BEGIN:VCALENDAR
VERSION:2.0
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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Priyavrat Deshpande (Chennai Mathematical Institute)
DTSTART:20200715T053000Z
DTEND:20200715T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/1
DESCRIPTION:Title: Th
e Combinatorics of Counting Faces of a Hyperplane Arrangement\nby Priy
avrat Deshpande (Chennai Mathematical Institute) as part of Applications o
f Combinatorics in Algebra\, Topology and Graph Theory\n\n\nAbstract\nAn a
rrangement of hyperplanes is a finite collection of hyperplanes in a vecto
r space. In the case of a Euclidean space the arrangement describes a stra
tification where each stratum\, also called a face\, is a convex subset. I
t is a classical problem to determine the number of various-dimensional fa
ces in terms of the combinatorics of intersection of hyperlpanes. In this
talk I will focus on a class of arrangements called rational arrangements
and explain the finite field method which helps count the codimension-$0$
strata. With the help of many examples I will demonstrate how various comb
inatorial techniques play an important role in this counting problem. This
talk is self-contained and mainly a survey of interesting results in the
field.\n
LOCATION:https://researchseminars.org/talk/CATGT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sajith P. (Indian Institute of Sciences)
DTSTART:20200722T053000Z
DTEND:20200722T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/2
DESCRIPTION:Title: Di
stinguishing coloring and its variants\nby Sajith P. (Indian Institute
of Sciences) as part of Applications of Combinatorics in Algebra\, Topolo
gy 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 of the g
raph preserves all the color classes. The minimum positive integer $k$ ne
eded to have a $k$-distinguishing coloring of a graph $G$ is called distin
guishing number of $G$ and is denoted by $D(G)$. This coloring was introdu
ced by Albertson and Collinns in 1996 (https://www.combinatorics.org/ojs/i
ndex.php/eljc/article/view/v3i1r18). There are more than 300 research arti
cles in this area by now. I will discuss about distinguishing coloring of
certain graphs and some of the variants of distinguishing coloring.\n
LOCATION:https://researchseminars.org/talk/CATGT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Biplab Basak (Indian Institute of Technology Delhi)
DTSTART:20200729T053000Z
DTEND:20200729T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/3
DESCRIPTION:Title: Th
ree-dimensional normal pseudomanifolds with relatively few edges\nby B
iplab Basak (Indian Institute of Technology Delhi) as part of Applications
of Combinatorics in Algebra\, Topology and Graph Theory\n\n\nAbstract\nFr
om the Lower Bound Theorem\, we know that if $\\Delta$ is a $d$-dimensiona
l normal pseudomanifold then $g_2(\\Delta):= f_1(\\Delta)-(d+1)f_0(\\Delt
a) + \\binom{d+2}{2}\\geq 0$ and equality holds if and only if $\\Delta$ i
s a stacked sphere for $d\\geq 3$. Thus\, Lower Bound Theorem classifies n
ormal pseudomanifolds of dimension $d\\geq 3$ with $g_2=0$. Later\, Nevo a
nd Novinsky have classified homology $d$-spheres with $g_2=1$ for $d\\ge
q 3$. Zheng has shown that homology manifolds of dimension $d\\geq 3$ wi
th $g_2=2$ are polytopal spheres. From the works of Kalai and Fogelsanger
it follows that $g_2(\\Delta) \\geq g_2({\\rm lk}(v\, \\Delta))$ for an
y vertex $v$ of $\\Delta$.\n\nIn this talk\, I shall show that the topolog
ical and combinatorial classification of normal $3$-pseudomanifolds $\\De
lta$ when $\\Delta$ has at most two singularity and $g_2(\\Delta) = g_2({\
\rm lk}(v\, \\Delta))$ for some vertex $v$ of $\\Delta$. In particular\, I
shall show that normal $3$-pseudomanifolds with $g_2=3$ are either sph
ere or suspension of $\\mathbb{RP}^2$.\n
LOCATION:https://researchseminars.org/talk/CATGT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Venkitesh (Indian Institute of Technology Bombay)
DTSTART:20200812T053000Z
DTEND:20200812T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/4
DESCRIPTION:Title: A
Tour of Chip-firing Games\nby S. Venkitesh (Indian Institute of Techno
logy Bombay) as part of Applications of Combinatorics in Algebra\, Topolog
y and Graph Theory\n\n\nAbstract\nThe term `chip-firing' can now be used t
o refer to any among a plethora of variants of a game\, which\, in its sim
plest form\, is a discrete dynamical system with chips placed at the verti
ces of a connected graph\, with the vertices being allowed to fire and sen
d its chips to its neighbouring vertices\, provided some degree conditions
are met. Originating in the work of Bj{\\"o}rner\, Lov{\\'a}sz and Shor
(1991) (in the context of graphs) and Bak\, Tang and Weisenfeld (1987) 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 algebr
aic and combinatorial aspects.\n\nWe will have an overview of some recent
work on `chip-firing'\, with a focus on its combinatorial connections with
other ideas.\n
LOCATION:https://researchseminars.org/talk/CATGT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiranya Kishore Dey (Indian Institute of Technology Bombay)
DTSTART:20200805T053000Z
DTEND:20200805T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/5
DESCRIPTION:Title: On
the determining number of Kneser graphs\nby Hiranya Kishore Dey (Indi
an Institute of Technology Bombay) as part of Applications of Combinatoric
s in Algebra\, Topology and Graph Theory\n\n\nAbstract\nThe determining nu
mber of a graph $G = (V\,E)$ is the minimum cardinality of a set $S\\subse
teq V$ such that pointwise stabilizer of $S$ under the action of $Aut(G)$
is trivial. In this talk\, we will discuss on some improved upper and lowe
r 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 given de
termining number $r$ is an increasing function of $r$.\n
LOCATION:https://researchseminars.org/talk/CATGT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dharm Veer (Chennai Mathematical Institute)
DTSTART:20200819T053000Z
DTEND:20200819T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/6
DESCRIPTION:Title: On
h-Polynomials of Hibi rings\nby Dharm Veer (Chennai Mathematical Inst
itute) as part of Applications of Combinatorics in Algebra\, Topology and
Graph Theory\n\n\nAbstract\nLet $L$ be a finite distributive lattice. By a
theorem of Birkhoff\, $L$ is the ideal lattice $\\mathcal{I}(P)$ of its s
ubposet $P$ 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 $n+1$ variab
les over a field $K.$ The {\\em Hibi ring} associated with $L$\, denoted b
y $R[L]$\, 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 prove that
CDS conjecture is true for all Gorenstein Hibi rings of regularity $4$.\n
LOCATION:https://researchseminars.org/talk/CATGT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navnath Daundkar (Chennai Mathematical Institute)
DTSTART:20200826T053000Z
DTEND:20200826T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/7
DESCRIPTION:Title: As
phericity of chain spaces\nby Navnath Daundkar (Chennai Mathematical I
nstitute) as part of Applications of Combinatorics in Algebra\, Topology a
nd Graph Theory\n\n\nAbstract\nThe moduli space of chains (i.e. piece-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 discre
te torus such that the quotient under this action is a simple polytope\, m
aking 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 for whic
h the moduli space is aspherical. If time permits I will also show that th
e quotient polytope depends only on the combinatorial data\, called the ge
netic code of the length vector. This is ongoing work with my adviser Priy
avrat Deshpande.\n
LOCATION:https://researchseminars.org/talk/CATGT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K Somasundaram (Amrita Vishwa Vidyapeetham\, Coimbatore)
DTSTART:20200909T053000Z
DTEND:20200909T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/8
DESCRIPTION:Title: Co
mbinatorial Matrix Theory\nby K Somasundaram (Amrita Vishwa Vidyapeeth
am\, Coimbatore) as part of Applications of Combinatorics in Algebra\, Top
ology and Graph Theory\n\n\nAbstract\nThe following will be part of my tal
k: 1. Introduction to permanents\, 2. Permanents and graphs\, 3. Some conj
ectures in permanents\, like Lie-wang conjecture\, permanent dominance con
jecture..\,\n
LOCATION:https://researchseminars.org/talk/CATGT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manjil Saikia (Cardiff University)
DTSTART:20200923T053000Z
DTEND:20200923T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/9
DESCRIPTION:Title: Re
fined enumeration of symmetry classes of Alternating Sign Matrices\nby
Manjil Saikia (Cardiff University) as part of Applications of Combinatori
cs in Algebra\, Topology and Graph Theory\n\n\nAbstract\nThe sequence $1\,
1\,2\,7\,42\,429\, \\ldots$ counts several combinatorial objects\, some of
which I will describe in this talk. The major focus would be one of these
objects\, alternating sign matrices (ASMs). ASMs are square matrices with
entries in the set $\\{0\,1\,-1\\}$\, where non-zero entries alternate in
sign along rows and columns\, with all row and column sums being 1. I wil
l discuss some questions that are central to the theme of ASMs\, mainly de
aling with their enumeration. In particular we shall prove some conjecture
s of Fischer\, Robbins and Duchon. This is based on joint work with Ilse F
ischer.\n
LOCATION:https://researchseminars.org/talk/CATGT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eshita Mazumdar (ISI Bangalore)
DTSTART:20200930T053000Z
DTEND:20200930T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/10
DESCRIPTION:Title: I
terated sumsets and Hilbert functions\nby Eshita Mazumdar (ISI Bangalo
re) as part of Applications of Combinatorics in Algebra\, Topology and Gra
ph Theory\n\n\nAbstract\nLet $A$ be a finite subset of an abelian group $(
G\,+)$. Let $h \\ge 2$ be an integer. If $|A| \\ge 2$ and the cardinality
$|hA|$ of the $h$-fold iterated sumset $hA=A+\\dots+A$ is known\, what 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 improve
d 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 a
pply Macaulay's 1927 theorem on the growth of Hilbert functions\, and 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 factor $\\th
eta(x\,h) > 1$\, where $x$ is a real number closely linked to $|hA|$. More
over\, we show that $\\theta(x\,h)$ asymptotically tends to $e\\approx 2.7
18$ as $|A|$ grows and $h$ lies in a suitable range varying with $|A|$. Th
is is a joint work with Prof. Shalom Eliahou.\n
LOCATION:https://researchseminars.org/talk/CATGT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samir Shukla (Indian Institute of Technology Bombay)
DTSTART:20200916T053000Z
DTEND:20200916T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/11
DESCRIPTION:Title: H
igher independence complexes of graphs\nby Samir Shukla (Indian Instit
ute of Technology Bombay) as part of Applications of Combinatorics in Alge
bra\, Topology and Graph Theory\n\n\nAbstract\nIn 2006\, Szabó and Tardos
generalized the concept of independence complex by defining $r$-independe
nce complex of a graph $G$ for any $r \\geq 1$. Independence complexes ha
ve applications in several areas. The topology of independence complex is
related to many combinatorial properties of the underlined graph. The $
r$-independence complex of $G$\, denoted Ind$_r(G)$\, is the simplicial co
mplex whose simplices are those subsets $I \\subseteq V(G)$ such that each
connected component of the induced subgraph $G[I]$ has at most $r$ vertic
es.\n\nIn this talk\, we give a lower bound for the distance $r$-dominatio
n number of the graph $G$ (which is a very well studied notion in graph th
eory and a natural generalization of the domination number of the graph) i
n terms of the homological connectivity of the Ind$_r(G)$. We also prove t
hat Ind$_r(G)$\, for a chordal graph $G$\, is either contractible or homot
opy equivalent to a wedge of spheres. Given a wedge of spheres\, we also p
rovide a construction of a chordal graph whose $r$-independence complex ha
s the homotopy type of the given wedge. This is a joint work with Anurag S
ingh and Priyavrat Deshpande.\n
LOCATION:https://researchseminars.org/talk/CATGT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvind Kumar (IIT Delhi)
DTSTART:20201007T053000Z
DTEND:20201007T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/12
DESCRIPTION:Title: R
egularity of binomial edge ideals\nby Arvind Kumar (IIT Delhi) as part
of Applications of Combinatorics in Algebra\, Topology and Graph Theory\n
\n\nAbstract\nThis talk is going to be about the regularity of binomial ed
ge ideals. We will\ndiscuss a combinatorial proof of regularity upper boun
d for binomial edge ideals given by\nMatsuda and Murai. There are two regu
larity upper bound conjectures for binomial edge\nideals. We will be discu
ssing these two conjectures. Saeedi Madani and Kiani conjectured\nthat 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 re
gularity of the binomial\nedge ideal of a graph is bounded above by the de
gree of h polynomial of that graph.\n
LOCATION:https://researchseminars.org/talk/CATGT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Dochtermann (Texas State University)
DTSTART:20201021T140000Z
DTEND:20201021T150000Z
DTSTAMP:20260422T225718Z
UID:CATGT/13
DESCRIPTION:Title: S
hellings\, chordality\, and Simon's conjecture\nby Anton Dochtermann (
Texas State University) as part of Applications of Combinatorics in Algebr
a\, Topology and Graph Theory\n\n\nAbstract\nA simplicial complex X is "sh
ellable" if there exists an ordering of its facets that satisfies nice int
ersection properties. Shellability imposes strong topological and algebrai
c conditions on X and its Stanley-Reisner ring\, and has been an important
tool in geometric and algebraic combinatorics. Examples of shellable com
plexes include boundaries of simplicial polytopes and the independence com
plex of matroids. In general it is difficult (NP hard) to determine if a
given complex is shellable\, and X is said to be "extendably shellable" if
a greedy algorithm always succeeds. A conjecture of Simon posits that th
e k-skeleton of a simplex on vertex set [n] is extendably shellable. \n\n
Simon's conjecture has been established for k=2 but until recently all oth
er nontrivial cases were open. We show how the case k=n-3 follows from an
application of chordal graphs and the notion of "exposed edges"\, and in f
act prove that any shellable d-dimensional complex on at most d+3 vertices
is extendably shellable. This leads to a notion of higher-dimensional ch
ordality which connects Simon's conjecture to tools in commutative algebra
and simple homotopy theory. We also explore other cases of Simon's conjec
ture and for instance prove that any vertex decomposable complex can be co
mpleted to a shelling of a simplex skeleton. Parts of this are joint work
with Culertson\, Guralnik\, Stiller\, and Oh.\n
LOCATION:https://researchseminars.org/talk/CATGT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcin Wrochna (University of Oxford)
DTSTART:20201028T103000Z
DTEND:20201028T113000Z
DTSTAMP:20260422T225718Z
UID:CATGT/14
DESCRIPTION:Title: U
nderstanding homomorphism approximation problems using topology\nby Ma
rcin Wrochna (University of Oxford) as part of Applications of Combinatori
cs in Algebra\, Topology and Graph Theory\n\n\nAbstract\nWe consider an ap
proximation version of the graph colouring computational problem: can we e
fficiently distinguish a 3-colourable graph from a graph that is not even
100-colourable? More generally\, given a structure that is promised to hav
e a homomorphism to G\, can we at least find a (much weaker) homomorphism
to H? This is an ages-old question in which we recently made some surprisi
ng progress using topology and algebra\, e.g. studying maps from a torus t
o a sphere\, or looking at some adjoint functors in the category of graphs
. I will introduce all necessary basics to explain these unexpected connec
tions. Joint work with Andrei Krokhin\, Jakub Opršal\, and Standa Živný
.\n
LOCATION:https://researchseminars.org/talk/CATGT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Narayanan N (IIT Madras)
DTSTART:20201014T053000Z
DTEND:20201014T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/15
DESCRIPTION:Title: S
hitov's counterexample to Hedetniemi's conjecture\nby Narayanan N (IIT
Madras) as part of Applications of Combinatorics in Algebra\, Topology an
d Graph Theory\n\n\nAbstract\nWe give a sketch of the construction of Shit
ov's counterexamples to Hedetniemi's conjecture and some of the more rece
nt developments.\n
LOCATION:https://researchseminars.org/talk/CATGT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amit Roy (IISER Mohali)
DTSTART:20201104T053000Z
DTEND:20201104T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/16
DESCRIPTION:Title: S
tandard monomials of $1$-skeleton ideal of a graph\nby Amit Roy (IISER
Mohali) as part of Applications of Combinatorics in Algebra\, Topology an
d Graph Theory\n\n\nAbstract\nLet $G$ be a (multi) graph on the vertex set
$V=\\{0\,1\,\\ldots \,n\\}$ with root $0$. The $G$-parking function 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$_{\\mathbb{K}}\\big
(\\frac{R}{\\mathcal{M}_G}\\big)$ $=\\det\\left(\\widetilde{L}_G\\right)$\
, where $\\widetilde{L}_G$ is the truncated Laplace matrix of $G$. In othe
r words\, standard monomials of the Artinian quotient $\\frac{R}{M_G}$ cor
respond 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 monomial sub
ideal $\\mathcal{M}_G^{(k)}=\\left\\langle m_A:\\emptyset\\neq A\\subseteq
[n]\\text{ and }|A|\\leq k+1\\right\\rangle$ of the $G$-parking function i
deal $\\mathcal{M}_G=\\left\\langle m_A:\\emptyset\\neq A\\subseteq[n]\\ri
ght\\rangle\\subseteq R$. In this talk we will focus on the $1$-skeleton i
deal $\\mathcal{M}_G^{(1)}$ of a graph $G$ and see how the number of stand
ard monomials of $\\frac{R}{\\mathcal{M}_G^{(1)}}$ is related to the trunc
ated signless Laplace matrix $\\Q_G$ of $G$. This is based on joint work w
ith Chanchal Kumar and Gargi Lather.\n
LOCATION:https://researchseminars.org/talk/CATGT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arindam Banerjee (Ramakrishna Mission Vivekananda Educational and
Research Institute)
DTSTART:20201111T053000Z
DTEND:20201111T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/17
DESCRIPTION:Title: E
dge Ideals of Graphs and Their resolutions\nby Arindam Banerjee (Ramak
rishna Mission Vivekananda Educational and Research Institute) as part of
Applications of Combinatorics in Algebra\, Topology and Graph Theory\n\n\n
Abstract\nIn this talk we shall introduce the notion of the edge ideals of
a finite simple graphs. The study of the minimal free resolutions of thes
e ideals gave rise to many results where interplay between algebra and com
binatorics was the main essence. We shall discuss one such problem\, namel
y for which graphs this resolution consists of linear maps.\n
LOCATION:https://researchseminars.org/talk/CATGT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:D. Yogeshwaran (ISI Bangalore)
DTSTART:20201112T053000Z
DTEND:20201112T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/18
DESCRIPTION:Title: E
dge ideals of Random Graphs\nby D. Yogeshwaran (ISI Bangalore) as part
of Applications of Combinatorics in Algebra\, Topology and Graph Theory\n
\n\nAbstract\nIn this talk\, we shall look at four properties of edge idea
ls of Erdos-Renyi random graphs. Namely\, we shall consider asymptotics fo
r linear resolution\, linear presentation\, regularity and unmixedness. Th
ese properties have very explicit characterization in terms of graph-theor
etic properties such as co-chordality\, induced matching number and unique
ness of minimal vertex cover. In this talk\, we shall discuss asymptotics
for the latter properties of Erdos-Renyi random graphs and their consequen
ces 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 notions sha
ll be introduced in Arindam Banerjee's talk on November 11th and I shall o
nly recall them very briefly. On the random graph side\, I shall assume kn
owledge of graph theory and basic probability.\n\nThe talk is based on a j
oint work with Arindam Banerjee \; https://arxiv.org/abs/2007.08869\n
LOCATION:https://researchseminars.org/talk/CATGT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manisha Binjola (IIT Delhi)
DTSTART:20201118T053000Z
DTEND:20201118T063000Z
DTSTAMP:20260422T225718Z
UID:CATGT/19
DESCRIPTION:Title: O
n regular genus of PL 4-manifold with boundary\nby Manisha Binjola (II
T Delhi) as part of Applications of Combinatorics in Algebra\, Topology an
d Graph Theory\n\n\nAbstract\nA crystallization of a PL $d$-manifold is a
certain type of edge colored graph that represents the manifold. Extending
the notion of genus in dimension 2\, the notion of regular genus for a $d
$-manifold has been introduced\, which is strictly related to the existenc
e of regular embeddings of crystallizations of manifold into surfaces. The
regular genus of a closed connected orientable (resp. non-orientable) sur
face coincides with its genus (resp. half of its genus)\, while the regula
r genus of a closed connected 3-manifold coincides with its Heegaard genus
. Let $M$ be a compact connected PL 4-manifold with boundary. In this talk
\, I shall give lower bounds for regular genus of the manifold $M$. In par
ticular\, if $M$ is a connected compact PL $4$- manifold with $h$ boundary
components then its regular genus $\\mathcal{G}(M)$ satisfies the followi
ng inequalities: \n\n $\\mathcal{G}(M)\\geq 2\\chi(M)+3m+2h-4$ and $\\math
cal{G}(M)\\geq \\mathcal{G}(\\partial M)+2\\chi(M)+2m+2h-4\,$\n\n where $
m$ is the rank of the fundamental group of the manifold $M$.\n
LOCATION:https://researchseminars.org/talk/CATGT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuanning Zhang (The University of California)
DTSTART:20201125T043000Z
DTEND:20201125T053000Z
DTSTAMP:20260422T225718Z
UID:CATGT/20
DESCRIPTION:Title: F
iltering Grassmannian Cohomology via k-Schur Functions\nby Yuanning Zh
ang (The University of California) as part of Applications of Combinatoric
s in Algebra\, Topology and Graph Theory\n\n\nAbstract\nThis talk concerns
the cohomology rings of complex Grassmannians. In $2003$\, Reiner and Tud
ose conjectured the form of the Hilbert series for certain subalgebras of
these cohomology rings. We build on their work in two ways. First\, we con
jecture two natural bases for these subalgebras that would imply their con
jecture using notions from the theory of $k$-Schur functions. Second\, we
formulate an analogous conjecture for Lagrangian Grassmannians.\n
LOCATION:https://researchseminars.org/talk/CATGT/20/
END:VEVENT
END:VCALENDAR