This talk will be on certain new techniques for triangulated categories introduced by Neeman in a series of papers, which have been used to prove various new results and settling multiple open conjectures. We will give a broad overview of these techniques, and illustrate various applications in algebraic geometry. In particular, we will see a representability theorem and its application to a new proof of GAGA theorems, a result on transferring semiorthogonal decompositions, and a result on the non-existence of bounded t-structures for perfect complexes on singular finite-dimensional Noetherian schemes.

We all are familiar with the first order liquid-gas phase transition line ending at a critical point. This raises the question : Can a second order critical line have an end point such that we can go around that end point avoiding the criticality ? Such criticality would be then "unnecessary". In this talk, I shall discuss a simple example of a classical spin system in three spatial dimensions which shows such a transition. I will present our numerical calculations and discuss the mechanism of this unnecessary criticality.

Neutrinos are among the most elusive particles in nature. They interact so weakly with matter that trillions pass through our bodies every second without a trace. Yet these “ghost particles” can carry information from some of the most violent and distant environments in the universe - places that light, cosmic rays, and electromagnetic waves may not fully reveal. We will introduce neutrinos and highlight the role they play in our understanding of the universe. The first part of the talk will consist of an introduction to neutrino physics, along with a historical account of important discoveries. The 2026 Nobel Prize in Physics honoured Francis Halzen for his decisive contributions to the IceCube Neutrino Observatory and the discovery of high-energy neutrinos from astrophysical sources. This talk will explain why neutrinos are such powerful cosmic messengers, how IceCube turns Antarctic ice into a telescope, and what its discoveries tell us about extreme cosmic accelerators. We will also discuss how the detection of astrophysical neutrinos has opened a new window on the universe and helped establish high-energy neutrino astronomy as an important area of multi-messenger astronomy and astrophysics.

In this talk we describe $T_{comp}$-equivariant topological K-ring of $T$-cellular varieties. We apply our results to obtain the description of the equivariant topological K-ring of cellular toric varieties and hence the description of the $G_{comp}\times G_{comp}$-equivariant $K$-ring of cellular toroidal embeddings $\bar{G}$ of a complex reductive algebraic group $G$.

TBA