In this talk, we will introduce the concept of a smooth manifold and work out some examples. If time permits, we will define what is theTangent and Cotantent space of a manifold at a given point.

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Date/Time: Tuesday, August 8, 2017 - 18:00 to 19:30

Venue: Mathematics Seminar Room

Speaker: Anantadulal Paul, NISER

Title: Introduction to smooth manifolds

In this talk, we will introduce the concept of a smooth manifold and work out some examples. If time permits, we will define what is theTangent and Cotantent space of a manifold at a given point.

Date/Time: Friday, August 4, 2017 - 15:30 to 16:30

Venue: SMS Seminal Hall

Speaker: Mr. Biswajit Rajaguru, University of Kansas

Title: Projective normality of line bundles of the type $K_X+\pi^*L$ on a ramified double covering $\pi:X\to S$ of an anticanonical rational surface $S$

Abstract:- Suppose $X$ is a minimal surface, which is a ramified double covering $\pi:X\to S$, of a rational surface $S$, with dim $|-K_S|\geq 1$. And suppose $L$ is a divisor on $S$, such that $L^2\geq 7$ and $L\cdot C\geq 3$ for any curve $C$ on $S$. Then the divisor $K_X+\pi^*L$ on $X$, is...

Date/Time: Monday, July 24, 2017 - 11:30 to 12:30

Venue: SMS Seminal Hall

Speaker: Rahul Kumar Singh, HRI, Allahabad

Title: Maximal surfaces, Born-Infeld solitons and Ramanujan's identities

Abstract: In the first part of the talk we discuss a different formulation for describing maximal surfaces in Lorentz-Minkowski space $ \mathbb{L}^3:=(\mathbb{R}^3, dx^2+dy^2-dz^2) $ using the identification of $ \mathbb{R}^3 $ with $ \mathbb{C}\times \mathbb{R} $. This description of maximal...

Date/Time: Friday, July 14, 2017 - 11:30 to 12:30

Venue: SMS Seminal Hall

Speaker: Arvind Kumar, HRI, Allahabad

Title: Rankin-Cohen brackets and identities among eigenforms

Abstract :- Identities connecting modular forms (in particular, eigenforms) have attracted the attention of many mathematicians since they imply nice identities among their Fourier coefficients. It is quite natural to ask whether the property of being a Hecke eigenform is...

Date/Time: Monday, July 10, 2017 (All day) to Saturday, July 22, 2017 (All day)

Venue: NISER

This will be an introductory summer school on "J-Holomrphic Curves and Gromov-Witten Invariants".We hope to cover the foundations of this subject by following the book "J-Holomorphic Curves and Symplectic Topology" by Dusa McDuff and Dietmar Salamon. Quite a few young mathematicians from India...

Date/Time: Saturday, June 24, 2017 - 15:30 to 16:30

Venue: Seminar Room, School of Mathematical Sciences

Speaker: Dr. Soumyashant Nayak, University of Pennsylvania

Title: The Many Forms of the Pythagorean Theorem

The well-known Pythagorean theorem which relates the lengths of sides of a right triangle to the length of the hypotenuse dates as far back in time as the Babylonians. Later in school when one gets a flavour of trigonometry, this result is neatly packaged in the equation $cos^2 \theta + sin^2 \...

Date/Time: Monday, June 19, 2017 (All day) to Saturday, July 1, 2017 (All day)

Venue: Seminar Room, SMS

The purpose of SOPM...

Date/Time: Thursday, June 15, 2017 - 11:30 to 12:30

Venue: SMS Seminar Hall

Speaker: Dr Saswata Adhikari, IIT Madras

Title: Frames of twisted shift-invariant spaces in $L^{2}(\mathbb{R}^{2n})$ and shift-invariant spaces on the Heisenberg group

**Abstract:** A well known result on translates of a function $\varphi$ in $L^{2}(\mathbb{R})$ states that the collection $\{\tau_{k}\varphi: k\in\mathbb {Z}\}$ forms an orthonormal system in $L^{2}(\mathbb{R})$ iff $p_{\varphi}(\xi)=\sum\limits_{k\in\mathbb {Z}}|\widehat{\varphi...

Date/Time: Tuesday, May 30, 2017 - 11:30

Venue: Seminar Hall, SMS

Speaker: Anup Dixit, University of Toronto

Title: On the generalized Brauer-Siegel Theorem

For a number field K over Q, there is an associated invariant called the class number, which captures how far the ring of integers of K, is from being a principal ideal domain (PID). The study of class numbers is an important theme in algebraic number theory. In order to understand how the...

Date/Time: Tuesday, May 23, 2017 - 16:00 to 17:00

Venue: Seminar Room, School of Mathematical Sciences

Speaker: Dr. Rohit Dilip Holkar, IISER Pune

Title: Locally free actions of groupoids and proper correspondences

**School of Mathematical Sciences**

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