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Mathematical Reasoning, Formal Proof Systems and Mathematical Reasoning
Siddhartha GadgilICTS:28950
How hard is it to solve this?
Prerona ChatterjeeICTS:28971Which of the following problems is "harder" to solve? Adding two 5-digit numbers or multiplying them? In general, it seems that multiplying is harder, but is there a way to make this feeling formal?
The area of theoretical computer science tries to do just that for any given problem! In this talk, we will look at some examples of such problems and try to see how easy/hard it is to solve them.
Causal Inference: Evaluating Research Design
Nivedita BhakhtaICTS:28970Causal research is ubiquitous. But, are all causal claims sound and justified? This talk will introduce the basic concepts of causal inference.
The world of colours
Neeraja DashaputreICTS:28963Colour is a fundamental aspect of our world, shaping our perception, culture, and experiences. In this talk, we will explore the multifaceted science of colour, tracing its profound influence through history and delving into the fascinating interplay of physics, chemistry, and biology that brings colour to life. We will also discuss the mathematics of colour, which helps us to identify and represent colour effectively! Encompassing various aspects of how light and colour are interconnected, we will illustrate the principles of light dispersion, the visible spectrum, and the phenomena of reflection, refraction, and absorption that give rise to the colours we see. We will explore the chemistry and the molecular origin of colour in pigments and dyes, along with the biology of colour perception, and interpretation highlighting the evolutionary significance of colour. Join for a colourful journey through time and science with demonstrations that will make the science of colour come alive.
Regularities within irregularities
Nikita AgarwalICTS:28962Nature has been a great inspiration for many scientific developments. Fractal Geometry is a case in point. Fractals are mathematical objects resembling the irregularities that are observed in nature. Fractal geometry aims to understand the regularities that are hidden behind such irregularities. In this talk, we will discuss the key mathematical concepts related to Fractal Geometry using illustrative examples. We will also give an overview of the development of this field and their applications.
Social Cognition: a peek through a multimodal lens
K M SharikaICTS:28958According to the social brain hypothesis, primate brains evolved in size to adapt to the increasing demands of navigating a complex social network. Recent evidence has corroborated this by demonstrating how social interactions (or its lack of) can have measurable consequences on an organism’s biological fitness. However, the physiological mechanisms underlying our everyday decisions in a social context are not yet well-understood. In this talk, I will share some key findings from social neuroscience, highlighting some of our own work with non-human primates on valence based social decision-making. I will end with talking about another aspect of group behavior, a phenomenon known as ‘physiological synchrony’ and show, using our own data from a naturalistic group discussion task, how it could be a biomarker of effective group decision-making.
Navigating Uncertainty with the Power of Data: Probability and Statistics Unraveling Real-World Challenges
Sayantee JanaICTS:28957Dive into the fascinating world of probability, statistics and data mining as we embark on a journey to unravel complex real-world challenges. Through captivating examples, stories and anecdotes, discover how these statistical principles enable us to quantify the unknown, navigate uncertainty, and devise effective strategies for addressing a wide range of real-world problems. We also discuss about the journey of statistics through time.
Mathematical Games
Jyothi KrishnanICTS:28953In this session we will play games and develop the mathematics of some games (and maybe a puzzle or two).
Mathematical Reasoning, Formal Proof Systems and Mathematical Reasoning
Siddhartha GadgilICTS:28950Generative AI has become a popular sensation, showing remarkable abilities including with language, analogical reasoning and originality. But, as is well known, it is notoriously unreliable.
Less visible have been dramatic developments in Formal Proof Systems, where computers verify and help in finding proofs.
Formal proof systems perfectly complement generative AI for Mathematical reasoning, at least in principle. In this talk, I discuss these two developments and their relation.