Talks

A tower is an infinite sequence of deloopings of symmetric monoidal ever-higher categories. Towers are places where extended functorial field theories take values. Towers are a "deeper" version of commutative rings (as opposed to "higher rings" aka E∞-spectra). Notably, towers have their own opinions about Galois theory, and think that usual Galois groups are merely shallow approximations of deeper homotopical objects. In this talk, I will describe some steps in the construction and calculation of the deeper Galois group of a characteristic-zero field. In particular, I'll explain a homotopical version of the Kummer description of abelian extensions. This is joint work in progress with David Reutter.

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Zoom link: https://pitp.zoom.us/j/97950701035?pwd=Wk9FRSt2MkN3eWptTVltRVJncnFHdz09

The event horizon of a dynamical black hole is generically a non-smooth hypersurface. I shall describe the types of non-smooth structure that can arise on a horizon that is smooth at late time. This includes creases, corners and caustic points. I shall discuss ``perestroikas'' of these structures, in which they undergo a qualitative change at an instant of time. A crease perestroika gives an exact local description of the event horizon near the ``instant of merger'' of a generic black hole merger. Other crease perestroikas describe horizon nucleation or collapse of a hole in a toroidal horizon. I shall discuss the possibility that creases contribute to black hole entropy, and the implications of non-smoothness for higher derivative terms in black hole entropy. This talk is based on joint work with Maxime Gadioux.

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Zoom link: https://pitp.zoom.us/j/98839294408?pwd=cytNYThQaDV4Y2lob1REY0NyaTJNUT09

A stochastic gravitational wave background (SGWB) originates from numerous faint gravitational wave (GW) signals arising from coalescing compact binary objects. Based on the current estimated merger rate, the SGWB signal is expected to originate from non-overlapping GW waveforms where the chirping nature of individual events is expected to be preserved. In this talk, we present a novel technique, Spectrogram Correlated Stacking (or SpeCs), which goes beyond the usual cross-correlation (and to higher frequencies) by exploiting the higher-order statistics in the time-frequency domain. This method would account for the chirping nature of the individual events that comprise SGWB and enable us to extract more information from the signal due to its intrinsic non-gaussianity. We show that SpeCs improve the signal-to-noise for the detection of SGWB by a factor close to 8, compared to standard optimal cross-correlation methods which are tuned to measure only the power spectrum of the signal. SpeCs can probe beyond the power spectrum and its application to the GW data available from the current and next-generation detectors would speed up the SGWB discovery.

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Zoom link: https://pitp.zoom.us/j/91002244803?pwd=a0dnMjZEYTEwSHBCVGRSeHB2Y2pJdz09

An ongoing program of work in statistical physics and quantum dynamics is concerned with understanding the character of systems which follow an unconventional approach towards thermal equilibrium. In this talk, I will add to this story by introducing examples of simple 1D systems---both classical and quantum---which thermalize in very unusual ways. These examples have dynamics which is strictly local and translation-invariant, but in spite of this, they: a) can have very long thermalization times, with expectation values of local operators relaxing only over times exponential in the system size; and b) can thermalize only when they are placed in extremely large baths, with the required bath size growing exponentially (or even faster) in system size. Proofs of these results will be given using techniques from geometric group theory, a beautiful area of mathematics concerned with the complexity and geometry of infinite discrete groups. This talk will be based on a paper in preparation with Shankar Balasubramanian, Sarang Golaparakrishnan, and Alexey Khudorozhkov.

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Zoom link: https://pitp.zoom.us/j/99430001465?pwd=NENlS1M5UGc5UWM1ekQvRWFrZGYyUT09