Talks

This session will be mostly practical. Within the framework of the 2-species LV model, we will use nullcline analysis to predict the outcome of competition in different situations. These include cases in which either or both competitors are subject to cooperative growth, which can lead to alternative stable states that emerge in (2-species) co-culture, but that are absent in any of the (1-species) monocultures.

We investigate the implications of memory burden on the gravitational wave (GW) spectrum arising from the Hawking evaporation of light primordial black holes (PBHs). By considering both rotating (Kerr) and non-rotating (Schwarzschild) PBHs, we demonstrate that the overproduction of primordial GWs from burdened PBHs could impose stringent constraints on the parameters governing backreaction effects. These constraints, derived from ∆Neff measurements by Planck and prospective experiments such as CMB-S4 and CMB-HD, offer novel insights into the impact of memory burden on PBH dynamics.

Gravitational wave memory is a persistent non-oscillatory shift in the gravitational wave amplitude. Such effects are ubiquitous in astrophysical and cosmological cataclysmic events involving gravitational radiation. In this talk, we turn our attention to the case of a supernova neutrino burst generating gravitational radiation. Previous studies along this line have demonstrated that a neutrino burst in such scenarios gives rise to a gravitational memory signal. Here, we specifically inquire about the alterations to the memory signal when neutrinos emitted from a supernova undergo self-interaction, presenting an avenue for indirectly detecting neutrino self-interaction.

In this talk, I will discuss a phenomenon called cosmic inflation in which the Universe went through accelerated exponential expansion to solve the horizon problem of Cosmological Microwave Background within a billionth of a trillionth of a trillionth of a second, in the very early Universe. This accelerated expansion, in its minimal form, is driven by a scalar field (inflaton) and it takes place when this scalar field slowly rolls down a potential well. However, the origin of this scalar field and the correct form of the scalar potential remains an open question in cosmology. I will present a string theory motivated model where the inflaton is connected to the geometry of the internal space -- the overall volume of it drives the inflation. In particular, I will present a construction where the overall volume modulus (scalar field) is dynamically stabilized to an exponentially large value only via perturbative corrections, also known as perturbative large volume scenario (LVS). In this framework, the robustness of the single-field inflationary model is checked against possible sub-leading corrections. In the later part of my talk, I will focus on the global embedding of the fibre inflation in perturbative LVS and show how our constructions pose less challenge in realizing a successful period of inflation.

Axion inflation models are particularly interesting due to their shift symmetry, which protects the axion potential from large quantum corrections. In models where the axion couples to a gauge field, this coupling gives rise to a rich phenomenology, including the production of gravitational waves (GWs), primordial black holes, and primordial magnetic fields. In this talk, I will discuss our ongoing work that numerically explores axion inflation in the regime where a strong coupling between axions and gauge fields induces significant backreaction from amplified gauge fields during inflation. These amplified fields produce high-frequency GWs, which serve as a probe for constraining the coupling strength between axions and gauge fields. Our findings indicate that when backreaction is significant during inflation, constraints on coupling strength due to GW overproduction are relaxed compared to previous studies where backreaction occurs only after inflation. I will also discuss the generation of magnetic fields of astrophysical interest in this model.

In this talk, I will present recent progress in the study of domain wall networks. First, in terms of their gravitational relics - gravitational waves (GWs) and primordial black holes - that might be behind the recent signals observed at Pulsar Timing Arrays. Second, I will discuss the isotropic birefringence effect that domain wall networks coupled to photons cause on the polarization of the CMB, with striking connections to the recent evidence found in the CMB data.

In these lectures, I discuss how GWs are produced by cosmological phase transitions. We start by a short recap of gravitational waves and then move to early attempts using pairs of bubbles and the envelope approximation. Next we cover the energy budget of phase transitions and the impact of sound waves. Finally I comment on recent developments.

The Virasoro conformal blocks are very interesting since they have many connections to other areas of math and physics. For example, when $c=1$, they are related to tau functions of integrable systems of Painlev\'{e} equations. They are also closely related to non-perturbative completions in the topological string theories. I will first explain what Virasoro conformal blocks are. Then I will describe a new way to construct Virasoro blocks at $c=1$ on $C$ by using the "abelian" Heisenberg conformal blocks on a branched double cover of C. The main new idea in our work is to use a spectral network and I will show the advantages of this construction. This nonabelianization construction enables us to compute the harder-to-get Virasoro blocks using the simpler abelian objects. It is closely related to the idea of nonabelianization of the flat connections in the work of Gaiotto-Moore-Neitzke and Neitzke-Hollands. This is based on a joint work with Andrew Neitzke.