Date and Time: Monday 02 March, 05:15 pm - 06:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Cotangent complex and applications -- Lecture No. 2.
Abstract: Differential 1-forms are very useful in the study of
multivariate calculus or smooth manifolds. Algebraically, the module of
Kahler differentials is very useful in commutative algebra. When the
spaces (or varieties) are not smooth but have singularities, differential
1-forms are not enough. Instead there is available a more general gadget
called the cotangent complex in commutative algebra as well as in
algebraic geometry. This series of talks will begin by recalling usual
differential forms and Kahler differentials in familiar setting, and then
introduce the cotangent complex. Applications to smoothness, local
complete intersections and deformation theory will be shown. Some
familiarity with the language of commutative algebra will be assumed.
Time:
11:30am
Location:
Ramanujan Hall, Department of Mathematics
Description:
Commutative Algebra seminar.
Speaker: Manoj Kumar Keshari.
Affiliation: IIT Bombay.
Date and Time: Tuesday 03 March, 11:30 am - 12:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Tsen-Lang Theory of $C_i$-fields.
Abstract: We will define $C_i$-fields and prove results about algebraic
and transcendental extensions of such fields.
Time:
2:15pm-3:15pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Speaker: Harsha Hutridurga.
Affiliation: IIT Bombay.
Seminar I.
Date and Time: Tuesday 03 March, 02:15 pm - 03:15 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: On the Korn's inequality.
Abstract: Korn's inequality plays a fundamental role in elasticity theory
and also in hydrodynamics. This talk will aim at presenting the Korn's
inequality and some interesting observations around it. Furthermore, this
talk will some preliminary material for Friday's talk on 'Perturbative
analysis in linear elasticity'.
Time:
11:00am-12:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Combinatorics seminar.
Speaker: Subhajit Ghosh.
Affiliation: IISc Bengaluru.
Date and Time: Wednesday 04 March, 11:00 am - 12:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Total variation cutoff for the flip-transpose top with random shuffle.
Abstract:
Abstract. We consider a random walk on the hyperoctahedral
group Bn generated by the signed permutations of the forms (i, n)
and (−i, n) for 1 ≤ i ≤ n. We call this the flip-transpose top
with random shuffle on Bn. We find the spectrum of the transition
probability matrix for this shuffle. We obtain the sharp mixing
time for this shuffle by proving total variation cutoff phenomenon
with cutoff time n log n.
Time:
2:00pm-3:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Analysis seminar.
Speaker: Bata Krishna Das.
Affiliation: IIT Bombay.
Date and Time: Wednesday 04 March, 02:00 pm - 03:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Model of operators and their characteristic functions.
Abstract: In this talk, using Sz.-Nagy and Foias isometric dilation, we will de-scribe functional models of a class of operators. This will further lead us to define their characteristic functions which are complete unitary in- variants. We will also discuss the connection between invariant subspace problem and factorization of characteristic functions. If time permits we will see a recently developed multivariate analogue of these notions.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Mathematics Colloquium.
Speaker: Siddhartha Bhattacharya.
Affiliation: TIFR Mumbai.
Date and Time: Wednesday 04 March, 04:00 pm - 05:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Translational tilings of the plane.
Abstract: A set $A\subset {\mathbb R}^2$ is said to be a translational
tile if ${\mathbb R}^2$ can be expressed as a disjoint union of
translated copies of $A$. In this talk we will discuss the connection
between such tiles and measure preserving dynamical systems. We will show
that if the underlying set $A$ satisfies a certain regularity condition
then the question whether $A$ tiles the plane is decidable.
Time:
11:00am
Location:
Ramanujan Hall, Department of Mathematics
Description:
Algebraic geometry seminar.
Speaker: Arjun Paul.
Affiliation: IIT Bombay.
Date and Time: Friday 06 March, 11:00 am - 12:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Mehta-Ramanathan's restriction theorems and their applications.
Abstract: Fundamental groups of algebraic varieties and their
representations are very interesting objects, and have given rise to a lot
of mathematics. The famous Narasimhan-Seshadri Theorem states that on a
compact Riemann surface there is a bijective correspondence between stable
holomorphic vector bundles with vanishing Chern classes and unitary
representations of the topological fundamental group. This result was
generalized to smooth projective surfaces by Donaldson. The Stable
Restriction Theorem of Mehta-Ramanathan then enables us to generalize this
correspondence, between stable holomorphic vector bundles with vanishing
Chern classes and unitary representations of the fundamental group, to
arbitrary smooth projective varieties. This consequence is the main
application we have in mind. We will also give an overview of the proof of
the Stable and Semi-stable Restriction theorems.
Time:
2:15pm-3:15pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Seminar II.
Speaker: Harsha Hutridurga.
Affiliation: IIT Bombay.
Date and Time: Friday 06 March, 02:15 pm - 03:15 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Perturbative analysis in linear elasticity.
Abstract: In this talk, we aim to answer the following question: How does
the traction-to-displacement map change with respect to small volume
perturbation of elasticity parameters in a given medium. using some
elementary tools and building upon an idea of Friedman and Vogelius, we
demonstrate that the boundary measurements deviate only a little as long
as the defects are of small volume and more importantly, irrespective of
the elasticity properties of the defect.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
CACAAG seminar.
Speaker: Poornima.
Affiliation: IIT Bombay.
Date and Time: Friday 06 March, 04:00 pm - 05:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Elliptic Curves over the complex numbers and their uniformization.
Abstract: This talk will be a gentle introduction to elliptic curves. We
start with the algebraic definition of elliptic curves and then explain
uniformization of complex elliptic curves, i.e. realise each of them as a
quotient of the complex number by a lattice.