November 2019
Public Access Category: All |
4:15pm» Mrinal Kumar : Computer Science Department, IIT Bombay- Time:
- 4:15pm - 5:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.
Speaker: Mrinal Kumar.
Affiliation: Computer Science Department, IIT Bombay.
Date and Time: Friday 01 November, 4:15 pm - 5:15 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Polynomial Method in Combinatorics (Part III).
Abstract: Upper bounds on the size of 3-AP free sets over finite fields:
We will discuss a recent result of Ellenberg and Gijswijt who showed that
if F is a finite field with three elements, and S is a subset of of F^n
such that S does not that does not contain three elements in an
arithmetic progression, then |S| is upper bounded by c^n for a constant c
< 3.
- Time:
- 3:30pm - 5:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Commutative Algebra seminar I.
Speaker: Dilip Patil.
Affiliation: IISc Bengaluru.
Date and Time: Monday 04 November, 3:30 pm - 5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: Module of Kahler Differentials, smooth morphisms, Cohen Structure
Theorems.
Abstract:
(During the week 03 Nov – 08 Nov, 2019) We continue to study smooth morphisms. The
purpose of these two lectures is :
(1) Definitions and Basic properties of the Module of Käher differentials.
(2) Prove a criterion for when a quotient of a formally smooth algebra is again formally
smooth.
(3) Prove a characterisation of when a morphism is smooth called the J a c o b i a n c r i -
t e r i o n.
This is a preparation for the proof of Cohen’s structure theorem for complete local rings in
the inequicharacteritic case.
- Time:
- 5:00pm - 6:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Geometry and Topology seminar.
Speaker: Saurav Bhaumik.
Affiliation: IIT Bombay.
Date and Time: Monday 04 November, 5:00 pm - 6:30 pm.
Venue: Room 215, Department of Mathematics.
Title: Higgs bundles and the Hitchin fibration.
Abstract: We will introduce Higgs bundles on curves, discuss the Hitchin
fibration and its fibers in terms of spectral curves.
- Time:
- 3:30pm - 5:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Commutative Algebra seminar II.
Speaker: Tony Puthenpurakal.
Affiliation: IIT Bombay.
Date and Time: Thursday 07 November, 3:30 pm - 5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: An application of triangulated categories to linkage of ideals.
Abstract: We define and give elementary properties of triangulated
categories. We also give an application of triangulated categories to
linkage theory in commutative algebra.
- Time:
- 3:30pm - 5:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Commutative Algebra seminar III.
Speaker: Dilip Patil.
Affiliation: IISc Bengaluru.
Date and Time: Friday 08 November, 3:30 pm - 5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: Module of Kahler Differentials, smooth morphisms, Cohen Structure
Theorems.
Abstract:
(During the week 03 Nov – 08 Nov, 2019) We continue to study smooth morphisms. The
purpose of these two lectures is :
(1) Definitions and Basic properties of the Module of Käher differentials.
(2) Prove a criterion for when a quotient of a formally smooth algebra is again formally
smooth.
(3) Prove a characterisation of when a morphism is smooth called the J a c o b i a n c r i -
t e r i o n.
This is a preparation for the proof of Cohen’s structure theorem for complete local rings in
the inequicharacteritic case.
- Time:
- 5:00pm - 6:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Geometry and Topology seminar.
Speaker: Saurav Bhaumik.
Affiliation: IIT Bombay.
Date and Time: Tuesday 12 November, 5:00 pm - 6:30 pm.
Venue: Room 215, Department of Mathematics.
Title: Higgs bundles and the Hitchin fibration - II.
Abstract: We will introduce Higgs bundles on curves, discuss the Hitchin
fibration and its fibers in terms of spectral curves.
- Time:
- 3:00pm - 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Partial Differential Equations seminar.
Speaker: Arnab Roy.
Affiliation: INRIA, Nancy.
Date and Time: Wednesday 13 November, 3:00 pm - 4:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Stabilization of a rigid body moving in a compressible viscous fluid.
Abstract: In this talk, we discuss the stabilization of a fluid-structure
interaction system of a viscous, compressible fluid and rigid ball in a
three dimension space with an external force acting on the ball produced
by a spring and a damper connecting the centre of the ball to a fixed
point $h_1$. We prove global-in-time existence result for this model under
the condition that the initial velocities are small and the center of mass
of the body is sufficiently near to $h_1$. In this scenario, we discuss
the asymptotic behaviour of the whole system.
- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Algebraic geometry seminar.
Speaker: Chandranandan Gangopadhyay.
Affiliation: The Institute of Mathematical Sciences, Chennai.
Date and Time: Wednesday 13 November, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Quot schemes and Semistable Vector Bundles.
Abstract: Let C be a smooth projective curve over an algebraically closed
field k. Fix r, d ≥ 1. Let Q(r, d)
be the quot scheme parametrizing degree d torsion quotients of the trivial
vector bundle of rank r. Then we show that the universal
kernel bundle over C × Q(r, d) and its pushforward to Q(r, d) are stable
with respect to certain
natural ample bundles over C × Q(r, d) and Q(r, d) respectively.
- Time:
- 4:30pm - 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.
Speaker: Trygve Johnsen.
Affiliation: The Artic University of Norway.
Date and time: Friday 15 November, 4:30 pm - 5:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Greedy weights for codes and matroids.
Abstract: Greedy weights of linear codes measure the minimal support
cardinality
of chains of subcodes for a certain lexicographic order. We show how the
problem
of finding such weights can be studied by inspecting the poset of flats of
the generator matroid, or better: the (dual) poset of cycles for the
parity check matroid. The terms of a minimal resolution of the
Stanley-Reisner ring of the independence complex of the parity check
corresponds to the points of the poset. Optimal paths in the poset
diagram, and optimal chains of non-zero component maps in a minimal
resolution of the Stanley-Reisner ring. correspond to greedy weights Such
maps can be constructed using poset homology, or studied indirectly,
through the Taylor complex, which also provides a resolution, although
not minimal.
- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar (A discussion session).
Organisers: Trygve Johnsen and Madhusudan Manjunath.
Date and time: Monday 18 November, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Matroids, Coding Theory and Syzygies: A Discussion Session.
Abstract: We will discuss potential future directions in the interface
between matroids, coding theory and syzygies. This will be a platform to
share thoughts on this topic.
- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Number Theory seminar.
Speaker: Dinesh Thakur.
Affiliation: Rochester University.
Date and Time: Friday 22 November, 11:30 am - 12:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: What should pi, e, zeta(3), Gamma(1/7) be, if integers are replaced
by polynomials?
Abstract: In this talk, which should be accessible to all undergraduates,
we will explain the title, and explain how number theory understands
interesting numbers and relations between them by building appropriate
mathematical structures, from algebra, geometry, analysis.
- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium.
Speaker: Jinhyun Park.
Affiliation: KAIST, Republic of Korea.
Date and Time: Thursday 28 November, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: On motivic cohomology for schemes with singularities.
Abstract: On smooth k-schemes, it is known that the higher Chow groups of
S. Bloch give what is called the motivic cohomology theory on them. When
schemes admit singularities, this has been yet unresolved.
In this talk, I will give a sketch of a recent new construction, which
gives a functorial theory on the category of all schemes of finite type.
To motivate the audience, I will begin with basic motivating examples from
1st year graduate course level differential forms, and proceed to build up
on it to give a sketch, and discuss some consequences and questions.