November 2021
Public Access Category: All |
6:30pm» Christopher Eur, Harvard University, Cambridge, MA, USA.- Time:
- 6:30pm
- Description:
- Speaker: Christopher Eur, Harvard University, Cambridge, MA, USA.
Date/Time: 5 November 2021, 6:30pm IST/ 1:00pm GMT / 9:00am ET (joining
time 6:15pm IST).
Gmeet link: meet.google.com/vya-nyta-kac
Title: Tautological classes of matroids.
Abstract: Algebraic geometry has furnished fruitful tools for studying
matroids, which are combinatorial abstractions of hyperplane arrangements.
We first survey some recent developments, pointing out how these
developments remained partially disjoint. We then introduce certain vector
bundles (K-classes) on permutohedral varieties, which we call
"tautological bundles (classes)" of matroids, as a new framework that
unifies, recovers, and extends these recent developments. Our framework
leads to new questions that further probe the boundary between
combinatorics and geometry. Joint work with Andrew Berget, Hunter Spink,
and Dennis Tseng.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar
- Time:
- 5:30pm
- Description:
- Speaker: Seyed Amin Seyed Fakhari, University of Tehran, Tehran, Iran.
Date/Time: 12 November 2021, 5:30pm IST/ 12:00pm GMT / 7:00am ET (joining
time 5:15pm IST).
Gmeet link: meet.google.com/mgo-iemn-dra
Title: Homological properties of symbolic powers of cover ideals of graphs.
Abstract: To every simple graph one associates its edge ideal which is
generated by quadratic squarefree monomials corresponding to edges of the
graph. In this talk, we study the Alexander dual of edge ideals, which is
called the cover ideal. The reason for this naming is that the cover ideal
is minimally generated by squarefree monomials corresponding to the
minimal vertex covers of the given graph. We review the recent results
about the symbolic powers of cover ideals. In particular, we characterize
all graphs with the property that every symbolic power of its cover ideal
has a linear resolution. Also, we determine an upper bound for the
regularity of symbolic powers of certain classes of graphs including
bipartite graphs, unmixed graphs and claw-free graphs. Moreover, we study
the asymptotic behavior of depth of symbolic powers of cover ideals.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar
- Time:
- 5:30pm
- Description:
- Speaker: Nursel Erey, Gebze Technical University, Gebze, Turkey.
Date/Time: 26 November 2021, 5:30pm IST/ 12:00pm GMT / 7:00am ET (joining
time 5:15pm IST).
Gmeet link: meet.google.com/egt-ffkz-rcv
Title: Squarefree powers of edge ideals.
Abstract: Let $G$ be a finite simple graph. The edge ideal of $G$, denoted
by $I(G)$, is a monomial ideal generated by the monomials that correspond
to the edges of the graph. In this talk, we will be interested in
resolutions of squarefree powers of edge ideals. The $k$th squarefree
power $I(G)^{[k]}$ of $I(G)$ is generated by the squarefree monomials in
$I(G)^k$. We will explore the question of when squarefree powers of edge
ideals are linearly related or have linear resolution. This talk is based
on joint work with Jürgen Herzog, Takayuki Hibi and Sara Saeedi Madani.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar