Calendar

A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of {\L}uczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size, which seems to be a barrier for certain natural approaches. Recently, in joint work with Dragani\’c and Krivelevich, we solved this problem. In the talk, I will discuss the history of the problem and give an overview of the proof.

Zoom link: https://harvard.zoom.us/j/99715031954?pwd=eVRvbERvUWtOWU9Vc3M2bjN3VndBQT09

Password: 1251442

I will give an overview of recent joint work with Jinmin Wang, Shmuel Weinberger, and Zhizhang Xie on the resolutions of several open questions of Gromov on positive scalar curvatures using higher invariants of Dirac operators.

I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

https://harvard.zoom.us/j/95767170359 (Password: cmsa)

A central challenge in quantum many-body physics is to estimate the properties of natural quantum states, such as the quantum ground states and Gibbs states. Quantum Hamiltonian complexity offers a computational perspective on this challenge and classifies these natural quantum states using the language of quantum complexity classes. This talk will provide a gentle introduction to the field and highlight its success in pinning down the hardness of a wide variety of quantum states. In particular, we will consider the gapped ground states and Gibbs states on low dimensional lattices, which are believed to exhibit `low complexity’ due to the widely studied area law behaviour. Here, we will see the crucial role of complexity-theoretic methods in progress on the `area law conjecture’ and in the development of efficient algorithms to classically simulate quantum many-body systems.

https://harvard.zoom.us/j/99651364593?pwd=Q1R0RTMrZ2NZQjg1U1ZOaUYzSE02QT09

Zoom ID: 950 2372 5230 (Password: cmsa)