Abstract: Fix your favorite smooth, compact curve C in the plane. How many rational points of a prescribed denominator size are in a given neighborhood of C? In the first part of the talk, we motivate this question and discuss a simple random model predicting the answer. 

In the second part, we use (purely) analytic and geometric tools to approach the question. Special emphasis will be placed on explaining the role of the Fourier transform of the surface measure.

All are cordially invited to the seminar.

Whole-cell modelling (WCM) is a grand challenge for 21st-century science,
demanding an interdisciplinary approach to create predictive tools that bridge the gap from
fundamental molecular structures to the emergent behaviours of life. While a spatially-
resolved model of a minimal cell has recently been proposed, its scalability to more complex
cells remains a major hurdle. The most formidable computational bottleneck of these multi-
physics, modular, WCMs lies in simulating stochastic reaction-diffusion processes. Reaction-

The effect of malaria on the developing world is devastating.  Each year there are
more than 200 million cases and over 400,000 deaths, with children under the age of five
the most vulnerable. Ambitious malaria elimination targets have been set by the World
Health Organization for 2030. These involve the elimination of the disease in at least 35
countries. However, these malaria elimination targets rest precariously on us being able to
identify, diagnose and treat the disease appropriately.   
  

Abstract: 

In this expository talk, we describe the dynamics of holomorphic rational maps defined on the Riemann sphere and narrate a result concerning the normality of the family of iterates of the map and the equidistribution of inverse images of points. We then generalise the same to the setting of holomorphic correspondences, explaining our way and motivation from the study of maps to that of correspondences. 

All are cordially invited to the seminar.

Abstract: 

If a holomorphic map f: C→D of compact Riemann surfaces has no ramification points, then the induced map of their fundamental group is injective.

So for the surjectivity of the fundamental group of the induced map, it is necessary to ramify.. But being ramified alone does not imply surjectivity. Those maps where the induced map has the surjectivity of the fundamental group are called genuinely ramified. In this talk, we will show many equivalent conditions for genuine ramification. It is shown that the genuine ramification is equivalent to: 

Abstract: 

The different ways that a rope can be knotted has been an important area of study, both from applied and theoretical points of view. The mathematics tools that are used to study knots begin with simple combinatorial ideas and progress to deep mathematical theories. In this talk we will introduce knot theory and talk about some of its basic invariants. There are no prerequisites for this talk and it should be accessible to everyone.

All are cordially invited to the seminar.

Venue: Room 303, Samgatha, Nila campus