STEMS Camp Schedule

All sessions will be conducted in the Seminar Hall.

All CMI students and faculty are welcome to attend.

Professor Rahul Siddharthan, IMSc

Application of Fundamental Algorithms in Computer Science in Biology

9:30 - 10:45

Computational biology refers to the use of data analysis, mathematical modeling and computational simulations to understand biological systems and relationships. We will explore how algorithms fundamental in computer science can also be applied to biology.

Snack Break

10:45 - 11:15

Professor Amitabh Virmani, CMI

Gravitational Waves And Black Holes

11:15 - 12:30

I will share the excitement of the discovery of Gravitational Waves, first announced on 11th Feb 2016. Then I will say a few things about the upcoming projects LIGO India and LISA.

Lunch

12:30 - 14:00

Professor Amritanshu Prasad, IMSc

Computing the Sum of kth Powers of the First n Positive Integers

14:00 - 15:15

How do we find nice formulas for sums of the form 1^{k} + 2^{k} + ... + n^{k} for a general positive integer k? You are probably familiar with the formulas for k=1, 2, and maybe 3. In this talk we will look at some interesting mathematical ideas that arise from an exploration of these formulas for larger values of k.

Break

15:15 - 15:30

Prof. Sushmita Venugopalan, IMSc

Euler Characteristic

15:30 - 16:45

Consider a planar graph with V vertices, E edges and F faces. Do you know the value of the expression V-E+F? What if the graph is drawn on a sphere? And what about a graph drawn on a coffee cup? Or on a trophy -- which is a cup with two handles? The answer to these questions leads us to define a quantity called Euler characteristic. We will see why this quantity is a topological invariant of surfaces. Time permitting, we will also see the statement of the Poincare-Hopf theorem for surfaces, which tells us how to read off the Euler characteristic of a surface from a vector field on the surface.

Snack Break

16:45 - 17:15

Rohan Goyal, CMI (BSc III)

Introduction to Randomization (Student Talk)

17:15 - 18:30

We will introduce the idea of randomized computation, demonstrate some classical algorithms, analysis techniques and related inequalities!

Siddhant Shah, CMI (BSc III)

Options 101 (Informal Session)

21:00 - 22:15

Professor Joseph Samuel, ICTS

Space, Time and Disorder

9:00 - 10:15

Einstein's theory of relativity revolutionised our ideas of space and time. The theory predicts the existence of gravitational waves and led to the big bang model of an expanding Universe. The theory also predicts that sufficiently massive stars will collapse under their own weight into black holes. Astrophysicists have been able to confirm all these predictions. Black holes are known to exist in our Universe. This brings up serious conceptual questions which are at the forefront of current research. There are well established laws of thermodynamics governing the working of steam engines, which tell us that the Universe gets progressively more disordered. Do black holes break this law? This talk will try to bring out the excitement of the subject, using almost no mathematics. Instead, I will use simple physics demonstrations to bring out the main conceptual ideas. No background beyond high school physics is needed to follow the talk.

Snack Break

10:45 - 11:15

Professor Anand Louis, IISc Bangalore

Certifying Non-Negativity of Polynomials

11:15 - 12:30

In 1900 Hilbert asked how can one "certify" that a non-negative polynomial is indeed non-negative? Though this question was answered in 1927 by Artin, the study of this and related questions and their computational aspects has lead to a rich theory and many new results in the study of algorithms, combinatorics, optimization, etc. In this talk I will talk about the history and some of the recent exciting developments related to these problems.

Lunch

12:30 - 14:00

Professor Saket Saurabh, IMSc

14:00 - 15:15

Break

15:15 - 15:30

Sunaina Pati, CMI (BSc I)

On Calkin-Wilf Tree (Student Talk)

15:30 - 16:45

We define a set as countable if it has a bijection to naturals. Are rationals countable? How about Reals? After discussing countability and uncountability of sets, we'll dive into recounting rationals using the Calkin Wilf tree. Our journey to prove rationals countable will lead us to discover a lot of calkin wilf tree properties!

Snack Break

16:45 - 17:15

Adhvik Jagannathan, CMI (BSc III)

From Classical Mechanics to Quantum Fields (Student Talk)

17:15 - 18:30

The advent of Quantum Field Theory is one of the most celebrated moments in modern physics. It efficiently provides a multi-particle description of quantum mechanics, and incorporates special relativity at the same time, while matching experimental data in all senses very faithfully. In this talk, we will explore the various ideas which lead to the birth of this subject, starting from the failures of classical mechanics and ending with some important applications of Quantum Field Theory in High Energy Physics.

Siddhant Shah, CMI (BSc III)

Option Pricing As Diffusion (Informal Session)

21:00 - 22:15

We begin by introducing Options as a financial instrument and proceed to dicuss their use cases in building portfolios. We then use portfolio construction to derive the partial differential equation for Option Pricing and explore the similarities between this PDE and the Diffusion PDE.

Professor B.V. Rao, CMI

9:30 - 10:45

Snack Break

10:45 - 11:15

Professor Prabha Mandayam, IIT Madras

Computing With Quantum Bits

11:15 - 12:30

Quantum computing is a rapidly-emerging field that harnesses the laws of quantum mechanics to solve problems too complex for classical computers. In this talk, we will get an introduction to quantum computing.

Lunch

12:30 - 14:00

Professor Shweta Aggarwal, IIT Madras

Cryptography: The Art of The Paradox

14:00 - 15:15

Break

15:15 - 15:30

Certificates Distribution

15:30 - 16:45

Snack Break

16:45 - 17:15

Informal Discussion

17:15 - 18:30