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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
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Posts
Thoughts on late-time physics in Quantum gravity
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In general, solving something like the Hamiltonian constraint (called the Wheeler-DeWitt equation, which we will abbreviate to “WDW”) in the framework of canonical quantum gravity is hard. Usually, one picks up an additional ansatz that simplifies the situation, such as minisuperspace and so on, although I am not aware of such cases. In a paper called “Hilbert Space of Quantum Gravity in de Sitter Space”, it was shown that the solutions to the WDW equation (while a WDW state also corresponds to the momentum constraint, usually it is more preferrable to consider the explicit study of the Hamiltonian constraint and an implicit study of the momentum constraint, due to certain reasons I will expand on at the end of this post) in de Sitter take up a nice form, which was found by an ansatz, where one starts by saying that at late-time slices (found by setting a conformal factor $\Omega$ such that $\log\int\sqrt{|g|}d^{D}x\to\infty$ corresponds to the factor $\Omega\to+\infty$), the wavefunctional takes up the form [\Psi=e^{i\mathcal{F}}\;,] where $\mathcal{F}$ is a functional that will not be explicitly worked with at the present level. Read more
Inception
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I am somewhat lame with writing things like this, but I think if I get right into it, it would save me from a lot of awkwardness that comes around with trying to explain why you are trying to explain things no one asked – but I bet people ask about von Neumann algebras (a really interesting thing), so I decided to try it this way. Read more
Poincare and h-cobordism theorem
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The way to define an h-cobordism is as follows: if the inclusion maps $\iota_{0}$ and $\iota_{1}$ corresponding to a cobordism $M$ are homotopy equivalences, then $M$ is said to be an h-cobordism. That is, if the inclusion maps $\iota_{0}:N_{0}\hookrightarrow M$ and $\iota_{1}: N_{1}\hookrightarrow M$ are homotopy equivalences, then we say that the cobordism $M$ is an h-cobordism. The h-cobordism theorem is as follows: Read more
Blog Post number 2
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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool. Read more
portfolio
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publications
talks
Aspects of the Generalized Second Law and the Covariant Entropy bound
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In this talk, we will look at generalized entropy and the generalized second law in the perspective of singularities. We will review the GSL in a cosmological perspective, and find motivation towards the GSL and entropy based singularity theorems. We will see how the fine-grained GSL and the covariant entropy bound provide a physical tool for singularity theorems, replacing topological conditions such as the presence of a non-compact Cauchy surface with instead the quantum focusing conjecture. We will then discuss further aspects of the GSL such as quantum holographic screens in different cosmologies, and if time permits we will provide an outlook for the role of generalized entropy in the asymptotic nature of null hypersurfaces, which will formulate a quantum Penrose inequality for null hypersurfaces on the basis of the generalized entropy. Recording available at https://www.youtube.com/watch?v=dH2IhL_s3o8. Read more
Holographic Quantum Gravity and Horizon Instability
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In this talk, we will look at the relation between the No Transmission principle and the Strong cosmic censorship (SCC), which we will highlight in the background of quantum gravity. We show that taking quantum gravity into account, one can provide a complete picture of the instability of the inner horizon and the principle that two independent CFTs, under the gauge-gravity duality, imply that the dual bulks must also be independent in that there must not exist a way to transmit a signal between the two spacetimes. We show that this can simply be interpreted as SCC, and that the inner horizon must be unstable (at either linear or nonlinear orders) to be in accordance with holographic quantum gravity. Read more
The Definition of Holography
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In this talk, we will review the notion of holography in quantum gravity. We will discuss some subtleties around the definition of holography, and the implications of holography. In the first half, we will discuss some elementary aspects of (A)dS/CFT, some comparisons, and how certain technicalities complicate the general notion of holography as a bulk-(cutoff-)boundary duality. In the second half, we will discuss some aspects in more technical detail, especially in the direction of establishing holography mathematically. Read more
teaching
On the Poincare conjecture, Ricci flow and all that
Lecture notes, math.DG, 2023
This set of notes contains some things I found interesting about the Poincare conjecture. I must say that I am not an expert, due to which I am not sure when or if at all these notes will be complete. However, this is a very fascinating subject, and I have written these for the sake of capturing some results I found, that discuss some of the more nontrivial aspects of the then Poincare conjecture. Read more
Bulk Physics, Algebras and All That
Lecture notes, hep-th, 2023
This is a course on AdS/CFT in the direction of bulk physics, operator algebras, and other recent developments. Originally a three-part series, now an N-part series in the large N limit. :) Read more