CMSA

Hybrid Fracton Orders
2021-07-15 10:30 - 12:30 (America/New_York) | Virtual
Nathanan Tantivasadakarn (Harvard)
Video
Title: Hybrid Fracton Orders
Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”. First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.
Based on 2102.09555 and 2106.03842

7/21/2021 Quantum Matter Seminar
2021-07-21 10:30 - 12:00 | MA

7/22/2021 Quantum Matter Seminar
2021-07-22 08:00 - 09:30 | MA

Moduli spaces of stable pairs on algebraic surfaces
2021-07-22 09:00 - 10:00 | Virtual
Interdisciplinary Science Seminar
Speaker: Yinbang Lin (Tongji University)
Title: Moduli spaces of stable pairs on algebraic surfaces
Abstract: As a variant of Grothendieck’s Quot schemes, we introduce the moduli space of limit stable pairs. We show an example over a smooth projective algebraic surface where there is a virtual fundamental class. We are able to describe this class explicitly. We will also show an application towards moduli of sheaves.

The nu=5/2 enigma: Recent insights from theory and experiment
2021-07-29 10:30 - 12:00 | Virtual
peaker: Ady Stern & David Mross (Weizmann)
Speaker: Ady Stern & David Mross (Weizmann
Title: The nu=5/2 enigma: Recent insights from theory and experiment
Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.

Big Data Conference 2021
2021-08-24 | Virtual
On August 24, 2021, the CMSA hosted our seventh annual Conference on Big Data. The Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.
The 2021 Big Data Conference took place virtually on Zoom.
Organizers:

Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
Horng-Tzer Yau, Professor of Mathematics, Harvard University
Sergiy Verstyuk, CMSA, Harvard University

Speakers:

Andrew Blumberg, University of Texas at Austin
Moran Koren, Harvard CMSA
Hima Lakkaraju, Harvard University
Katrina Ligett, The Hebrew University of Jerusalem

Time (ET; Boston time)
Speaker
Title/Abstract

9:00AM
Conference Organizers
Introduction and Welcome

9:10AM – 9:55AM
Andrew Blumberg, University of Texas at Austin
Title: Robustness and stability for multidimensional persistent homology
Abstract: A basic principle in topological data analysis is to study the shape of data by looking at multiscale homological invariants. The idea is to filter the data using a scale parameter that reflects feature size. However, for many data sets, it is very natural to consider multiple filtrations, for example coming from feature scale and density. A key question that arises is how such invariants behave with respect to noise and outliers. This talk will describe a framework for understanding those questions and explore open problems in the area.

10:00AM – 10:45AM
Katrina Ligett, The Hebrew University of Jerusalem
Title: Privacy as Stability, for Generalization
Abstract: Many data analysis pipelines are adaptive: the choice of which analysis to run next depends on the outcome of previous analyses. Common examples include variable selection for regression problems and hyper-parameter optimization in large-scale machine learning problems: in both cases, common practice involves repeatedly evaluating a series of models on the same dataset. Unfortunately, this kind of adaptive re-use of data invalidates many traditional methods of avoiding overfitting and false discovery, and has been blamed in part for the recent flood of non-reproducible findings in the empirical sciences. An exciting line of work beginning with Dwork et al. in 2015 establishes the first formal model and first algorithmic results providing a general approach to mitigating the harms of adaptivity, via a connection to the notion of differential privacy. In this talk, we’ll explore the notion of differential privacy and gain some understanding of how and why it provides protection against adaptivity-driven overfitting. Many interesting questions in this space remain open.
Joint work with: Christopher Jung (UPenn), Seth Neel (Harvard), Aaron Roth (UPenn), Saeed Sharifi-Malvajerdi (UPenn), and Moshe Shenfeld (HUJI). This talk will draw on work that appeared at NeurIPS 2019 and ITCS 2020

10:50AM – 11:35AM
Hima Lakkaraju, Harvard University
Title: Towards Reliable and Robust Model Explanations
Abstract: As machine learning black boxes are increasingly being deployed in domains such as healthcare and criminal justice, there is growing emphasis on building tools and techniques for explaining these black boxes in an interpretable manner. Such explanations are being leveraged by domain experts to diagnose systematic errors and underlying biases of black boxes. In this talk, I will present some of our recent research that sheds light on the vulnerabilities of popular post hoc explanation techniques such as LIME and SHAP, and also introduce novel methods to address some of these vulnerabilities. More specifically, I will first demonstrate that these methods are brittle, unstable, and are vulnerable to a variety of adversarial attacks. Then, I will discuss two solutions to address some of the vulnerabilities of these methods – (i) a framework based on adversarial training that is designed to make post hoc explanations more stable and robust to shifts in the underlying data; (ii) a Bayesian framework that captures the uncertainty associated with post hoc explanations and in turn allows us to generate explanations with user specified levels of confidences. I will conclude the talk by discussing results from real world datasets to both demonstrate the vulnerabilities in post hoc explanation techniques as well as the efficacy of our aforementioned solutions.

11:40AM – 12:25PM
Moran Koren, Harvard CMSA
Title: A Gatekeeper’s Conundrum
Abstract: Many selection processes contain a “gatekeeper”. The gatekeeper’s goal is to examine an applicant’s suitability to a proposed position before both parties endure substantial costs. Intuitively, the introduction of a gatekeeper should reduce selection costs as unlikely applicants are sifted out. However, we show that this is not always the case as the gatekeeper’s introduction inadvertently reduces the applicant’s expected costs and thus interferes with her self-selection. We study the conditions under which the gatekeeper’s presence improves the system’s efficiency and those conditions under which the gatekeeper’s presence induces inefficiency. Additionally, we show that the gatekeeper can sometimes improve selection correctness by behaving strategically (i.e., ignore her private information with some probability).

12:25PM
Conference Organizers
Closing Remarks

Naturalness and muon anomalous magnetic moment
2021-09-01 18:31 - 19:31 | Virtual
Title: Naturalness and muon anomalous magnetic moment
Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.

Eppur si muovono: rotations in active matter
2021-09-02 13:00 - 14:30 | MA
Abstract: Living matter relies on the self organization of its components into higher order structures, on the molecular as well as on the cellular, organ or even organism scale. Collective motion due to active transport processes has been shown to be a promising route for attributing fascinating order formation processes on these different length scales. Here I will present recent results on structure formation on actively transported actin filaments on lipid membranes and vesicles, as well as the cell migration induced structure formation in the developmental phase of mammary gland organoids. For both systems spherical structures with persistent collective rotations are observed.

Exotic quantum matter: From lattice gauge theory to hyperbolic lattices
2021-09-02 18:34 - 19:34 | Virtual
Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices
Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.

Swampland Seminar Series
2021-09-03 10:30 - 12:00 | MA
During the 2021-22 academic year, the CMSA will be co-hosting a seminar on Swampland, with the Harvard Physics Department, organized by Miguel Montero, Cumrun Vafa, Irene Valenzuela. This seminar is a part of the Swampland Program. This seminar will take place on Mondays at 10:00 am – 11:30 am (Boston time). To learn how to attend, please subscribe here.
Talks will be posted on the Swampland Seminars YouTube channel. The schedule below will be updated as talks are confirmed.
Spring 2022

Date
Speaker
Title/Abstract

1/31/2022
Rafael Álvarez-García (DESY Hamburg)
Title: Membrane Limits in Quantum Gravity

2/7/2022
Du Pei (Harvard CMSA)
Title: Holomorphic CFTs and topological modular forms
Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories, and some of them might have interesting implications for the swampland program. In this talk, I will show that a conjecture by Segal, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of “extremal CFTs”, including those with central charges c = 48, 72, 96 and 120.

2/28/2022
Tom Rudelius (UC, Berkeley)
Title: Generalized Global Symmetries and the Weak Gravity Conjecture

3/7/2022
Fernando Marchesano (UAM-CSIC, Madrid) and Max Wiesner (Harvard CMSA)
Title: 4d strings at strong coupling

3/21/2022
Patrick Draper (Univ. of Illinois) and Alvaro Herraez (IPhT Saclay).
Open Mic Discussion
Topic: Entropy bounds (species bound, Bekenstein bound, CKN bound, and the like)

3/28/2022
Fernando Quevedo (Cambridge)
Title: On renormalisation group induced moduli stabilisation and brane-antibrane inflation
Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.

4/5/2022
Simon Caron-Huot (McGill University) and Julio Parra (Caltech)
Title: Causality constraints on corrections to Einstein gravity
Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher-spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

4/11/2022
Timm Wrase and Eduardo Gonzalo (Lehigh)
Title: Type IIB flux compactifications with $h^{1,1}=0$
Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.

4/18/2022
José Calderón (IFT Madrid)
Open mic Swampland Discussion
Topic: Cobordism

5/9/2022
Georges Obie (Harvard)
Title: Inflation and light Dark Matter constraints from the Swampland
Abstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally, I will review another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.

Fall 2021

Date
Speaker
Title/Abstract

9/13/2021
John Stout (Harvard)
Title: Decoding Divergent Distances
Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.

9/20/2021
Manki Kim (MIT)
Title: Small Cosmological Constants in String Theory
Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10^{-123} in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

9/27/2021
Eran Palti (Ben Gurion)
Title: Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture
Abstract: In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we propose a conjecture that this convexity is a general property of all CFTs, not just those with weakly-curved gravitational duals. It is possible to test this in simple CFTs, the conjecture passes all the tests performed so far.

10/18/2021
Thomas Van Riet (KU Leuven)
Title: The Festina Lente Bound
Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for phenomenology, both top-down and bottom-up.

10/25/2021
Joe Conlon (Oxford)
Title: Exploring the Holographic Swampland
Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space, such as LVS in type IIB or the DGKT flux vacua in type IIA, the dual moduli conformal dimensions reduce to fixed values – in a certain sense, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer, for reasons we do not understand.

11/01/2021
Pieter Bomans (Princeton)
Title: Bubble instability of mIIA on AdS_4 x S^6
Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of non-perturbative decay channels. Hence, at this point, they represent a serious challenge to the AdS swampland conjecture. In my talk, I will review in detail the construction of these vacua as well as introduce a new decay channel, ultimately sealing their fate as being unstable.

11/15/2021
Nima Arkani-Hamed (IAS), and Gary Shiu (UW-Madison)
This week’s seminar will be an open mic discussion which will be led by Nima Arkani-Hamed (IAS), and by Gary Shiu (UW-Madison), and the topic will be “Swampland constraints, Unitarity and Causality”. They will start with a brief introduction sharing their thoughts about the topic and moderate a discussion afterwards.

11/22/2021
Thomas Grimm (Utrecht University)
Title: Taming the Landscape
Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.

11/29/2021
Timm Wrase (Lehigh University)
Title: Scale separated AdS vacua?
Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.

12/6/2021
Lars Aalsma (University of Wisconsin-Madison)
Title: Extremal Black Hole Corrections from Iyer-Wald
Abstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically, corrections to extremality need to be computed on a case-by-case basis, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.

Derived categories of nodal quintic del Pezzo threefolds
2021-09-07 09:30 - 10:30 | MA
Abstract: Conifold transitions are important algebraic geometric constructions that have been of special interests in mirror symmetry, transforming Calabi-Yau 3-folds between A- and B-models. In this talk, I will discuss the change of the quintic del Pezzo 3-fold (Fano 3-fold of index 2 and degree 5) under the conifold transition at the level of the bounded derived category of coherent sheaves. The nodal quintic del Pezzo 3-fold X has at most 3 nodes. I will construct a semiorthogonal decomposition for D^b(X) and in the case of 1-nodal X, detail the change of derived categories from its smoothing to its small resolution.

Cornering the universal shape of fluctuations and entanglement
2021-09-08 18:37 - 19:37 | Virtual
Title: Cornering the universal shape of fluctuations and entanglement
Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.
Ref: arXiv:2102.06223

The complexity of matrix multiplication approached via algebraic geometry and representation theory
2021-09-09 14:00 - 15:00 | MA
Speaker: JM Landsberg, Texas A&M
Title: The complexity of matrix multiplication approached via algebraic geometry and representation theory
Abstract: In 1968 V. Strassen discovered the way we usually multiply matrices is not the most efficient possible, and after considerable work by many authors, it is generally conjectured by computer scientists that as the size of matrices becomes large, it becomes almost as easy to multiply them as it is to add them. I will give a brief history of the problem, explain how this conjecture is naturally understood in the framework of classical algebraic geometry and representation theory, and conclude by describing recent advances using more sophisticated tools from algebraic geometry. For most of the talk, no knowledge of algebraic geometry or representation theory will be needed.

Quantum gravity from quantum matter
2021-09-09 18:38 - 19:38 | Virtual
Title: Quantum gravity from quantum matter
Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

9/10/2021 General Relativity Seminar
2021-09-10 09:30 - 10:30 | MA
Title: Asymptotic localization, massive fields, and gravitational singularities
Abstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First, the Seed-to-Solution Method for Einstein’s constraint equations, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass, Schwarzschild decay, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second, the Euclidian-Hyperboloidal Foliation Method, introduced in collaboration with Yue Ma, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third, in collaboration with Bruno Le Floch and Gabriele Veneziano, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and, by analyzing Einstein’s constraint equations, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org

Threshold phenomena in random graphs and hypergraphs
2021-09-10 09:30 - 10:30 | MA
Member Seminar
Speaker: Michael Simkin
Title: Threshold phenomena in random graphs and hypergraphs
Abstract: In 1959 Paul Erdos and Alfred Renyi introduced a model of random graphs that is the cornerstone of modern probabilistic combinatorics. Now known as the “Erdos-Renyi” model of random graphs it has far-reaching applications in combinatorics, computer science, and other fields.
The model is defined as follows: Given a natural number $n$ and a parameter $p in [0,1]$, let $G(n;p)$ be the distribution on graphs with $n$ vertices in which each of the $binom{n}{2}$ possible edges is present with probability $p$, independent of all others. Despite their apparent simplicity, the study of Erdos-Renyi random graphs has revealed many deep and non-trivial phenomena.
A central feature is the appearance of threshold phenomena: For all monotone properties (e.g., connectivity and Hamiltonicity) there is a critical probability $p_c$ such that if $p >> p_c$ then $G(n;p)$ possesses the property with high probability (i.e., with probability tending to 1 as $n to infty$) whereas if $p << p_c$ then with high probability $G(n;p)$ does not possess the property. In this talk we will focus on basic properties such as connectivity and containing a perfect matching. We will see an intriguing connection between these global properties and the local property of having no isolated vertices. We will then generalize the Erdos-Renyi model to higher dimensions where many open problems remain.

More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking
2021-09-10 18:44 - 19:44 | Virtual
Title: More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking
Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory.
Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.

Gradient flows on totally nonnegative flag varieties
2021-09-11 09:30 - 10:30 | MA
Abstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic, geometric, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications, we show how the classical Toda flow fits into this framework, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.

Swampland Program
2021-09-13 09:00 - 2022-05-13 17:00 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
During the 2021–2022 academic year, the CMSA will host a program on the so-called “Swampland.”
The Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology, which has led to a great deal of activity in the field in the last years.
The Swampland is intrinsically interdisciplinary, with ramifications in string compactifications, holography, black hole physics, cosmology, particle physics, and even mathematics.
This program will include an extensive group of visitors and a slate of seminars. Additionally, the CMSA will host a school oriented toward graduate students.
More information will be posted here.
Seminars
Swampland Seminar Series & Group Meetings
Program Visitors

Pieter Bomans, Princeton, 10/30/21 – 11/02/21
Irene Valenzuela, Instituto de Física Teórica, 02/14/22 – 02/21/22
Mariana Grana, CEA/Saclay, 03/21/22 – 03/25/22
Hector Parra De Freitas, IPHT Saclay, 03/21/22 – 04/01/22
Timo Weigand, 03/21/22 – 03/28/22
Gary Shiu, University of Wisconsin-Madison, 04/03/22 – 04/10/22
Thomas van Riet, Leuven University, 04/03/22 – 04/09/22
Lars Aalsma, University of Wisconsin-Madison, 04/11/22 – 04/15/22
Sergio Cecotti, 05/08/22 – 05/21/22
Tom Rudelius, 05/09/22 – 05/13/22

Decoding Divergent Distances
2021-09-13 10:00 - 11:30 | MA
Speaker: John Stout, Harvard University
Title: Decoding Divergent Distances
Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.

Simplices in the Calabi–Yau web
2021-09-14 11:02 - 12:02 | MA
Abstract: Calabi–Yau manifolds of a given dimension are connected by an intricate web of birational maps. This web has deep consequences for the derived categories of coherent sheaves on such manifolds, and for the associated string theories. In particular, for 4-folds and beyond, I will highlight certain simplices appearing in the web, and identify corresponding derived category structures.

Hyperbolic Geometry and Quantum Invariants
2021-09-15 09:30 - 10:30 | Virtual
Speaker: Tian Yang (Texas A&M University)
Title: Hyperbolic Geometry and Quantum Invariants
Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

CMSA Colloquium 9/15/2021 - 5/25/2022
2021-09-15 09:30 - 2022-05-25 10:30 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.
Spring 2022

Date
Speaker
Title/Abstract

1/26/2022
Samir Mathur (Ohio State University)
Title: The black hole information paradox
Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.
Video

2/2/2022
Adam Smith (Boston University)
Title: Learning and inference from sensitive data
Abstract: Consider an agency holding a large database of sensitive personal information—say, medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.
I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

2/8/2022
Wenbin Yan (Tsinghua University)
(special time: 9:30 pm ET)
Title: Tetrahedron instantons and M-theory indices
Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.
Video

2/16/2022
Takuro Mochizuki (Kyoto University)
Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles
Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.
In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

2/23/2022
Bartek Czech (Tsinghua University)
Title: Holographic Cone of Average Entropies and Universality of Black Holes
Abstract: In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

3/2/2022
Richard Kenyon (Yale University)

3/9/2022
Richard Tsai (UT Austin)

3/23/2022
Joel Cohen (University of Maryland)

3/30/2022
Rob Leigh (UIUC)

4/6/2022
Johannes Kleiner (LMU München)

4/13/2022
Yuri Manin (Max-Planck-Institut für Mathematik)

4/20/2022
TBA

4/27/2022
TBA

5/4/2022
Melody Chan (Brown University)

5/11/2022
TBA

5/18/2022
TBA

5/25/2022
Heeyeon Kim (Rutgers University)

Fall 2021

Date
Speaker
Title/Abstract

9/15/2021
Tian Yang, Texas A&M
Title: Hyperbolic Geometry and Quantum Invariants
Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

9/29/2021
David Jordan, University of Edinburgh
Title: Langlands duality for 3 manifolds
Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten. However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.
In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.
Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

10/06/2021
Piotr Sulkowski, U Warsaw
Title: Strings, knots and quivers
Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

10/13/2021
Alexei Oblomkov, University of Massachusetts
Title: Knot homology and sheaves on the Hilbert scheme of points on the plane.
Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane. The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

10/20/2021
Peng Shan, Tsinghua U
Title: Categorification and applications
Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

10/27/2021
Karim Adiprasito, Hebrew University and University of Copenhagen
Title: Anisotropy, biased pairing theory and applications
Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.
I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

11/03/2021
Tamas Hausel, IST Austria
Title: Hitchin map as spectrum of equivariant cohomology
Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

11/10/2021
Peter Keevash, Oxford
Title: Hypergraph decompositions and their applications
Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.

11/17/2021
Andrea Brini, U Sheffield
Title: Curve counting on surfaces and topological strings
Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

12/01/2021
Richard Wentworth, University of Maryland
Title: The Hitchin connection for parabolic G-bundles
Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

12/08/2021
Maria Chudnovsky, Princeton
Title: Induced subgraphs and tree decompositions
Abstract: Tree decompositions are a powerful tool in both structural
graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.
Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

12/15/21
Constantin Teleman (UC Berkeley)
Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system
Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

Why abstraction is the key to intelligence, and what we’re still missing
2021-09-15 15:00 - 16:00 | MA
Speaker: Francois Chollet, Google
Title: Why abstraction is the key to intelligence, and what we’re still missing
Abstract: This talk provides a personal perspective on the way forward towards more human-like and more intelligent artificial systems. Traditionally, symbolic and probabilistic methods have dominated the domains of concept formation, abstraction, and automated reasoning. More recently, deep learning-based approaches have led to significant breakthroughs, including successes in games and combinatorial search tasks. However, the resulting systems are still limited in scope and capabilities — they remain brittle, data-hungry, and their generalization capabilities are limited. We will address a set of questions: why is conceptual abstraction essential for intelligence? What is the nature of abstraction, and its relationship to generalization? What kind of abstraction can deep learning models generate, and where do they fail? What are the methods that are currently successful in generating strong conceptual abstraction? Finally, we will consider how to leverage a hybrid approach to reinforce the strength of different approaches while compensating for their respective weaknesses.

Three-particle mechanism for pairing and superconductivity
2021-09-15 18:46 - 19:46 | Virtual
Title: Three-particle mechanism for pairing and superconductivity
Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.
[1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
[2] V. Crepel and L. Fu, arXiv:2103.12060
[3] K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020)

The Hilbert Space of large N Chern-Simons matter theories
2021-09-16 18:47 - 19:47 | Virtual
Title: The Hilbert Space of large N Chern-Simons matter theories
Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular, implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit; the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.

9/17/2021 General Relativity Seminar
2021-09-17 09:30 - 10:30 | MA
Title: Stable Big Bang formation for the Einstein equations
Abstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature, going back more than 50 years, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.

Geometry, Entanglement and Quasi Local Data
2021-09-17 09:30 - 10:30 | MA
Member Seminar
Speaker: Itamar Shamir
Title: Geometry, Entanglement and Quasi Local Data
Abstract: I will review some general ideas about gravity as motivation for an approach based on quasi local quantities.

Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction
2021-09-17 18:54 - 19:54 | Virtual
Title: Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction
Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.

Small Cosmological Constants in String Theory
2021-09-20 10:00 - 11:00 | MA
Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10^{-123} in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.
