September 2017
Public Access Category: All |
3:30pm» Speaker: Prof. R. V. Gurjar- Time:
- 3:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Speaker: Prof. R. V. Gurjar
Complex Algebraic Surfaces III
- Time:
- 4:00pm - 6:30pm
- Location:
- Room 216, Department of Mathematics
- Description:
- Speaker: Nagarjuna Chary
Title: Local Fields
Abstract: In this second lecture we will continue with the material in
Chapter 1 in Cassels and Frohlich.
- Time:
- 9:30am - 10:30am
- Location:
- Ramanujan Hall
- Description:
- Title: Herzog-Kuhl Equations and its Applications - II
Abstract: In these talks, we will see relations between Hilbert series of
a module and its graded Betti numbers. This gives relations between the
graded Betti numbers of a modules which are known as Herzog-Kuhl
equations. As an application, we show that the property of R being
Cohen-Macaulay is characterized by the existence of a pure Cohen-Macaulay
R-module of finite projective dimension.
- Time:
- 10:30am - 11:30am
- Location:
- Ramanujan Hall
- Description:
- Title: Tate Resolutions - II
Abstract: Let S be a Noetherian ring, and R = S/I. It is always possible
to construct a differential graded algebra (DG-algebra) resolution of R
over S due to a result of Tate. If R is the residue field of S, then
Gulliksen proved that such a DG-algebra resolution is minimal. We shall
discuss the construction of the Tate resolution in our talk.
- Time:
- 4:00pm - 6:30pm
- Location:
- Room 216, Department of Mathematics
- Description:
- Speaker: Arghya Mondal
Title: Local Langlands Correspondence in the Archimedean case
Abstract: In this lecture, we will understand the statement of the local
Langlands correspondence in the Archimedean case. This lecture will be
based on the article available here https://www.math.stonybrook.ed
u/~aknapp/pdf-files/motives.pdf
- Time:
- 11:00am - 12:30pm
- Location:
- Ramanujan Hall
- Description:
- Title: The Szemeredi-Trotter Theorem (postponed from last week)
Speaker: Venkitesh S.I. (IITB)
Abstract:
Given a finite set of points P in R^2 and a finite family of lines L
in R^2, an incidence is a pair (p,l), where p\in P, l\in L and p is a
point in l.
The Szemeredi-Trotter Theorem states that the number of incidences is
atmost a constant multiple of (|L||P|)^{2/3} + |L| + |P|. We give a
proof by Tao, which uses the method of cell partitions.
- Time:
- 3:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Name: Dr Nigel Calder
Title: Using mobile technologies to enhance the learning of
mathematics
- Time:
- 3:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Title: Homotopy theory
Abstract: I will give introduce the basic ideas in homotopy theory, along the way
state some classical theorems and if time permits some recent results. The talk
will be expository and will have few or no proofs possibly.
- Time:
- 4:00pm - 6:30pm
- Location:
- Room 216, Department of Mathematics
- Description:
- Lecture in Algebraic Number Theory
Title: Local Fields
Speaker: Nagarjuna Chary
Abstract: We will continue with the material in Chapter 1 in Cassels and
Frohlich.
- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Eknath Ghate, TIFR Mumbai
Title: Reductions of Galois Representations: Act 1.5
Abstract: We shall describe recent progress on the question of writing
down the reductions of certain local Galois representations. We shall
focus on the case of half integral slopes (especially slope 3/2)
where the behaviour of the reduction is both more complicated and
more interesting.
Our proof uses the mod p Local Langlands Correspondence to reduce the
problem to computing the reductions of certain locally algebraic
representations of GL_2 of the p-adics on certain functions on
the underlying tree
- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Rational Singularities.
We will define special singularities of algebraic or analytic varieties
called rational singularities introduced my M. Artin. After discussing
some equivalent criterion for rationality we will give many naturally
occuring examples.
Next, we will describe the results of Artin in dimension 2.
Important results due to Brieskorn, Lipman, Mumford, Tjurina,...
will be mentioned.
If time permits some results by Spivakovsky, Le dung Trang-M. Tosun,
Gurjar-Wagh,...will be mentioned.
No proofs wil be given.
- Time:
- 11:30am
- Location:
- Ramanujan Hall
- Description:
- Seminar on Combinatorial aspects of
commutative algebra and algebraic geometry.
Title: What is a Syzygy?
This talk will be introduction to syzygies: basic theorems, examples and
some early applications. This is the first seminar on this topic.
- Time:
- 4:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Asymptotic estimates on the geometry of Laplace eigenfunctions
Abstract: Given a closed smooth Riemannian manifold M, the Laplace operator
is known to possess a discrete spectrum of eigenvalues going to infinity.
We are interested in the properties of the nodal sets and nodal domains of
corresponding eigenfunctions in the high energy (semiclassical) limit. We
focus on some recent results on the size of nodal domains and tubular
neighbourhoods of nodal sets of
such high energy eigenfunctions (joint work with Bogdan Georgiev).
- Time:
- 9:30am - 10:25am
- Location:
- Ramanujan Hall
- Description:
- Title: Huneke-Itoh Intersection Theorem and its Consequences - I
Abstract: Huneke and Itoh independently proved a celebrated result on
integral closure of powers of an ideal generated by a regular sequence. As
a consequence of this theorem, one can find the Hilbert-Samuel polynomial
of the integral closure filtration of I if the normal reduction number is
at most 2. We prove Hong and Ulrich's version of the intersection theorem.
- Time:
- 10:30am - 11:25am
- Location:
- Ramanujan Hall
- Description:
- Title: Tate Resolutions - III
Abstract: Let S be a Noetherian ring, and R = S/I. It is always possible
to construct a differential graded algebra (DG-algebra) resolution of R
over S due to a result of Tate. If R is the residue field of S, then
Gulliksen proved that such a DG-algebra resolution is minimal. We shall
discuss the construction of the Tate resolution in our talk.
- Time:
- 2:30pm - 5:30pm
- Location:
- Venue (tentative): Room 216, Department of Mathematics
- Description:
- Title: Local Fields
Speaker: Nagarjuna Chary
Venue (tentative): Room 216, Department of Mathematics
Abstract: We will continue with the material in Chapter 1 in Cassels and
Frohlich.
- Time:
- 2:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title : Hairy balls, fixed points and coffee!!!
Abstract :
Singularities occur naturally everywhere around us, may it be an eye of a
cyclone where there is no wind at all, or the north pole where the
different time zones converge. The purpose of this talk is to study these
patterns mathematically. Hairy ball theorem precisely states that: An even
dimensional sphere does not possess any continuous nowhere vanishing
tangent vector field". The basic notions of tangent vector field,
fundamental groups, some concepts of point set topology will be discussed
(at least intuitively) and then a geometric proof of the theorem will be
studied. It will be followed by a few applications in the end.
- Time:
- 11:00am - 12:30pm
- Location:
- Ramanujan Hall
- Description:
- Title: Ruzsa's theorem in additive combinatorics
Abstract: We show that in a finite group G of bouded torsion, any set
A \subseteq G such that |A + A| = O(|A|) generates a subgroup H of
size O(|A|). We will introduce some standard techniques in additive
combinatorics to prove this theorem.
- Time:
- 3:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Title:
Kodaira's theorem: criterion for embedding a compact Kahler manifold in
projective space
Abstract:
Let $M$ be a compact Kahler manifold and $\Omega (M)$ the canonical
$2$-form on $M$. When $M$ is projective $n$-spce $\P^n(\C)$ , $H^2(M,\C)$
is of dimension 1. It follows that for any Kahler metric on the projective
space, the cohomology class $[\Omega (M)$ of the canonical $2$-form is a
multiple of the (unique up to sign) of a generator of $H^2(M,\Z)$. It is
immediate from this that if $M$ is a complex sub-manifold of $\P^n(\C)$ for
some $n$, then for the Kahler metric on $M$ induced from one on $\P^n(\C)$,
it is clear that $[\Omega(M)] \in $\C \cdot H^2(M, Z)$. Kodaira's theorem
is a converse to this fact: If a complex manifold $M$ admits a Kahler
metric such that the class of $\Omega(M)$ is a multiple of an integral
class, then $M$ can be embedded in some projective space. This result was
conjectured by W V D Hodge.
- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title: Free Resolutions of Monomial Ideals.
Speaker: Prof. Madhusudan Manjunath
Abstract: We'll study free resolutions of monomial ideals via the notion
of a labelled simplicial complex. We derive a criterion due to Bayer,
Peeva and Sturmels for a labelled simplicial complex to define a free
resolution.
As consequences, we show that the Koszul complex is exact and prove the
Hilbert syzygy theorem.
- Time:
- 9:30am - 10:25am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title: Linear resolutions of monomial ideals - I
Abstract: Consider a graded ideal in the polynomial ring in several
variables. We shall discuss criterion for the graded ideal and its power
to have linear resolution. Then we focus our attention
to study linear resolution of monomial ideals.
Monomial ideals are the bridge between commutative algebra and the
combinatorics. Monomial ideals are also significant because they appear as
initial ideals of arbitrary ideals. Since many properties of an initial
ideal are inherited by its original ideal, one often adopt this strategy
to decipher properties of general ideals. The first talk is meant for
covering the preliminary results on resolution and regularity of monomial
ideal.The aim of this series of talk is to present the result in
arXiv:1709.05055
- Time:
- 10:30am - 11:25am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title: Huneke-Itoh Intersection Theorem and its Consequences - II
Abstract: Huneke and Itoh independently proved a celebrated result on
integral closure of powers of an ideal generated by a regular sequence. As
a consequence of this theorem, one can find the Hilbert-Samuel polynomial
of the integral closure filtration of I if the normal reduction number is
at most 2. We prove Hong and Ulrich's version of the intersection theorem.
- Time:
- 2:30pm - 5:30pm
- Location:
- Room 113, Department of Mathematics
- Description:
- Speaker: Nagarjuna Chary
Title: Local Fields
Abstract: We will cover the material in Chapter 2 in Cassels and Frohlich.