Talks

The series of three short lectures provides an introduction to the subject of subgroup growth and related directions of research in asymptotic group theory. For instance, we will discuss polynomial subgroup growth and look at subgroup zeta functions of finitely generated nilpotent groups. We also cover methods from the theory of compact p-adic Lie groups, which have applications to subgroup growth and representation growth.

Integrated photonics has progressed significantly in the past decade as a viable platform for quantum information processing. However, several challenges still remain in the path from demonstrating proofs of concept to providing solutions to problems which are interesting to the scientific community and society in general. In this talk I will discuss key challenges in the development of Noisy Intermediate-Scale Quantum (NISQ) photonic devices, and some solutions being investigated in our group.

In this talk, I will briefly present the timeline of quantum computing development. Focusing on current obstacles, I will discuss today’s challenges, highlighting the main types of quantum errors, such as coherent and incoherent errors, readout and initialization errors, and crosstalk, which represent significant obstacles in the noisy intermediate-scale quantum (NISQ) era. Building on this, I will explore the evolution of error-correcting codes, from classical foundations to the latest quantum approaches, as well as error mitigation strategies—essential tools for increasing computational reliability. This talk aims to shed light on the current barriers to quantum computing and the advances that drive the future viability of quantum algorithms.

Higgs branches in theories with 8 supercharges change as one tunes the gauge coupling to critical values.  This talk will focus on six dimensional (0,1) supersymmetric theories in studying the different phenomena associated with such a change. Based on a Type IIA brane system, involving NS5 branes, D6 branes and D8 branes, one can derive a "magnetic quiver” which enables the construction of the Higgs branch using a “magnetic construction” or as a more commonly known object “3d N=4 Coulomb branch”.  Interestingly enough, the magnetic construction opens a window to a new set of Higgs branches which were not available using the well studied method of hyperkähler quotient.  It turns out that exceptional global symmetries are fairly common in the magnetic construction, and few examples will be shown. In all such cases there are strongly coupled theories where Lagrangian description fails, and the magnetic construction is helpful in finding properties of the theory.  Each Higgs branch can be characterized by a phase diagram which describes the different sets of massless fields around vacua. We will use such diagrams to study how Higgs branches change.  If time permits we will show an interesting exceptional sequence consisting of SU(3) — G2 — SO(7).

The series of three short lectures provides an introduction to the subject of subgroup growth and related directions of research in asymptotic group theory. For instance, we will discuss polynomial subgroup growth and look at subgroup zeta functions of finitely generated nilpotent groups. We also cover methods from the theory of compact p-adic Lie groups, which have applications to subgroup growth and representation growth.