# Coming Events

## State of the art seminar

Date/Time:
Monday, November 20, 2017 - 15:30
Venue:
Seminar hall
Speaker:
Atibur Rahaman
Affiliation:
NISER
Title:
Partial dual construction for C*-Quantum groups

Given a Hopf algebra H in a braided category \mathcal{C} and a projection H\longrightarrow A to a Hopf subalgebra, one can construct a Hopf algebra r_{A}(H), called the partial dualization of H , with a projection to Hopf algebra dual to A​. A non-degenerate Hopf pairing \omega :A\otimes B \longrightarrow 1 induces a braided equivalence between the Yetter-Drinfeld modules over a Hopf algebra and its partial dualization. In this seminar, we shall discuss this procedure in the general setting of C*-Quantum groups.

Reference:

1. Alexander Barvels, Simon Lentner, Christoph Schweigert, Partially dualized Hopf algebras have equivalent Yetter–Drinfel’d modules, Journal of Algebra 430 (2015) 303–342

2. Ralf Meyer, Sutanu Roy, Stanislaw Lech Woronowicz, Quantum group-twisted tensor products of C*-algebras II, J. Noncommut. Geom., 10 (2016), no. 3, 859-888.

## State of the Art Seminar

Date/Time:
Tuesday, November 21, 2017 - 11:30
Venue:
Seminar Hall, SMS
Speaker:
Abhrojyoti Sen
Affiliation:
SMS, NISER
Title:
Vanishing Pressure Limit For a Non-strictly Hyperbolic System

In this talk we will be discussing about vanishing pressure limit for the equation

u_t + (u^2/2)_x = 0

ρ_t + (ρu)_x = 0,

with initial data

u(x, 0) = u_0(x),

ρ(x, 0) = ρ_0(x),

where u is the velocity component and ρ is the density component. This equation is considered as one of the model for the large scale structure formation of universe. In this direction we find some partial results for Reimann type initial data.

Attachments:

## Seminar by Ananta Majee

Date/Time:
Wednesday, November 22, 2017 - 11:00 to 12:00
Venue:
conference Room, School of Mathematical Sciences
Speaker:
Ananta Kumar Majee
Affiliation:
University of Tuebingen
Title:
Rate of convergence of a semi-discrete finite difference scheme for stochastic balance laws driven by Levy noise
Attachments:

Date/Time:
Wednesday, November 22, 2017 - 14:00 to 15:00
Venue:
Conference Room, School of Mathematical Sciences
Speaker:
Affiliation:
University of Hohenheim
Title:
TBA

TBA

## State of the Art Seminar

Date/Time:
Wednesday, November 22, 2017 - 15:30
Venue:
Seminar Hall
Speaker:
Affiliation:
NISER
Title:
Counting complex curves with singularity in CP^2

The study of of degree d curves in $\mathbb{CP}^2$ is one of the interesting topic which arises in the context of Enumerative Geometry. The specific problem, which I will talk about, can be stated as follows:

Let $\mathbb{CP}^2$ be a compact complex surface and $L \rightarrow \mathbb{CP}^2$ a holomorphic line bundle that is sufficiently ample. Let $\mathcal{D} := \mathbb{P}^\frac{d(d+3)}{2}$ be the space of all degree d complex curves in $\mathbb{CP}^2$ - What is $\mathcal{N}(\mathfrak{X}_{k})$, the number of curves in $\mathbb{CP}^2$, passing through $\frac{d(d+3)}{2} -k$ generic points, having singularity of type $\mathfrak{X}_{k}$, where $k$ is the codimension of the singularity $\mathfrak{X}_{k}$?

In this talk we will describe what is a zero set of vector bundle over $\mathbb{CP}^2$ and then calculate $\mathcal{N}({A_1})$ for degree d complex curves in $\mathbb{CP}^2$. Here
$\mathcal{N}({A_1})$ represents number of degree d curves in $\mathbb{CP}^2$ passing through $\frac{d(d+3)}{2} -1$ points having $A_1$ singularity.

## Seminar by A Parthasarathy

Date/Time:
Thursday, November 23, 2017 - 11:00 to 12:00
Venue:
Seminar Room, School of Mathematical Sciences
Speaker:
Aprameyan Parthasarathy
Affiliation:
Title:
Boundary values, resonances and scattering poles on rank one symmetric spaces

In this talk, we will report on recent work (with J. Hilgert and S. Hansen, Paderborn) relating resonances and scattering poles on Riemannian symmetric spaces of rank one. We use boundary values in the sense of Kashiwara and Oshima to show that resonances and scattering poles coincide, along with their residues. Our methods also enable us to give a new and simple proof of the Helgason's conjecture in the rank one case. Time permitting, we'll mention progress made for symmetric spaces of higher rank.

## State of the art seminar

Date/Time:
Thursday, November 23, 2017 - 15:30
Venue:
SMS Seminar hall
Speaker:
Nilkantha Das
Affiliation:
NISER
Title:
Riemann Roch Theorem

The Riemann-Roch Theorem is the foundation of the theory of algebraic curves. It gives a precise answer for the dimension of the space L(D) for a divisor D of an algebraic curve. The qualitative information that a Riemann surface is an algebraic curve is seen to be equivalent to more quantitative statement of Riemann-Roch.As an application of Riemann-Roch Theorem, it can be shown that any Algebraic curve can be holomorphically embedded into projective space. Any genus zero algebraic curve is isomorphic to the Riemann Sphere(C∞). Any non-degenerate smooth projective curve X in Pn of minimal degree n is a rational normal curve.