Calendar

**Note special time & location: 10 – 11 AM ET in Room G02**

https://cmsa.fas.harvard.edu/event/algebraic-geometry-in-string-theory/

Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In the first part of the talk, I will show that, by using supersymmetric localization, the gravitational path integral for 1/16-BPS black holes in supergravity can reproduce the index obtained in the string theory construction of such black holes. A more refined argument then shows that not only the black hole index but also the total number of black hole microstates within an energy window above extremality that is polynomially suppressed in the charges also matches this string theory index. In the second part of the talk, I will present a second perspective on this state count and show how the BPS Hilbert space can be obtained by directly preparing states using the gravitational path integral. While such a preparation naively gives rise to a Hilbert space of BPS states whose dimension is much larger than expected, I will explain how non-perturbative corrections in the overlap of such states are again responsible for reproducing the correct dimension of the Hilbert space.

Inspired from ideas in topology, Koszul modules and the associated resonance varieties turned out to have important algebro-geometric applications for instance to (i) Green’s Conjecture on syzygies of canonical curves, (ii) stabilization of cohomology of projective varieties in arbitrary characteristics and (iii) Chen invariants of hyperplane arrangements. I will discuss new developments related to this circle of ideas obtained in joint work with Aprodu, Raicu and Suciu.

Finding, applying and learning from the appropriate frameworks to use as lenses for educational research is an important task. In this talk I will share the three theoretical frameworks that I have used to study entry-level mathematics endeavors including: widespread change at a university (that involved implementation of TA training, course coordination, and many other efforts); leaders selected for funded efforts to incorporate active learning; and viability of mathematics tutoring centers. While I will give specific examples from my own research, each of the frameworks could be used to study a variety of university entities.

“TTbar” deformed 2d quantum field theory is a non-local theory in which Minkowski space is deformed in a state-dependent but consistent manner. For a massive theory this is equivalent to each particle acquiring a width proportional to its mass in its rest frame, giving rise to simple CDD factors dressing the $S$–matrix, but for deformed conformal field theories the spectrum becomes quite complicated, and the question of modular invariance of the torus partition function is non-trivial. I will show that this leads to a theory of TTbar deformed modular forms in general. Maass forms turn out to play an important role as eigenforms of the deformation.

The Math Picture Language seminar will be held at 9:30 a.m. Boston time.
Click the link for a Zoom Link for Tuesday Math Picture Language Seminars.
Recorded seminars can be viewed on the Mathematical Picture Language YouTube channel.