Speaker: Sayani Bera, Ramakrishna Mission Vivekanada Educational and
Research Institute.
Date and Time: 4:00 pm, Tuesday, 18th September.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Non-autonomous basins of attraction and short Ck's.
Abstract: In this talk, we first define the dynamical setting of a
non-autonomous system and its relation to Bedford conjecture. Further, we
will discuss about Short Ck's that arises as basins of attraction of a
fixed point in the non-autonomous setting. Lastly, we will see some
methods to construct short Ck's with pathological properties and discuss
some related problems.
Time:
5:00pm
Location:
Room 215, Department of Mathematics
Description:
CACAAG seminar.
Speaker: Dhruv Ranganathan
Time & Date: 5pm Tuesday, September 18.
Venue: Room 215
Title and abstract:
Curves, maps, and singularities in genus one
I will outline a new framework based on tropical geometry to study genus
one curve singularities and discuss its relationship with the geometry of
moduli spaces. I will focus on the application of this framework to
construct new nonsingular compact moduli spaces parameterizing elliptic
curves in projective space. This also reveals a modular interpretation for
Vakil and Zinger’s famous desingularization of the space of elliptic curves
in projective space, as well as a short and conceptual proof of that
result. If time permits, I will discuss applications to some questions in
the classical enumerative geometry of surfaces. This is based on joint work
with Keli Santos-Parker and Jonathan Wise, building on prior work of
Speyer, Smyth, Viscardi, Vakil, and Zinger.
Time:
4:00pm
Location:
Room 215, Department of Mathematics
Description:
Department Colloquium
Speaker: Dhruv Ranganathan
Time & Date: 4pm Wednesday, September 19
Venue : Room 215
Title and abstract:
The space of equations for an algebraic curve
The geometry of a Riemann surface is captured by the ways in which it can
manifest as a projective variety, or more precisely, by the geometry of
spaces parameterizing embeddings of the curve into projective space. These
“Brill-Noether varieties” of a curve are well understood in two cases. On
one end, work of Clifford gives a complete understanding of hyperelliptic
curves. On the other end, a curve that is general in moduli exhibits
expected behaviour. In recent joint work with Dave Jensen, building on
previous work of Nathan Pflueger, we determine formulas for the dimensions
of the Brill-Noether varieties for the intermediate cases, i.e. general
curves of a fixed gonality. Our methods blend the combinatorics of the
sandpile model on graphs with methods from non-archimedean analysis and
deformation theory. I will give an overview of ideas surrounding the
theorem and its proof, and try to give a sense of the link between
algebraic and combinatorial geometry.
Time:
2:00pm-3:30pm
Description:
Commutative algebra seminar
Who: Ananthnarayan H.
Where: Room 215, Maths Building
When: Thursday, 20th Sept, 2:00 - 3:30 p.m.
What: On generalizations of an inequality of Lech - I
In recent work (see https://arxiv.org/abs/1711.06951), Craig Huneke, Ilya
Smirnov, and Javid Validashti study conjectured generalisations of an
inequality of Lech, relating the multiplicity and the colength of an ideal
I of finite colength in a Noetherian local ring (R,m,k). Using mixed
multiplicities, they show that one of these conjectures regarding the
multiplicity of mI is true.
In this series of talks, we will discuss some of the results in t