#### Alladi Ramakrishnan Hall

#### Geometry and Graphs: A Tale of Two Worlds

#### Sujoy Bhore

##### IISER Bhopal

*Data visualization and massive data handling are some of the primary*

concerns of computer scientists. However, most big data sets are

relational, containing a set of objects and relations between these

objects. This translates to a natural mathematical model, called graph,

with the objects as the vertices and the relations as the edges. Many

important real-life problems can be modeled as combinatorial optimization

problems on graphs. In the first part of my talk, I will focus on some

classical combinatorial optimization problems, e.g., spanners, spanning

trees, Erdős-Szekeres-type problems, etc.

However, we live in a dynamic world where our everyday life involves

several decision making processes that are based on data changing

constantly over time. Algorithms are at the core of computer science. They

define the underlying computational processes of every complex system

running in today's digital world. These systems are fed enormous amounts of

data on a frequent basis. Therefore, a natural challenge for algorithms is

to not only do efficient computation at a particular point, but also to

maintain a good quality solution throughout. In the second part of my talk,

I will focus on the algorithmic journey from static to dynamic geometric

optimization problems.

Done