Department of

Mathematics


Seminar Calendar
for Mathematical Physics events the year of Thursday, November 21, 2019.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, February 4, 2019

12:00 pm in 343 Altgeld Hall,Monday, February 4, 2019

The integration problem for Courant algebroids

Rajan Mehta (Smith College)

Abstract: Courant algebroids originally appeared in the study of constrained Hamiltonian systems, but they are connected to many areas of mathematical physics, including multisymplectic geometry, double field theory, and (my personal interest) 3-dimensional topological field theory. Since a Courant structure involves a bracket that resembles a Lie bracket (but fails to be skew-symmetric), one might expect there to be some groupoid-like structure for which a Courant algebroid is the infinitesimal object. There is reason to believe that the answer should be a "symplectic 2-groupoid," but there are many devils in the details, including even the question of how "symplectic 2-groupoid" should be defined. I will describe various developments in this problem.

Thursday, March 14, 2019

12:30 pm in 464 Loomis,Thursday, March 14, 2019

A proposal for nonabelian mirrors in two-dimensional theories

Eric Sharpe (Virginia Tech)

Abstract: In this talk we will describe a proposal for nonabelian mirrors to two-dimensional (2,2) supersymmetric gauge theories, generalizing the Hori-Vafa construction for abelian gauge theories. By applying this to spaces realized as symplectic quotients, one can derive B-twisted Landau-Ginzburg orbifolds whose classical physics encodes quantum cohomology rings of those spaces. The proposal has been checked in a variety of cases, but for sake of time the talk will focus on exploring the proposal in the special case of Grassmannians.

Thursday, September 5, 2019

1:00 pm in 464 Loomis,Thursday, September 5, 2019

FROM LOCALITY TO NON-LOCALITY: FERMIONIC ENTANGLEMENT ON THE TORUS

Ignacio A. Reyes (Max Planck Institute, Potsdam)

Abstract: We uncover various novel aspects of the entanglement of free fermions at finite temperature on the circle. The modular flow involves a bi-local coupling between a discrete but infinite set of points, even for a single interval. The modular Hamiltonian transitions from locality to complete non-locality as a function of temperature. We derive the entanglement and relative entropies, and comment on the applications to bulk reconstruction in higher spin holography.

Thursday, September 12, 2019

1:00 pm in 464 Loomis,Thursday, September 12, 2019

EXPERIMENTS WITH MACHINE LEARNING IN STRING GEOMETRY

Vishnu Jejjala (University of Witwatersrand)

Abstract: Identifying patterns in data enables us to formulate questions that can lead to exact results. Since many of the patterns are subtle, machine learning has emerged as a useful tool in discovering these relationships. We show that topological features of Calabi–Yau geometries are machine learnable. We indicate the broad applicability of our methods to existing large data sets by finding relations between knot invariants, in particular, the hyperbolic volume of the knot complement and the Jones polynomial.

Thursday, September 19, 2019

1:00 pm in 464 Loomis,Thursday, September 19, 2019

QUANTUM GRAVITY AND THE SWAMPLAND

Gary Shiu (University of Wisconsin)

Abstract: String theory seems to offer an enormous number of possibilities for low energy physics. The huge set of solutions is often known as the String Theory Landscape. In recent years, however, it has become clear that not all quantum field theories can be consistently coupled to gravity. Theories that cannot be ultraviolet completed in quantum gravity are said to be in the Swampland. In this talk, I’ll discuss some conjectured properties of quantum gravity, evidences for them, and their applications to cosmology.

Thursday, September 26, 2019

1:00 pm in 464 Loomis,Thursday, September 26, 2019

Holographic entanglement and quantum gravity in finite regions

Will Donnelly (Perimeter Institute)

Abstract: The T\bar{T} deformation of two-dimensional holographic conformal field theory is conjectured to be dual to quantum gravity in a finite region of three-dimensional anti-de Sitter spacetime. We study entanglement entropy in this theory and its relation to quantum fluctuations of the dual geometry. We derive the correspondence between the T\bar{T} flow equation and the Wheeler-DeWitt equation with a negative cosmological constant. By fixing the resulting emergent diffeomorphism symmetry, we obtain a differential equation for the sphere partition function which can be solved exactly. The solution can be expressed as a Euclidean path integral along a particular complex contour. We then apply this result to study entanglement entropy of the boundary theory for an entangling surface consisting of two antipodal points on the sphere. The entanglement entropy gives the Ryu-Takayanagi formula for a geodesic in a finite region plus quantum corrections. We suggest an interpretation of the latter as entropy of fluctuations of the bulk geodesic length, in accordance with the proposal of Faulkner, Lewkowycz, and Maldacena.

Thursday, October 3, 2019

1:00 pm in 464 Loomis Laboratory ,Thursday, October 3, 2019

The power of string theory in TTbar and related theories

David Kutasov (University of Chicago Physics)

Abstract: I describe the recent discovery of a class of non-local field theories that can be thought of as irrelevant deformations of two dimensional conformal field theories, focusing on their description as deformations of string theory on three dimensional anti-de-Sitter space.

Thursday, October 17, 2019

1:00 pm in 464 Loomis Laboratory ,Thursday, October 17, 2019

Sphere packing, modular bootstrap and extremal functionals

Dalimil Mazac

Abstract: I will prove a new theorem about 2D CFTs: Every unitary 2D CFT must contain a non-trivial Virasoro primary of scaling dimension at most c/8 + 1/2, where c is the central charge. At large c, this is an improvement of the Hellerman bound c/6 + O(1), and is relevant for constraining the spectrum of gravitational theories in AdS3. The proof follows from the modular bootstrap and uses analytic extremal functionals, originally developed in the context of four-point SL(2) conformal bootstrap. In the second part of the talk, I will discuss a surprising connection between modular bootstrap and the sphere-packing problem from discrete geometry. In particular, the above bound on the gap becomes a bound on the sphere-packing density. In 8 and 24 dimensions, this bound is sharp and leads to a solution of the sphere-packing problem in these dimensions, as originally proved by Viazovska et al. The talk will be based on arXiv:1905.01319.

Thursday, October 24, 2019

1:00 pm in 464 Loomis Laboratory,Thursday, October 24, 2019

Simple holographic models of black hole evaporation

Chris Akers (Berkeley Physics)

Abstract: Several recent papers have shown a close relationship between entanglement wedge reconstruction and the unitarity of black hole evaporation in AdS/CFT. The analysis of these papers however has a rather puzzling feature: all calculations are done using bulk dynamics which are essentially those Hawking used to predict information loss, but applying ideas from entanglement wedge reconstruction seems to suggest a Page curve which is consistent with information conservation. In this note we present a new pair of models which clarify this situation. Our first model gives a holographic illustration of unitary black hole evaporation, in which the analogue of the Hawking radiation purifies itself as expected, and this purification is reproduced by the entanglement wedge analysis. Moreover a smooth black hole interior persists until the last stages the evaporation process. Our second model gives an alternative holographic interpretation of the situation where the bulk evolution leads to information loss: unlike in the models proposed so far, this bulk information loss is correctly reproduced by the entanglement wedge analysis. In both models no bulk quantum corrections need to be considered: classical extremal surfaces are enough to do the job. We argue that our first model is a better analogy for what actually happens to evaporating black holes, but we also emphasize that any complete resolution of the information problem will require an understanding of non-perturbative bulk dynamics.

Thursday, October 31, 2019

1:00 pm in 464 Loomis Laboratory,Thursday, October 31, 2019

Multitrace excited states and perturbative entropy divergences

Antony Speranza (Perimeter Institute)

Abstract: Perturbative calculations of entanglement entropy have found a number of recent applications in understanding field theory, holography, and quantum gravity. In this talk, I will discuss a class of excited states of a CFT formed from a Euclidean path integral with nonlocal multitrace insertions, with an eye toward understanding their entanglement structure holographically. Such states are argued to have good semiclassical holographic duals, but can possess nontrivial bulk entanglement structure at order N^0. A surprising feature of these states is that divergences occur quite generically in the perturbative expansion of their entanglement entropy. These divergences signal a nonanalyticity in the expansion, and must be resummed in computing the full expression for the entropy. This resummation is challenging in general, but I will describe some simplified examples in which it may be tractable. In the process, I will also give some general techniques for diagnosing when such nonanalyticities occur, and point to some indications that they may in general be calculable. This talk is based on arXiv:1904.01584 and ongoing work.