Frontiers in Mathematics is an intensive three-day conference in Mathematics held at Kerala School of Mathematics (KSoM), in association with the National Board for Higher Mathematics (NBHM), for research scholars, postdoctoral fellows, and advanced graduate students.

We plan to make it a bi-annual event. Each edition is built around a simple idea: devote one full day to one topic. A leading specialist takes you from the foundations all the way to the state of the art, through a series of lectures complemented by tutorial and problem-solving sessions. It is an opportunity for focused, deep learning, and collaboration.

The first edition features three lecture series:

• Matrix Positivity and its Preservers with connections to symmetric functions and majorization, and to distance geometry and sphere packing
• Geometry of Coxeter groups Coxeter groups are an abstraction of reflection groups, i.e. subgroups of isometries of Euclidean space that are generated by finitely many reflections. Coxeter completely classified all finite Coxeter groups in 1935. These groups find applications in many diverse areas of mathematics. In this mini-course, we will study Coxeter groups (with a focus on infinite ones) from the perspective of geometric group theory. Specifically, we will build the lectures towards showing that every Coxeter group acts properly and cocompactly on a non-positively curved simply connected space (also called a CAT(0) space). We will then use this action to derive some group theoretic properties of Coxeter groups. The lectures will roughly be divided as:
  • Introduction to geometric group theory and Coxeter groups
  • Introduction to CAT(0) geometry
  • Every Coxeter group is CAT(0)
  • Applications
• To be announced

We welcome applications from motivated participants across India. Limited funding is available to support travel expenses.