorem of Birkhoff\, $L$ is the ideal lattice $\\mathcal{I}(P)$ o
f its subposet $P$ of join-irreducible elements. Let $P=\\{p_1\,\\ldots\,p
_n\\}$ and let $R=K[t\,z_1\,\\ldots\,z_n]$ be the polynomial ring in $n+1$
variables over a field $K.$ The {\\em Hibi ring} associated with $L$\, de
noted by $R[L]$\, is the subring of $R$ generated by the monomials $u_{\
\alpha}=t\\prod_{p_i\\in \\alpha}z_i$ where $\\alpha\\in L$. In this talk
we will state the Charney–Davis-Stanley(CDS) conjecture and we will prov
e that CDS conjecture is true for all Gorenstein Hibi rings of regularity
$4$.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navnath Daundkar (Chennai Mathematical Institute)
DTSTART:20200826T053000Z
DTEND:20200826T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/7
DESCRIPTION:Title: Asphericity of chain spaces\nby Navnath Daundkar (Chennai Mathema
tical Institute) as part of Applications of Combinatorics in Algebra\, Top
ology and Graph Theory\n\n\nAbstract\nThe moduli space of chains (i.e. pie
ce-wise linear paths) in the plane with generic side lengths is a smooth\,
closed manifold. It turns out that this manifold has a natural action of
discrete torus such that the quotient under this action is a simple polyt
ope\, making it into a small cover (in fact a real toric variety). In this
talk I will show that in every dimension there are three length vectors f
or which the moduli space is aspherical. If time permits I will also show
that the quotient polytope depends only on the combinatorial data\, called
the genetic code of the length vector. This is ongoing work with my advis
er Priyavrat Deshpande.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K Somasundaram (Amrita Vishwa Vidyapeetham\, Coimbatore)
DTSTART:20200909T053000Z
DTEND:20200909T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/8
DESCRIPTION:Title: Combinatorial Matrix Theory\nby K Somasundaram (Amrita Vishwa Vid
yapeetham\, Coimbatore) as part of Applications of Combinatorics in Algebr
a\, Topology and Graph Theory\n\n\nAbstract\nThe following will be part of
my talk: 1. Introduction to permanents\, 2. Permanents and graphs\, 3. So
me conjectures in permanents\, like Lie-wang conjecture\, permanent domina
nce conjecture..\,\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manjil Saikia (Cardiff University)
DTSTART:20200923T053000Z
DTEND:20200923T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/9
DESCRIPTION:Title: Refined enumeration of symmetry classes of Alternating Sign Matrices<
/a>\nby Manjil Saikia (Cardiff University) as part of Applications of Comb
inatorics in Algebra\, Topology and Graph Theory\n\n\nAbstract\nThe sequen
ce $1\,1\,2\,7\,42\,429\, \\ldots$ counts several combinatorial objects\,
some of which I will describe in this talk. The major focus would be one o
f these objects\, alternating sign matrices (ASMs). ASMs are square matric
es with entries in the set $\\{0\,1\,-1\\}$\, where non-zero entries alter
nate in sign along rows and columns\, with all row and column sums being 1
. I will discuss some questions that are central to the theme of ASMs\, ma
inly dealing with their enumeration. In particular we shall prove some con
jectures of Fischer\, Robbins and Duchon. This is based on joint work with
Ilse Fischer.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eshita Mazumdar (ISI Bangalore)
DTSTART:20200930T053000Z
DTEND:20200930T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/10
DESCRIPTION:Title: Iterated sumsets and Hilbert functions\nby Eshita Mazumdar (ISI
Bangalore) as part of Applications of Combinatorics in Algebra\, Topology
and Graph Theory\n\n\nAbstract\nLet $A$ be a finite subset of an abelian g
roup $(G\,+)$. Let $h \\ge 2$ be an integer. If $|A| \\ge 2$ and the cardi
nality $|hA|$ of the $h$-fold iterated sumset $hA=A+\\dots+A$ is known\, w
hat can one say about $|(h-1)A|$ and $|(h+1)A|$? It is known that $$|(h-1)
A| \\ge |hA|^{(h-1)/h}\,$$ a consequence of Pl\\"unnecke's inequality. we
improved this bound with a new approach. Namely\, we model the sequence $|
hA|_{h \\ge 0}$ with the Hilbert function of a standard graded algebra. We
then apply Macaulay's 1927 theorem on the growth of Hilbert functions\, a
nd more specifically a recent condensed version of it. Our bound implies $
$|(h-1)A| \\ge \\theta(x\,h)\\hspace{0.4mm}|hA|^{(h-1)/h}$$ for some facto
r $\\theta(x\,h) > 1$\, where $x$ is a real number closely linked to $|hA|
$. Moreover\, we show that $\\theta(x\,h)$ asymptotically tends to $e\\app
rox 2.718$ as $|A|$ grows and $h$ lies in a suitable range varying with $|
A|$. This is a joint work with Prof. Shalom Eliahou.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samir Shukla (Indian Institute of Technology Bombay)
DTSTART:20200916T053000Z
DTEND:20200916T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/11
DESCRIPTION:Title: Higher independence complexes of graphs\nby Samir Shukla (Indian
Institute of Technology Bombay) as part of Applications of Combinatorics
in Algebra\, Topology and Graph Theory\n\n\nAbstract\nIn 2006\, Szabó and
Tardos generalized the concept of independence complex by defining $r$-in
dependence complex of a graph $G$ for any $r \\geq 1$. Independence compl
exes have applications in several areas. The topology of independence com
plex is related to many combinatorial properties of the underlined graph.
The $r$-independence complex of $G$\, denoted Ind$_r(G)$\, is the simpli
cial complex whose simplices are those subsets $I \\subseteq V(G)$ such th
at each connected component of the induced subgraph $G[I]$ has at most $r$
vertices.\n\nIn this talk\, we give a lower bound for the distance $r$-do
mination number of the graph $G$ (which is a very well studied notion in g
raph theory and a natural generalization of the domination number of the g
raph) in terms of the homological connectivity of the Ind$_r(G)$. We also
prove that Ind$_r(G)$\, for a chordal graph $G$\, is either contractible o
r homotopy equivalent to a wedge of spheres. Given a wedge of spheres\, we
also provide a construction of a chordal graph whose $r$-independence com
plex has the homotopy type of the given wedge. This is a joint work with A
nurag Singh and Priyavrat Deshpande.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvind Kumar (IIT Delhi)
DTSTART:20201007T053000Z
DTEND:20201007T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/12
DESCRIPTION:Title: Regularity of binomial edge ideals\nby Arvind Kumar (IIT Delhi)
as part of Applications of Combinatorics in Algebra\, Topology and Graph T
heory\n\n\nAbstract\nThis talk is going to be about the regularity of bino
mial edge ideals. We will\ndiscuss a combinatorial proof of regularity upp
er bound for binomial edge ideals given by\nMatsuda and Murai. There are t
wo regularity upper bound conjectures for binomial edge\nideals. We will b
e discussing these two conjectures. Saeedi Madani and Kiani conjectured\nt
hat the regularity of the binomial edge ideal of a graph is bounded above
by the number\nof cliques of that graph. Hibi and Matsuda conjectured that
the regularity of the binomial\nedge ideal of a graph is bounded above by
the degree of h polynomial of that graph.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Dochtermann (Texas State University)
DTSTART:20201021T140000Z
DTEND:20201021T150000Z
DTSTAMP:20260404T111108Z
UID:CATGT/13
DESCRIPTION:Title: Shellings\, chordality\, and Simon's conjecture\nby Anton Dochte
rmann (Texas State University) as part of Applications of Combinatorics in
Algebra\, Topology and Graph Theory\n\n\nAbstract\nA simplicial complex X
is "shellable" if there exists an ordering of its facets that satisfies n
ice intersection properties. Shellability imposes strong topological and a
lgebraic conditions on X and its Stanley-Reisner ring\, and has been an im
portant tool in geometric and algebraic combinatorics. Examples of shella
ble complexes include boundaries of simplicial polytopes and the independe
nce complex of matroids. In general it is difficult (NP hard) to determin
e if a given complex is shellable\, and X is said to be "extendably shella
ble" if a greedy algorithm always succeeds. A conjecture of Simon posits
that the k-skeleton of a simplex on vertex set [n] is extendably shellable
. \n\nSimon's conjecture has been established for k=2 but until recently
all other nontrivial cases were open. We show how the case k=n-3 follows f
rom an application of chordal graphs and the notion of "exposed edges"\, a
nd in fact prove that any shellable d-dimensional complex on at most d+3 v
ertices is extendably shellable. This leads to a notion of higher-dimensi
onal chordality which connects Simon's conjecture to tools in commutative
algebra and simple homotopy theory. We also explore other cases of Simon's
conjecture and for instance prove that any vertex decomposable complex ca
n be completed to a shelling of a simplex skeleton. Parts of this are join
t work with Culertson\, Guralnik\, Stiller\, and Oh.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcin Wrochna (University of Oxford)
DTSTART:20201028T103000Z
DTEND:20201028T113000Z
DTSTAMP:20260404T111108Z
UID:CATGT/14
DESCRIPTION:Title: Understanding homomorphism approximation problems using topology
\nby Marcin Wrochna (University of Oxford) as part of Applications of Comb
inatorics in Algebra\, Topology and Graph Theory\n\n\nAbstract\nWe conside
r an approximation version of the graph colouring computational problem: c
an we efficiently distinguish a 3-colourable graph from a graph that is no
t even 100-colourable? More generally\, given a structure that is promised
to have a homomorphism to G\, can we at least find a (much weaker) homomo
rphism to H? This is an ages-old question in which we recently made some s
urprising progress using topology and algebra\, e.g. studying maps from a
torus to a sphere\, or looking at some adjoint functors in the category of
graphs. I will introduce all necessary basics to explain these unexpected
connections. Joint work with Andrei Krokhin\, Jakub Opršal\, and Standa
Živný.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Narayanan N (IIT Madras)
DTSTART:20201014T053000Z
DTEND:20201014T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/15
DESCRIPTION:Title: Shitov's counterexample to Hedetniemi's conjecture\nby Narayanan
N (IIT Madras) as part of Applications of Combinatorics in Algebra\, Topo
logy and Graph Theory\n\n\nAbstract\nWe give a sketch of the construction
of Shitov's counterexamples to Hedetniemi's conjecture and some of the mo
re recent developments.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amit Roy (IISER Mohali)
DTSTART:20201104T053000Z
DTEND:20201104T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/16
DESCRIPTION:Title: Standard monomials of $1$-skeleton ideal of a graph\nby Amit Roy
(IISER Mohali) as part of Applications of Combinatorics in Algebra\, Topo
logy and Graph Theory\n\n\nAbstract\nLet $G$ be a (multi) graph on the ver
tex set $V=\\{0\,1\,\\ldots \,n\\}$ with root $0$. The $G$-parking functio
n ideal $\\M_G$ is a monomial ideal in the polynomial ring $R=\\mathbb{K}[
x_1\,\\ldots \,x_n]$ over a field $\\mathbb{K}$ such that dim$_{\\mathbb{K
}}\\big(\\frac{R}{\\mathcal{M}_G}\\big)$ $=\\det\\left(\\widetilde{L}_G\\r
ight)$\, where $\\widetilde{L}_G$ is the truncated Laplace matrix of $G$.
In other words\, standard monomials of the Artinian quotient $\\frac{R}{M_
G}$ correspond bijectively with the spanning trees of $G$. For $0\\leq k\\
leq n-1$\, the $k$-skeleton ideal $\\mathcal{M}_G^{(k)}$ of $G$ is a monom
ial subideal $\\mathcal{M}_G^{(k)}=\\left\\langle m_A:\\emptyset\\neq A\\s
ubseteq[n]\\text{ and }|A|\\leq k+1\\right\\rangle$ of the $G$-parking fun
ction ideal $\\mathcal{M}_G=\\left\\langle m_A:\\emptyset\\neq A\\subseteq
[n]\\right\\rangle\\subseteq R$. In this talk we will focus on the $1$-ske
leton ideal $\\mathcal{M}_G^{(1)}$ of a graph $G$ and see how the number o
f standard monomials of $\\frac{R}{\\mathcal{M}_G^{(1)}}$ is related to th
e truncated signless Laplace matrix $\\Q_G$ of $G$. This is based on joint
work with Chanchal Kumar and Gargi Lather.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arindam Banerjee (Ramakrishna Mission Vivekananda Educational and
Research Institute)
DTSTART:20201111T053000Z
DTEND:20201111T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/17
DESCRIPTION:Title: Edge Ideals of Graphs and Their resolutions\nby Arindam Banerjee
(Ramakrishna Mission Vivekananda Educational and Research Institute) as p
art of Applications of Combinatorics in Algebra\, Topology and Graph Theor
y\n\n\nAbstract\nIn this talk we shall introduce the notion of the edge id
eals of a finite simple graphs. The study of the minimal free resolutions
of these ideals gave rise to many results where interplay between algebra
and combinatorics was the main essence. We shall discuss one such problem\
, namely for which graphs this resolution consists of linear maps.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:D. Yogeshwaran (ISI Bangalore)
DTSTART:20201112T053000Z
DTEND:20201112T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/18
DESCRIPTION:Title: Edge ideals of Random Graphs\nby D. Yogeshwaran (ISI Bangalore)
as part of Applications of Combinatorics in Algebra\, Topology and Graph T
heory\n\n\nAbstract\nIn this talk\, we shall look at four properties of ed
ge ideals of Erdos-Renyi random graphs. Namely\, we shall consider asympto
tics for linear resolution\, linear presentation\, regularity and unmixedn
ess. These properties have very explicit characterization in terms of grap
h-theoretic properties such as co-chordality\, induced matching number and
uniqueness of minimal vertex cover. In this talk\, we shall discuss asymp
totics for the latter properties of Erdos-Renyi random graphs and their co
nsequences for random edge ideals. Though the random graph theory results
will be stated in a self-contained manner\, the interest in these results
is due to their connection to edge ideals.\n\nEdge ideals and related noti
ons shall be introduced in Arindam Banerjee's talk on November 11th and I
shall only recall them very briefly. On the random graph side\, I shall as
sume knowledge of graph theory and basic probability.\n\nThe talk is based
on a joint work with Arindam Banerjee \; https://arxiv.org/abs/2007.08869
\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manisha Binjola (IIT Delhi)
DTSTART:20201118T053000Z
DTEND:20201118T063000Z
DTSTAMP:20260404T111108Z
UID:CATGT/19
DESCRIPTION:Title: On regular genus of PL 4-manifold with boundary\nby Manisha Binj
ola (IIT Delhi) as part of Applications of Combinatorics in Algebra\, Topo
logy and Graph Theory\n\n\nAbstract\nA crystallization of a PL $d$-manifol
d is a certain type of edge colored graph that represents the manifold. Ex
tending the notion of genus in dimension 2\, the notion of regular genus f
or a $d$-manifold has been introduced\, which is strictly related to the e
xistence of regular embeddings of crystallizations of manifold into surfac
es. The regular genus of a closed connected orientable (resp. non-orientab
le) surface coincides with its genus (resp. half of its genus)\, while the
regular genus of a closed connected 3-manifold coincides with its Heegaar
d genus. Let $M$ be a compact connected PL 4-manifold with boundary. In th
is talk\, I shall give lower bounds for regular genus of the manifold $M$.
In particular\, if $M$ is a connected compact PL $4$- manifold with $h$ b
oundary components then its regular genus $\\mathcal{G}(M)$ satisfies the
following inequalities: \n\n $\\mathcal{G}(M)\\geq 2\\chi(M)+3m+2h-4$ and
$\\mathcal{G}(M)\\geq \\mathcal{G}(\\partial M)+2\\chi(M)+2m+2h-4\,$\n\n
where $m$ is the rank of the fundamental group of the manifold $M$.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuanning Zhang (The University of California)
DTSTART:20201125T043000Z
DTEND:20201125T053000Z
DTSTAMP:20260404T111108Z
UID:CATGT/20
DESCRIPTION:Title: Filtering Grassmannian Cohomology via k-Schur Functions\nby Yuan
ning Zhang (The University of California) as part of Applications of Combi
natorics in Algebra\, Topology and Graph Theory\n\n\nAbstract\nThis talk c
oncerns the cohomology rings of complex Grassmannians. In $2003$\, Reiner
and Tudose conjectured the form of the Hilbert series for certain subalgeb
ras of these cohomology rings. We build on their work in two ways. First\,
we conjecture two natural bases for these subalgebras that would imply th
eir conjecture using notions from the theory of $k$-Schur functions. Secon
d\, we formulate an analogous conjecture for Lagrangian Grassmannians.\n
LOCATION:https://stable.researchseminars.org/talk/CATGT/20/
END:VEVENT
END:VCALENDAR